diff --git "a/data/train-all.jsonl" "b/data/train-all.jsonl"
new file mode 100644--- /dev/null
+++ "b/data/train-all.jsonl"
@@ -0,0 +1,11174 @@
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aubrey does not know whether or not everyone is thirsty. It is publicly announced that Aubrey does not know whether Jeremy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] Agentd knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Nichole can now know whether Aubrey can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aubrey","Jeremy","William","Nichole"],"index":61652,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985565543,"difficulty":0.0014434457}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that James does not know whether Ernestine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Maria can now know that Ernestine can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Ernestine","Walter","James"],"index":18233,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5733772516,"difficulty":0.4266227484}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gabriel knows whether or not everyone is thirsty. It is publicly announced that Gabriel knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Gabriel can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Donna","Gabriel"],"index":14405,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997755885,"difficulty":0.0002244115}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Kevin can now know that Tracie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leon","Kevin","Tracie"],"index":48205,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984305501,"difficulty":0.0015694499}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Gregory can now know that Chasity can know that Chasity's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Gregory","Margaret","Chasity"],"index":64687,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983538389,"difficulty":0.0016461611}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Annie. Nona's card is shown to Annie. Mary's card is shown to Mary. Annie's card is shown to Nona. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nona can now know whether Nona picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annie","Mary","Nona"],"index":1845,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8086408377,"difficulty":0.1913591623}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dominic is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Rogelio can now know whether Mary can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dominic","Rogelio","Mary"],"index":44838,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994835854,"difficulty":0.0005164146}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina knows whether Lisa's forehead is muddy. It is publicly announced that Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] Agentb knows that (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"Linda can now know that Tina can know whether Lisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Linda","Lisa","Tina"],"index":22913,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997416139,"difficulty":0.0002583861}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marguerite is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Christine can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marguerite","Christine","Rodney","Lorraine"],"index":17309,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985105395,"difficulty":0.0014894605}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy. It is publicly announced that Trenton knows whether Gerald's forehead is muddy. It is publicly announced that Richard knows whether Trenton's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agentb knows whether (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Richard can now know whether Trenton can know that Gerald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Richard","Trenton","Gerald"],"index":65712,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996874332,"difficulty":0.0003125668}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Jeremy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentc knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Bessie can now know whether Daniel can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kerry","Jeremy","Bessie","Daniel"],"index":50369,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997074008,"difficulty":0.0002925992}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tyree does not know whether Michelle is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Michelle can now know whether Tyree can know whether Tyree is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michelle","Tyree"],"index":18013,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986502528,"difficulty":0.0013497472}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Michael can now know that Allan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Michael","Allan"],"index":47371,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9942902327,"difficulty":0.0057097673}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charissa does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robert can now know that Karen can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Charissa","Domingo","Karen"],"index":41198,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephanie's card is shown to Stephanie. Estella's card is shown to Stephanie. Samuel's card is shown to Samuel. Estella's card is shown to Estella. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephanie can now know whether Estella can know whether Stephanie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephanie","Samuel","Estella"],"index":3393,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970097542,"difficulty":0.0029902458}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernice knows whether Bernice is thirsty. It is publicly announced that Paul does not know whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Paul can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bernice","Paul","Christopher"],"index":34657,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997190833,"difficulty":0.0002809167}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mavis's card is shown to Mavis. Velma's card is shown to Mavis. Kevin's card is shown to Kevin. Kevin's card is shown to Velma. Velma's card is shown to Velma. Kevin's card is shown to Marc. It is publicly announced that someone picked a red card. It is publicly announced that Mavis does not know whether Marc picked a red card. It is publicly announced that Velma picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(3) ] 0","hypothesis":"Mavis can now know whether Velma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mavis","Kevin","Velma","Marc"],"index":41014,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5754438043,"difficulty":1.5754438043}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erica does not know whether Sherman is thirsty. It is publicly announced that Erica knows whether or not everyone is thirsty. It is publicly announced that Erica does not know whether Larry is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Larry can now know that Erica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erica","Sherman","Larry"],"index":52505,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8972045779,"difficulty":0.1027954221}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karl does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Karl can now know that Hyacinth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Karl","Hyacinth"],"index":52755,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7446508408,"difficulty":0.2553491592}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew does not know whether Jeanne is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Joann is thirsty. It is publicly announced that Joann is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Jeanne can now know whether Jeanne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joann","Jeanne","Frances","Matthew"],"index":42434,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991256595,"difficulty":0.0008743405}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to George. George's card is shown to Gary. Gary's card is shown to Doris. It is publicly announced that someone picked a red card. It is publicly announced that George does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"George can now know whether Gary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Gary","Doris"],"index":52587,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.878172636,"difficulty":0.121827364}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Gloria's forehead is muddy. It is publicly announced that Peter knows whether Gloria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Gloria can now know that Peter can know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Gloria","Peter"],"index":46319,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997859776,"difficulty":0.002140224}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Paul does not know whether Terry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Deena can now know that Paul can know that Terry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deena","Paul","Terry","Edith"],"index":24913,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949312806,"difficulty":0.0050687194}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Van does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jill can now know whether Daniel can know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Van","Jill","Daniel"],"index":52920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8188638687,"difficulty":0.1811361313}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy's forehead is muddy. It is publicly announced that Randy knows whether Randy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Randy can now know whether Adalberto can know that Randy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adalberto","King","Randy"],"index":30504,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999589622,"difficulty":0.000410378}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Terry is thirsty. It is publicly announced that Mary knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"George can now know that Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Michael","George","Terry"],"index":24236,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981473684,"difficulty":0.0018526316}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether John is thirsty. It is publicly announced that Jennifer does not know whether Eloise is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Eloise can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eloise","John","Jennifer"],"index":45495,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973221421,"difficulty":0.0026778579}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Mary can now know that Patricia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Patricia","Mary"],"index":40968,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9627153873,"difficulty":1.9627153873}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Marilyn can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Freddie","Ralph","Marilyn","Charles"],"index":10455,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997634292,"difficulty":0.0002365708}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susie knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Susie can now know that Alan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alan","Susie","Dorothy"],"index":18313,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982231259,"difficulty":0.0017768741}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luther does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Krista can now know whether Luther can know whether Peter is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Luther","Krista","Robert"],"index":59374,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985098243,"difficulty":0.0014901757}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol does not know whether Carol's forehead is muddy. It is publicly announced that Gregory knows whether Gregory's forehead is muddy. It is publicly announced that Gregory knows whether Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Sophie can now know whether Gregory can know that Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sophie","Carol","Gregory"],"index":65819,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9379869699,"difficulty":0.0620130301}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Florida. Florida's card is shown to Lawrence. Marivel's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Lawrence knows whether Florida picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Lawrence can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Florida","Lawrence","Marivel"],"index":37267,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999769628,"difficulty":0.000230372}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Joseph is thirsty. It is publicly announced that Thomas is thirsty. It is publicly announced that Joseph is thirsty. It is publicly announced that Joseph is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Joseph can now know that Thomas can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Joseph"],"index":33521,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neil does not know whether or not everyone's forehead is muddy. It is publicly announced that Neil does not know whether Neil's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Herbert can now know whether Neil's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Herbert","Maria","Dana","Neil"],"index":38099,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994445443,"difficulty":0.0005554557}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon knows whether someone is thirsty. It is publicly announced that Sharon knows whether Sharon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Richard can now know that Sharon can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kendrick","Richard","Sharon"],"index":26163,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998378396,"difficulty":0.001621604}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether or not everyone's forehead is muddy. It is publicly announced that Heather knows whether or not nobody's forehead is muddy. It is publicly announced that Paul does not know whether Paul's forehead is muddy. It is publicly announced that Heather knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Paul can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Paul","Heather"],"index":32894,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974287152,"difficulty":0.0025712848}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Roy can now know that Roy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Jason","Damon","Roy"],"index":39532,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.995963037,"difficulty":0.004036963}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Pauline can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Silvia","Carol","Pauline"],"index":5129,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997465014,"difficulty":0.0002534986}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jackie's card is shown to Jackie. Megan's card is shown to Jackie. Kris's card is shown to Jackie. Megan's card is shown to Megan. Megan's card is shown to Kris. It is publicly announced that someone picked a red card. It is publicly announced that Megan knows whether or not everyone picked a red card. It is publicly announced that Kris knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Megan can now know whether Jackie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","Megan","Kris"],"index":38467,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Miyoko. Miyoko's card is shown to Janet. Janet's card is shown to Janet. Maurice's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janet can now know that Maurice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Miyoko","Janet","Maurice"],"index":15606,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982677698,"difficulty":0.0017322302}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Maria can now know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Glenda","Alex","Maria","Mary"],"index":5509,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957774878,"difficulty":0.0042225122}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Laura can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Laura","Glynda","Theresa"],"index":58231,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997841716,"difficulty":0.0002158284}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy. It is publicly announced that Randy knows whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Carl can now know that Carl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carl","Barbara","Randy","Mattie"],"index":18197,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974671602,"difficulty":0.0025328398}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether Daniel can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Abraham","Robert"],"index":61742,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9231024981,"difficulty":0.0768975019}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Dorian's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Dorian can now know whether Dorian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Donald","Dorian"],"index":46650,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9865105748,"difficulty":0.0134894252}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Molly knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Molly can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Molly","Cecile"],"index":65691,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997445941,"difficulty":0.0002554059}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terrence's card is shown to Ruth. Ruth's card is shown to Terrence. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dena can now know that Ruth can know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruth","Dena","Terrence"],"index":12902,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.93458426,"difficulty":1.93458426}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Carl can now know that Rebecca can know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebecca","Carl","Joe"],"index":44022,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985691309,"difficulty":0.0014308691}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Kathleen can now know that Natasha can know that Natasha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Charles","Linda","Natasha"],"index":40339,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998313427,"difficulty":0.001686573}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daryl's card is shown to Anna. Anna's card is shown to Rachel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know that Rachel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Rachel","Daryl","Matthew"],"index":22874,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984657764,"difficulty":0.0015342236}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Francis can now know whether Helen can know that Carole's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Carole","Helen","Steven"],"index":56710,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.997777164,"difficulty":0.002222836}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Christopher knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Christopher can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Brendan"],"index":20126,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9942003489,"difficulty":0.0057996511}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Anja. Willie's card is shown to Grace. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Willie can now know whether Anja can know whether Anja picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anja","Grace","Willie","Robert"],"index":35251,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9917164445,"difficulty":0.0082835555}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Pete can now know whether Pete's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Linda","David","Pete"],"index":4609,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9169532061,"difficulty":1.9169532061}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol does not know whether Marion is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Carol can now know whether Larry can know that Ruth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Larry","Carol","Marion"],"index":12808,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9951648712,"difficulty":0.0048351288}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Christopher knows whether Claude's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Claude can now know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Christopher","Claude","Julia"],"index":25273,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999717772,"difficulty":0.000282228}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pei's card is shown to Gary. Danielle's card is shown to Gary. Ignacio's card is shown to Ignacio. Danielle's card is shown to Pei. Gary's card is shown to Danielle. Danielle's card is shown to Danielle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pei can now know that Danielle can know whether Pei picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Ignacio","Pei","Danielle"],"index":5414,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6739808917,"difficulty":0.3260191083}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oliver's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Kimberly knows whether Oliver's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Shannon can now know whether Kimberly can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","Shannon","Oliver"],"index":56657,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997503161,"difficulty":0.0002496839}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia knows whether Virginia is thirsty. It is publicly announced that Cara knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Billy can now know whether Cara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cara","Billy","Virginia"],"index":18509,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.902964294,"difficulty":0.097035706}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether Paul's forehead is muddy. It is publicly announced that Ozell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Louis can now know that Paul can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kyle","Paul","Louis","Ozell"],"index":58277,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997139573,"difficulty":0.0002860427}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Seymour does not know whether or not everyone is thirsty. It is publicly announced that Seymour does not know whether Todd is thirsty. It is publicly announced that Todd does not know whether Genevieve is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Todd can now know that Genevieve is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Genevieve","Seymour","Todd"],"index":38245,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9870304465,"difficulty":0.0129695535}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Wilfred's card is shown to Wilfred. It is publicly announced that someone picked a red card. It is publicly announced that Wilfred knows whether Wilfred picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Wilfred can now know that Robert can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Wilfred"],"index":35452,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9809651971,"difficulty":0.0190348029}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Philip knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Elizabeth can now know whether Philip can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Philip","Elizabeth"],"index":28895,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9972535968,"difficulty":0.0027464032}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Darlene's card is shown to Melissa. Roy's card is shown to Melissa. Darlene's card is shown to Michael. Darlene's card is shown to Darlene. Darlene's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that Melissa does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Melissa can now know that Roy can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melissa","Michael","Darlene","Roy"],"index":9610,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9392580986,"difficulty":0.0607419014}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margo knows whether someone's forehead is muddy. It is publicly announced that Margo does not know whether or not everyone's forehead is muddy. It is publicly announced that Margo does not know whether or not everyone's forehead is muddy. It is publicly announced that Jeannine knows whether Jeannine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jordan can now know that Jeannine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jordan","Jeannine","Margo"],"index":21959,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9128984213,"difficulty":0.0871015787}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Shannon. Shirley's card is shown to Shirley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stacy can now know that Shannon can know that Stacy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shannon","Stacy","Shirley"],"index":4284,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980587363,"difficulty":0.0019412637}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether Andrew's forehead is muddy. It is publicly announced that Eric does not know whether or not everyone's forehead is muddy. It is publicly announced that Andrew knows whether or not everyone's forehead is muddy. It is publicly announced that Andrew knows whether Eric's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Andrew can now know that Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eric","Andrew"],"index":18495,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8037225604,"difficulty":1.8037225604}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Bruce can now know that Linda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rebecca","Linda","Ryan","Bruce"],"index":24507,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976078272,"difficulty":0.0023921728}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy knows whether Wendy's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Wendy can now know whether Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Woodrow","Wendy","Donald"],"index":28354,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997202754,"difficulty":0.0002797246}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lourdes's forehead is not muddy. It is publicly announced that Lourdes's forehead is not muddy. It is publicly announced that Lourdes's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] Agentb knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Lourdes can now know that William can know that Gertrude's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gertrude","Lourdes","William","Tiffany"],"index":36280,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7610971928,"difficulty":0.2389028072}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Christopher's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Donald can now know that Christopher can know that Jesse's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Donald","Christopher","Jesse"],"index":60391,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973270893,"difficulty":0.0026729107}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacey's card is shown to Robert. Robert's card is shown to Rachael. Stacey's card is shown to Rachael. Rachael's card is shown to Stacey. Stacey's card is shown to Stacey. It is publicly announced that someone picked a red card. It is publicly announced that Rachael does not know whether Rachael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Rachael can now know that Stacey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Rachael","Stacey"],"index":3298,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9888734818,"difficulty":0.0111265182}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Cheryl can now know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joe","Cheryl","Ronald","Sandra"],"index":55985,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984804988,"difficulty":0.0015195012}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Kevin knows whether Michael's forehead is muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Athena can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kevin","Thomas","Michael","Athena"],"index":28934,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967448711,"difficulty":0.0032551289}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Kimberly. Kimberly's card is shown to Patricia. Donna's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Donna knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Kimberly can now know that Donna can know that Donna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kimberly","Donna","Patricia"],"index":67521,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946419001,"difficulty":0.0053580999}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason does not know whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Vickie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bailey","Jason","Vickie","Paul"],"index":62264,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986090064,"difficulty":0.0013909936}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Arthur can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Arthur","Joseph","Dawn"],"index":13345,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9911796451,"difficulty":1.9911796451}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Janet. Carrie's card is shown to Janet. Janet's card is shown to Suzanne. Janet's card is shown to Carrie. Carrie's card is shown to Carrie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janet can now know whether Carrie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janet","Suzanne","Carrie"],"index":2692,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6038895249,"difficulty":1.6038895249}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nell can now know that Madeleine can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lilly","Madeleine","Valerie","Nell"],"index":59678,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997290969,"difficulty":0.0002709031}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darlene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Darlene can now know that Patrick can know that Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darlene","Francis","Patrick"],"index":59476,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9933325648,"difficulty":0.0066674352}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Stephen can now know that Shasta's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Keith","Liliana","Shasta","Stephen"],"index":37734,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9930134416,"difficulty":0.0069865584}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Mildred can now know whether Rose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jerry","Mildred","Paul","Rose"],"index":9978,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997399449,"difficulty":0.0002600551}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tracey knows whether or not nobody is thirsty. It is publicly announced that Loretta does not know whether Tracey is thirsty. It is publicly announced that Tracey knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Estela can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tracey","Estela","Sheri","Loretta"],"index":46745,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979021549,"difficulty":0.0020978451}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jarvis knows whether Donald's forehead is muddy. It is publicly announced that Victoria's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Victoria can now know whether Donald can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Victoria","Jarvis","Donald","Steve"],"index":15350,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996888638,"difficulty":0.0003111362}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Kathryn. Emily's card is shown to Kathryn. Samuel's card is shown to Samuel. Emily's card is shown to Samuel. Kathryn's card is shown to Scott. Scott's card is shown to Emily. Emily's card is shown to Emily. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Samuel can now know whether Scott can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Samuel","Scott","Emily"],"index":50455,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shellie's card is shown to Shellie. Willie's card is shown to Shellie. Shellie's card is shown to Willie. Willie's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Shellie knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Willie can now know that Shellie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Shellie","Willie"],"index":28392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6069005728,"difficulty":0.3930994272}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Gracie can now know that Charlotte is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Charlotte","Michael","Gracie"],"index":30715,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9505621195,"difficulty":0.0494378805}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Bart. Mildred's card is shown to James. James's card is shown to Mildred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mildred can now know that Mildred picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bart","James","Mildred"],"index":47396,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943717718,"difficulty":0.0056282282}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwayne's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Dwayne can now know that Christopher can know that Dwayne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dwayne","Christopher"],"index":29674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9554914236,"difficulty":0.0445085764}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley knows whether Larry's forehead is muddy. It is publicly announced that John's forehead is not muddy. It is publicly announced that Stanley knows whether Stanley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"John can now know whether Stanley can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stanley","Cody","Larry","John"],"index":63540,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9965165854,"difficulty":0.0034834146}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Silvia is thirsty. It is publicly announced that Silvia knows whether or not nobody is thirsty. It is publicly announced that Silvia does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Silvia can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Silvia","James","Rose","Lawrence"],"index":60,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7707207799,"difficulty":1.7707207799}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Milton can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jane","Milton"],"index":50703,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric is not thirsty. It is publicly announced that Jerry does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Daisy can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daisy","Jerry","John","Eric"],"index":41398,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9741591215,"difficulty":0.0258408785}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Lisa. Monica's card is shown to Carol. Kyle's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Lisa does not know whether Carol picked a red card. It is publicly announced that Kyle picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(4) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Monica can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Monica","Lisa","Carol","Kyle"],"index":59118,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982977509,"difficulty":0.0017022491}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lisa can now know whether Carolyn can know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Lisa","Joseph","Edith"],"index":31301,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9100697637,"difficulty":0.0899302363}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephanie knows whether or not nobody is thirsty. It is publicly announced that Stephanie does not know whether Tracey is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Stephanie can now know whether Vickie can know whether Stephanie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vickie","Jessica","Tracey","Stephanie"],"index":63403,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988142252,"difficulty":0.0011857748}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodney knows whether Rodney's forehead is muddy. It is publicly announced that Lisa knows whether Rodney's forehead is muddy. It is publicly announced that Rodney knows whether Lorena's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Lorena can now know that Patricia can know that Lorena's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Lorena","Rodney","Patricia"],"index":46583,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996668756,"difficulty":0.003331244}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Doris can now know whether Dewey can know whether Lucille's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucille","Dewey","Doris"],"index":16566,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997219443,"difficulty":0.0002780557}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Joshua can now know whether Timothy can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joshua","Betty","Pamela","Timothy"],"index":14946,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997857213,"difficulty":0.0002142787}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy. It is publicly announced that Joseph knows whether Frankie's forehead is muddy. It is publicly announced that Joseph's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Frankie can now know whether Joseph can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Frankie"],"index":44358,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996384382,"difficulty":0.0003615618}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kellie knows whether someone is thirsty. It is publicly announced that Kellie does not know whether Larry is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Larry can now know that Kellie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Larry","Kellie"],"index":67092,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999783814,"difficulty":0.000216186}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Amber. Amber's card is shown to Brenda. Brenda's card is shown to Brenda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brenda can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amber","Brenda","Patricia"],"index":67213,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Patricia is thirsty. It is publicly announced that Benjamin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] 0","hypothesis":"Benjamin can now know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Benjamin","Daniel","Jennifer"],"index":11829,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9699543118,"difficulty":0.0300456882}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether William is thirsty. It is publicly announced that Doris is thirsty. It is publicly announced that William is thirsty. It is publicly announced that Doris is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 1 ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 1 ] 0","hypothesis":"Doris can now know whether Thomas can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","William","Thomas"],"index":51654,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tricia does not know whether Mildred is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Harry can now know that Mildred can know whether Virginia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tricia","Harry","Virginia","Mildred"],"index":22722,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969524145,"difficulty":0.0030475855}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. David's card is shown to Richard. Richard's card is shown to Richard. Richard's card is shown to Susie. Catherine's card is shown to Susie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Catherine can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Richard","Catherine","Susie"],"index":27344,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978629947,"difficulty":0.0021370053}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cara's card is shown to Vasiliki. Cara's card is shown to Conrad. Jennifer's card is shown to Conrad. Vasiliki's card is shown to Cara. It is publicly announced that someone picked a red card. It is publicly announced that Vasiliki knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Cara can now know whether Conrad picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vasiliki","Conrad","Cara","Jennifer"],"index":40244,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9662374854,"difficulty":0.0337625146}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Lester. Lester's card is shown to Nathan. Robert's card is shown to Nathan. Nathan's card is shown to Karen. Lester's card is shown to Robert. Karen's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Robert picked a red card. It is publicly announced that Lester knows whether or not nobody picked a red card. It is publicly announced that Karen picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Karen can now know that Lester can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lester","Nathan","Karen","Robert"],"index":51097,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.66116786,"difficulty":1.66116786}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachel's card is shown to Rachel. Patrica's card is shown to Stephen. Rachel's card is shown to Larry. Stephen's card is shown to Patrica. It is publicly announced that someone picked a red card. It is publicly announced that Rachel does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Rachel can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rachel","Stephen","Larry","Patrica"],"index":53867,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997010231,"difficulty":0.0002989769}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin knows whether Justin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jim can now know whether Justin can know that Justin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Justin","Jim"],"index":1946,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996982813,"difficulty":0.0003017187}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Ruth can now know whether Jenna can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Ruth","Jenna"],"index":56539,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999705255,"difficulty":0.000294745}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Laura can now know that James can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Robin","Laura"],"index":24568,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9964558482,"difficulty":0.0035441518}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Nathaniel. Robert's card is shown to Nathaniel. Nathaniel's card is shown to John. Nathaniel's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nathaniel","John","Robert"],"index":29032,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997261167,"difficulty":0.0002738833}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Freda can now know that Carolyn can know that Carolyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Freda","Carolyn"],"index":24972,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972735047,"difficulty":0.0027264953}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shannon can now know whether Jason can know that Jason's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shannon","Thomas","Martin","Jason"],"index":52251,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8644528389,"difficulty":0.1355471611}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Salvatore's card is shown to Salvatore. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Salvatore can now know whether Dorothy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Salvatore"],"index":2077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9689156413,"difficulty":0.0310843587}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angel's card is shown to Angel. Warren's card is shown to Angel. Warren's card is shown to Warren. Angel's card is shown to Alexandria. Warren's card is shown to Alexandria. Alexandria's card is shown to Alexandria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Warren can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angel","Warren","Alexandria"],"index":43096,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9879034162,"difficulty":0.0120965838}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"James can now know that Nilda can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Victor","Nilda","Ronald"],"index":24614,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996435642,"difficulty":0.0003564358}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carole knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Karen can now know whether Andrew can know whether Carole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Carole","Andrew"],"index":42968,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997214675,"difficulty":0.0002785325}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Margaret can now know that Mark is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Margaret","Eduardo"],"index":18327,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985305071,"difficulty":0.0014694929}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lori can now know that Marie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Petra","Marie","Lori","Maria"],"index":54900,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983426332,"difficulty":0.0016573668}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether Gary's forehead is muddy. It is publicly announced that Irving knows whether Jolanda's forehead is muddy. It is publicly announced that Gary does not know whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jolanda can now know that Irving can know whether Irving's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Irving","Tyrone","Jolanda"],"index":45643,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9387222528,"difficulty":0.0612777472}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Junior's card is shown to Junior. Sharon's card is shown to Junior. Jacqueline's card is shown to Junior. Junior's card is shown to Sharon. Sharon's card is shown to Sharon. Jacqueline's card is shown to Jacqueline. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sharon can now know whether Junior can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Junior","Sharon","Jacqueline"],"index":12509,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997074008,"difficulty":0.0002925992}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Burton's card is shown to Ruth. Randall's card is shown to Burton. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Burton can now know whether Ruth can know that Burton picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Burton","Randall"],"index":35597,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9541877508,"difficulty":0.0458122492}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Angela. Craig's card is shown to Craig. Angela's card is shown to Clare. Clare's card is shown to Clare. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether Angela picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Clare can now know that Angela can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Craig","Clare"],"index":51142,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982016087,"difficulty":0.0017983913}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth does not know whether or not everyone's forehead is muddy. It is publicly announced that Elizabeth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Evelyn can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bruce","Stefanie","Elizabeth","Evelyn"],"index":32591,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9682585001,"difficulty":0.0317414999}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Kathy's card is shown to Robert. Monique's card is shown to Robert. Robert's card is shown to Kathy. Kathy's card is shown to Kathy. Monique's card is shown to Kathy. Kathy's card is shown to Monique. Monique's card is shown to Monique. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Kathy","Monique"],"index":62793,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997263551,"difficulty":0.0002736449}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise does not know whether Louise's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Louise can now know that Louise's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lorena","Louise","Kenneth"],"index":2887,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9938830137,"difficulty":0.0061169863}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether Cynthia's forehead is muddy. It is publicly announced that Myrna knows whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentd knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jack can now know that Elizabeth can know that Jack's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Myrna","Cynthia","Elizabeth","Jack"],"index":1650,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998003304,"difficulty":0.001996696}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Glennie can now know that Kirk can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kirk","Nancy","Timothy","Glennie"],"index":59642,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that Patricia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] 0","hypothesis":"Gay can now know whether William can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gay","William","Alfred","Patricia"],"index":37872,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9309937358,"difficulty":0.0690062642}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aaron's card is shown to Cheryl. Cheryl's card is shown to Aaron. Todd's card is shown to Aaron. Todd's card is shown to Todd. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cheryl can now know that Todd can know that Todd picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cheryl","Aaron","Todd"],"index":43098,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9820482731,"difficulty":0.0179517269}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Elizabeth. Evan's card is shown to Evan. Evan's card is shown to Joy. It is publicly announced that someone picked a red card. It is publicly announced that Evan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Evan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Evan","Joy"],"index":9838,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997970283,"difficulty":0.002029717}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Herman. Charles's card is shown to Charles. Judith's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Charles can now know whether Herman can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herman","Charles","Judith"],"index":21738,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Jeffrey. Jessica's card is shown to Jeffrey. Jessica's card is shown to Spencer. Jessica's card is shown to Elizabeth. Elizabeth's card is shown to Jessica. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessica can now know whether Elizabeth can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Spencer","Elizabeth","Jessica"],"index":3054,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8386368155,"difficulty":1.8386368155}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffery's card is shown to Mary. Mary's card is shown to Jeffery. Jeffery's card is shown to Jeffery. Sheldon's card is shown to Jeffery. Mary's card is shown to Sheldon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Jeffery","Sheldon"],"index":19160,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. James's card is shown to Maria. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Maria can now know that James can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Maria"],"index":51269,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999697566,"difficulty":0.000302434}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Patty does not know whether Christopher is thirsty. It is publicly announced that Christopher knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Christopher can now know that Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Christopher","Patty"],"index":37229,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962967038,"difficulty":0.0037032962}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Joshua. Joshua's card is shown to Joshua. Mitchell's card is shown to Mitchell. It is publicly announced that someone picked a red card. It is publicly announced that Joshua picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Joshua can now know that Joshua picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cindy","Joshua","Mitchell"],"index":15778,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9195466042,"difficulty":0.0804533958}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Shannon. Cody's card is shown to Shannon. Mariann's card is shown to Lisa. Shannon's card is shown to Cody. Cody's card is shown to Mariann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lisa can now know whether Shannon can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shannon","Lisa","Cody","Mariann"],"index":18373,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997108579,"difficulty":0.0002891421}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vernon's forehead is not muddy. It is publicly announced that Anne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Vernon can now know that Douglas can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anne","Judith","Vernon","Douglas"],"index":66887,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983244538,"difficulty":0.0016755462}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lauren knows whether Lauren's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Carl can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lauren","Denise","Austin","Carl"],"index":57196,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983257651,"difficulty":0.0016742349}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Dale can now know whether Ashley can know whether Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dale","William","Ashley"],"index":9324,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9138918519,"difficulty":0.0861081481}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Krista's card is shown to Gene. Krista's card is shown to Anna. Thomas's card is shown to Krista. Gene's card is shown to Thomas. Krista's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Anna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know that Gene can know whether Krista picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gene","Anna","Krista","Thomas"],"index":17010,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8488942981,"difficulty":0.1511057019}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marlene does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Zaida can now know that Marlene can know whether Zaida is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marlene","Zaida","Mary","Elizabeth"],"index":42614,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971764088,"difficulty":0.0028235912}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Sherry. Jonathan's card is shown to David. Alice's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jonathan","Alice","Sherry","David"],"index":10648,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7276941538,"difficulty":1.7276941538}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Victor can now know that Jose can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gary","Jose","Victor"],"index":11378,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983887672,"difficulty":0.0016112328}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mike knows whether someone is thirsty. It is publicly announced that Mike knows whether Mike is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Mike can now know whether Elizabeth can know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","Bryan","Mike"],"index":18581,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5764211416,"difficulty":1.5764211416}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Mary can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Vicki","George","Mary"],"index":11408,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997624755,"difficulty":0.0002375245}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy. It is publicly announced that Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Gerri can now know that Albert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Albert","James","Gerri","Lisa"],"index":1807,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7208368778,"difficulty":0.2791631222}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olive's card is shown to Olive. Jospeh's card is shown to Olive. Olive's card is shown to Mattie. Jospeh's card is shown to Mattie. Jospeh's card is shown to Jospeh. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jospeh can now know that Mattie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Olive","Mattie","Jospeh"],"index":13581,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984343648,"difficulty":0.0015656352}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Stephen's card is shown to Rachel. Rachel's card is shown to Rachel. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether Rachel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Stephen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephen","Rachel","Carolyn"],"index":13603,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristine knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Kristine can now know that Christopher can know whether Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kristine","Michael","Christopher"],"index":35007,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9862653613,"difficulty":0.0137346387}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel knows whether or not everyone is thirsty. It is publicly announced that Kris knows whether Kris is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kris can now know whether Kris is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kris","Daniel"],"index":65959,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989953637,"difficulty":0.0010046363}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Nancy can now know that Walter is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Walter","Carol","Joel"],"index":22248,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977251887,"difficulty":0.0022748113}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith knows whether Keith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Diana can now know whether Annette can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Annette","Madeline","Diana"],"index":65897,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997051358,"difficulty":0.0002948642}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Troy can now know whether Maria can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Maria","Clifford","Troy"],"index":44357,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maggie does not know whether Lori is thirsty. It is publicly announced that Stephanie does not know whether Lori is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Lori can now know whether Maggie can know whether Stephanie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Birdie","Maggie","Lori","Stephanie"],"index":36518,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985578656,"difficulty":0.0014421344}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Manuel can now know whether Tommie can know whether Joy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Manuel","Wilma","Tommie","Joy"],"index":27648,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993700385,"difficulty":0.0006299615}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis does not know whether or not everyone's forehead is muddy. It is publicly announced that Jennifer knows whether Francis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Francis can now know whether Jenny can know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Francis","Jennifer","Jenny"],"index":46643,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8942055106,"difficulty":0.1057944894}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Yvonne. Yvonne's card is shown to Yvonne. Anthony's card is shown to Carl. Yvonne's card is shown to Carl. Yvonne's card is shown to Jim. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know whether Jim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Yvonne","Carl","Jim"],"index":39282,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9043669105,"difficulty":0.0956330895}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Esther does not know whether Connie is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Esther can now know whether Connie can know that Connie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Connie","Esther","Leonard"],"index":11305,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8975757957,"difficulty":1.8975757957}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to James. Jerry's card is shown to Jerry. James's card is shown to Robert. Jerry's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Jerry can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Jerry","Robert","Charles"],"index":17980,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.843547523,"difficulty":0.156452477}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva's forehead is muddy. It is publicly announced that Nancy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Eva can now know that Nancy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nancy","Eva"],"index":55640,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984001517,"difficulty":0.0015998483}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Russell. Russell's card is shown to Christine. Russell's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Christine knows whether someone picked a red card. It is publicly announced that Russell does not know whether Travis picked a red card. It is publicly announced that Russell does not know whether Travis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Christine can now know that Russell picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Russell","Christine","Amy","Travis"],"index":49108,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786994457,"difficulty":0.0213005543}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rodney's card is shown to David. Daniel's card is shown to David. Lillie's card is shown to David. David's card is shown to Rodney. It is publicly announced that someone picked a red card. It is publicly announced that Rodney does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rodney can now know whether Lillie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Rodney","Daniel","Lillie"],"index":16350,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5317273736,"difficulty":0.4682726264}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra's forehead is muddy. It is publicly announced that Ronald does not know whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Sandra can now know that Carmen can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Carmen","Ronald","Arthur"],"index":65734,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8069016933,"difficulty":0.1930983067}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward does not know whether Lien is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Randy knows whether someone is thirsty. It is publicly announced that Lien does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Lien can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Randy","Edward","Lien"],"index":3605,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9948520064,"difficulty":0.0051479936}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Shelia. Shelia's card is shown to Brenda. Paul's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether someone picked a red card. It is publicly announced that Paul picked a red card. It is publicly announced that Shelia knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 2 ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Shelia can now know that Paul can know that Shelia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shelia","Paul","Brenda"],"index":22856,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.644996047,"difficulty":1.644996047}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eula can now know whether Charles can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Delores","Judith","Eula"],"index":3971,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995961785,"difficulty":0.0004038215}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Kristen can now know whether Kyle can know whether Kristen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kristen","Kyle"],"index":39038,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996575117,"difficulty":0.0003424883}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregorio's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Gregorio can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Gregorio","William","Russell"],"index":42695,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984157085,"difficulty":0.0015842915}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy. It is publicly announced that Kenneth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Forest","Mary","Kenneth"],"index":24278,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather knows whether Jerome's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Thomas can now know whether Jerome can know whether Jerome's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Jerome","Heather"],"index":7499,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996726513,"difficulty":0.0003273487}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy does not know whether Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lucy can now know whether Nancy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Lucy"],"index":11009,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995104074,"difficulty":0.0004895926}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cameron's card is shown to Cameron. Cameron's card is shown to Eleanor. Eleanor's card is shown to Eleanor. Paula's card is shown to Paula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eleanor can now know that Cameron picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cameron","Eleanor","Paula"],"index":23368,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979032278,"difficulty":0.0020967722}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Ricky's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Mona","Ricky","Alfred"],"index":31494,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997408986,"difficulty":0.0002591014}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy does not know whether Judy's forehead is muddy. It is publicly announced that Gerald knows whether Gerald's forehead is muddy. It is publicly announced that Gerald knows whether Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gerald can now know that Elise can know whether Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elise","Judy","Gerald"],"index":61557,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995859265,"difficulty":0.0004140735}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Shara can now know that Thomas can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shara","Denise","Thomas","Wayne"],"index":38031,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972078204,"difficulty":0.0027921796}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith does not know whether Judith's forehead is muddy. It is publicly announced that Judith's forehead is muddy. It is publicly announced that Crystal's forehead is muddy. It is publicly announced that Rutha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Janet can now know that Rutha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Judith","Rutha","Crystal","Janet"],"index":27191,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5852362514,"difficulty":0.4147637486}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph knows whether Joseph is thirsty. It is publicly announced that Luann does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Beulah can now know that Luann can know whether Beulah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Luann","Beulah"],"index":51039,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.82149297,"difficulty":0.17850703}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marion's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Marion can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marion","Kenneth","Olga","Elva"],"index":7585,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill knows whether Andy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Andy can now know whether Bill can know whether Bill's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Andy","Bill"],"index":20023,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9446620941,"difficulty":0.0553379059}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol does not know whether Dorothy is thirsty. It is publicly announced that Gertrude does not know whether Carol is thirsty. It is publicly announced that Dorothy does not know whether or not everyone is thirsty. It is publicly announced that Mary does not know whether Carol is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] Agentd knows that (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Dorothy can now know that Gertrude can know whether Carol is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Gertrude","Mary","Dorothy"],"index":22312,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8560051918,"difficulty":0.1439948082}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dominick does not know whether or not everyone is thirsty. It is publicly announced that Teresa does not know whether Patrick is thirsty. It is publicly announced that Patrick does not know whether or not everyone is thirsty. It is publicly announced that Patrick does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Dominick can now know that Teresa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Teresa","Patrick","Dominick"],"index":19006,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7431720495,"difficulty":0.2568279505}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Enrique. Enrique's card is shown to Lois. It is publicly announced that someone picked a red card. It is publicly announced that Enrique does not know whether Enrique picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lois can now know whether Enrique can know whether Lois picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Enrique","Lois"],"index":35204,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970781803,"difficulty":0.0029218197}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Robert can now know that Dennis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Dennis","Robert"],"index":2714,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980565906,"difficulty":0.0019434094}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steve","Derek","Richard"],"index":58718,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5448138118,"difficulty":1.5448138118}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Nicholas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Nicholas can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nicholas","Jose"],"index":47767,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9974555373,"difficulty":0.0025444627}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teri knows whether someone's forehead is muddy. It is publicly announced that Anna knows whether Teri's forehead is muddy. It is publicly announced that Phyllis does not know whether Phyllis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Phyllis can now know whether Anna can know that Phyllis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anna","Phyllis","Teri"],"index":48307,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7009189725,"difficulty":0.2990810275}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] 0","hypothesis":"Arletta can now know that Evelyn can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arletta","Evelyn","Shirley","Jessica"],"index":35760,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997625947,"difficulty":0.0002374053}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isaias does not know whether Isaias's forehead is muddy. It is publicly announced that Rhonda knows whether or not nobody's forehead is muddy. It is publicly announced that Rhonda does not know whether Rhonda's forehead is muddy. It is publicly announced that Amy knows whether Isaias's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Amy can now know that Isaias's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Isaias","Rhonda","Amy"],"index":40335,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9769067168,"difficulty":0.0230932832}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether or not everyone's forehead is muddy. It is publicly announced that Robin knows whether Gladys's forehead is muddy. It is publicly announced that Robin's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Robin can now know whether Gladys can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robin","Gladys"],"index":56271,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997835755,"difficulty":0.0002164245}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy. It is publicly announced that Kerry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Kerry can now know that Paul can know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Kerry","Richard","Arlene"],"index":65422,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9936060905,"difficulty":0.0063939095}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Scott. Kevin's card is shown to Scott. Scott's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Scott can now know whether Kevin can know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Scott","Kevin"],"index":31046,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9935907125,"difficulty":0.0064092875}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Carl. Madison's card is shown to Madison. Marie's card is shown to Marie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Madison can now know whether Carl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carl","Madison","Marie"],"index":37804,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9246406555,"difficulty":0.0753593445}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Ollie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] 0","hypothesis":"Michael can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Ollie","Thomas","Dorothy"],"index":13409,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997788072,"difficulty":0.0002211928}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether Jackie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ruth can now know whether Mae can know that Mae's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jackie","Mae","Ruth","Sandy"],"index":16788,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9119730592,"difficulty":0.0880269408}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that June knows whether June's forehead is muddy. It is publicly announced that Amos knows whether Belinda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Belinda can now know whether Belinda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Belinda","June","Amos","Raymond"],"index":54758,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993960857,"difficulty":0.0006039143}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Adriana's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Clarence can now know whether Adriana can know that Clarence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clarence","Adriana","Richard"],"index":12161,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994392991,"difficulty":0.0005607009}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether Mary is thirsty. It is publicly announced that Mary does not know whether Patricia is thirsty. It is publicly announced that Mary is thirsty. It is publicly announced that Mary knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Gordon can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gordon","Mary","Patricia","Margaret"],"index":11540,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985324144,"difficulty":0.0014675856}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Craig's forehead is muddy. It is publicly announced that Donald knows whether Kelsey's forehead is muddy. It is publicly announced that Jessica knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agentd knows that (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kelsey can now know that Craig can know that Kelsey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Craig","Jessica","Donald","Kelsey"],"index":47322,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9714134932,"difficulty":0.0285865068}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Susan can now know that Richard can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amy","Duane","Susan","Richard"],"index":34902,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997194409,"difficulty":0.0002805591}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Elsie can now know that Lawrence can know that Bradley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elsie","Bradley","Lawrence"],"index":61769,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6699928641,"difficulty":1.6699928641}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Leah's forehead is muddy. It is publicly announced that Bruce knows whether or not nobody's forehead is muddy. It is publicly announced that Leah knows whether Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Raymond can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Bruce","Leah"],"index":24119,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937247634,"difficulty":0.0062752366}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melvin does not know whether Mary is thirsty. It is publicly announced that Matthew knows whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Pedro can now know that Melvin can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melvin","Mary","Pedro","Matthew"],"index":14259,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983971715,"difficulty":0.0016028285}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yolanda's card is shown to Yolanda. David's card is shown to Yolanda. Yolanda's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Yolanda knows whether David picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"David can now know that Yolanda can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Yolanda","David"],"index":25997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935905933,"difficulty":0.0064094067}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Lynn. Lynn's card is shown to Lynn. William's card is shown to James. Lynn's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Lynn knows whether or not nobody picked a red card. It is publicly announced that William knows whether Lynn picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Lynn can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Lynn","James"],"index":51271,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6756027341,"difficulty":1.6756027341}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon knows whether Marc's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Ronald can now know whether Gordon can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Marc","Teresa","Gordon"],"index":1322,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9961020947,"difficulty":0.0038979053}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Lonnie. Donald's card is shown to Lonnie. Danielle's card is shown to Donald. Jody's card is shown to Donald. Donald's card is shown to Jody. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Danielle can now know whether Lonnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lonnie","Danielle","Donald","Jody"],"index":65646,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.854802072,"difficulty":0.145197928}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aubrey knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Aubrey can now know whether William can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aubrey","Margery","William","Laurie"],"index":24549,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975277781,"difficulty":0.0024722219}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Beatrice can now know that Sarah can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Beatrice","Joe","Sarah","George"],"index":29957,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985209107,"difficulty":0.0014790893}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Rochelle knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Earnest can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Glen","Earnest","Rochelle"],"index":12431,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997115731,"difficulty":0.0002884269}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Michael can now know that Jamie can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Gina","Jamie","Beatrice"],"index":28600,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997488856,"difficulty":0.0002511144}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that George knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jennifer can now know that Domingo can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Jennifer","George","Domingo"],"index":15262,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997716546,"difficulty":0.0002283454}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that Mary does not know whether Vita is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Vita can now know that Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vita","Charles","Mary"],"index":60091,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8443546891,"difficulty":0.1556453109}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Cole can now know that Michael can know whether Jeffrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Michael","Cole","Robert"],"index":23470,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9956203103,"difficulty":0.0043796897}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Nathan can now know whether Nathan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patrick","Gary","Nathan","Robert"],"index":9000,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9883531928,"difficulty":1.9883531928}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Travis does not know whether Bruce is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Richard can now know that Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Bruce","Travis"],"index":21137,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979118705,"difficulty":0.0020881295}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Estela's card is shown to Estela. Eugene's card is shown to Estela. Jennifer's card is shown to Jennifer. Estela's card is shown to Eugene. Jennifer's card is shown to Eugene. It is publicly announced that someone picked a red card. It is publicly announced that Eugene does not know whether Eugene picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jennifer can now know whether Eugene can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Estela","Jennifer","Eugene"],"index":1390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9461049438,"difficulty":0.0538950562}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dana does not know whether or not everyone is thirsty. It is publicly announced that Sarah is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (~(1&2)) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (~(1&2)) ] 0","hypothesis":"Dana can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dana","Sarah"],"index":24038,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99662292,"difficulty":0.00337708}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that April's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Charles can now know whether April can know whether April's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["April","Charles"],"index":43632,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9563079476,"difficulty":0.0436920524}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Sharon's card is shown to Barbara. Janice's card is shown to Barbara. Sharon's card is shown to Sharon. Janice's card is shown to Sharon. Sharon's card is shown to Jeff. Barbara's card is shown to Janice. Sharon's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Sharon","Jeff","Janice"],"index":67156,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997418046,"difficulty":0.002581954}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Donald can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Craig","Donald","Edward"],"index":31062,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959635735,"difficulty":0.0040364265}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Samuel. Esther's card is shown to Samuel. Samuel's card is shown to Madeline. Samuel's card is shown to Esther. Esther's card is shown to Esther. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Madeline can now know that Cheryl can know whether Madeline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Samuel","Madeline","Esther"],"index":20449,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8949557543,"difficulty":0.1050442457}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Ramona's card is shown to Ramona. It is publicly announced that someone picked a red card. It is publicly announced that Ramona picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Ramona can now know that Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mark","Ramona"],"index":45206,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9966121316,"difficulty":0.0033878684}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Roderick can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Luis","John","Donnie","Roderick"],"index":48264,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997830987,"difficulty":0.0002169013}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether or not nobody's forehead is muddy. It is publicly announced that Julia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] 0","hypothesis":"Julia can now know that Corey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Corey","Lori","Wanda","Julia"],"index":59061,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9901890159,"difficulty":0.0098109841}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Helen. Karissa's card is shown to Karissa. Joseph's card is shown to Karissa. Earl's card is shown to Joseph. Earl's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether Earl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Karissa can now know that Joseph can know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Karissa","Joseph","Earl"],"index":8538,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7044989467,"difficulty":1.7044989467}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Amy can now know that Jim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jim","Richard","Amy"],"index":56202,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9962622523,"difficulty":0.0037377477}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith does not know whether Edith's forehead is muddy. It is publicly announced that Edith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 0","hypothesis":"Francis can now know that April can know whether April's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rita","Francis","April","Edith"],"index":28203,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6842875481,"difficulty":1.6842875481}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Barbara can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Sarah","Barbara"],"index":22629,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989888072,"difficulty":0.0010111928}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Bridget can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rose","James","Bridget"],"index":50360,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958677292,"difficulty":0.0041322708}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy. It is publicly announced that Nicole's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Nicole can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Douglas","Nicole","Thomas"],"index":33046,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5133621097,"difficulty":1.5133621097}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Raymond. Raymond's card is shown to Bernice. It is publicly announced that someone picked a red card. It is publicly announced that Bernice does not know whether Bernice picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Raymond can now know whether Bernice can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Bernice"],"index":7590,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996874332,"difficulty":0.0003125668}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Linda can now know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debra","Lara","Linda","Tia"],"index":5974,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9822263718,"difficulty":0.0177736282}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jason can now know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Sharon","John","Dana"],"index":33529,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936661124,"difficulty":0.0063338876}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra does not know whether Terri is thirsty. It is publicly announced that Julie does not know whether Morris is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sandra can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sandra","Morris","Julie","Terri"],"index":64499,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Lillian does not know whether Avery is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Avery can now know that Lillian can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Josephine","Avery","Lillian"],"index":56461,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984391332,"difficulty":0.0015608668}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"James can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Kyle","Janean","William"],"index":55772,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997132421,"difficulty":0.0002867579}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacelyn's card is shown to Linda. Janice's card is shown to Janice. Isaac's card is shown to Janice. Jacelyn's card is shown to Janice. Janice's card is shown to Isaac. Isaac's card is shown to Jacelyn. It is publicly announced that someone picked a red card. It is publicly announced that Jacelyn does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Janice can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Janice","Isaac","Jacelyn"],"index":35008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979861975,"difficulty":0.0020138025}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah does not know whether Todd is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"John can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sarah","Todd","John"],"index":9629,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9918352365,"difficulty":0.0081647635}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Jay can now know that Jay's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carl","Jay","Sharon","Karen"],"index":48903,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9815717936,"difficulty":0.0184282064}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angel does not know whether Nelson is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Edmund can now know whether Angel can know that Jeffrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edmund","Jeffrey","Nelson","Angel"],"index":17427,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9916364551,"difficulty":0.0083635449}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Toni does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jinny can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Toni","Jinny"],"index":54697,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982434511,"difficulty":0.0017565489}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gladys knows whether Gladys is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robin can now know that Gladys can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ryan","Robin","Gladys"],"index":32263,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999769032,"difficulty":0.000230968}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Brandi is thirsty. It is publicly announced that Thomas does not know whether Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Maria can now know whether Brandi can know that Brandi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brandi","Maria","Jennifer","Thomas"],"index":19921,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8205658793,"difficulty":1.8205658793}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. Daniel's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Brian knows whether or not nobody picked a red card. It is publicly announced that Brian knows whether Daniel picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brian can now know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Daniel","Brian"],"index":56949,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5293607712,"difficulty":0.4706392288}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Margaret can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shane","Margaret","George"],"index":20649,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985468984,"difficulty":0.0014531016}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet knows whether James's forehead is muddy. It is publicly announced that James knows whether Janet's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Janet can now know that James can know that Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Janet"],"index":65645,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971359968,"difficulty":0.0028640032}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dan can now know whether Mark can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dan","Lillian","Michael","Mark"],"index":62907,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975546002,"difficulty":0.0024453998}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Marie can now know whether Percy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Percy","Steve","Marie","Steven"],"index":11711,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9954198599,"difficulty":0.0045801401}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene knows whether Gustavo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Gustavo can now know that Gustavo's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Margaret","Arlene","Gustavo","Chester"],"index":64958,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966373444,"difficulty":0.0033626556}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jennifer can now know that Gregory can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gregory","Paul","Jennifer"],"index":39588,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984182119,"difficulty":0.0015817881}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marge's card is shown to Marge. Jana's card is shown to Marge. Marge's card is shown to Clara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marge can now know that Clara can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marge","Clara","Jana"],"index":28471,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9830523729,"difficulty":0.0169476271}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marvin does not know whether Rebecca is thirsty. It is publicly announced that Helen does not know whether or not everyone is thirsty. It is publicly announced that Helen does not know whether Rebecca is thirsty. It is publicly announced that Rebecca does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Elmer can now know whether Marvin can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elmer","Rebecca","Marvin","Helen"],"index":38129,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9597238302,"difficulty":1.9597238302}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Marvin. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card. It is publicly announced that Carmen does not know whether Marvin picked a red card. It is publicly announced that Marvin picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] 0","hypothesis":"Marvin can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marvin","Carmen"],"index":1550,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985266924,"difficulty":0.0014733076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hector knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Herbert can now know whether Herbert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nick","Hector","Jill","Herbert"],"index":51620,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9961141348,"difficulty":0.0038858652}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Douglas can now know that Elmer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Gloria","Elmer","Douglas"],"index":2798,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967948794,"difficulty":0.0032051206}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jeremy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Jeremy can now know whether Mario can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mario","Kelly","Jeremy"],"index":64113,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997509122,"difficulty":0.0002490878}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clayton's card is shown to Gregg. Clayton's card is shown to Clayton. Brandon's card is shown to Clayton. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Gregg can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregg","Clayton","Brandon"],"index":54570,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983995557,"difficulty":0.0016004443}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether Jose is thirsty. It is publicly announced that Barbara does not know whether Bonnie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Bonnie can now know whether Shane is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shane","Jose","Barbara","Bonnie"],"index":19664,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942889214,"difficulty":0.0057110786}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Mary can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charla","Mary","James"],"index":21538,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7349101305,"difficulty":0.2650898695}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Martha's card is shown to Melissa. James's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that Martha can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martha","James","Melissa"],"index":21107,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983567595,"difficulty":0.0016432405}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Otis knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Manuel can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Otis","Manuel","Mary","Wanda"],"index":32887,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that Mary can know that Irma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julie","Mary","Irma"],"index":47060,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985468984,"difficulty":0.0014531016}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bridgett knows whether Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Martha can now know that Dion's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bridgett","Martha","Dion"],"index":31585,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983383417,"difficulty":0.0016616583}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Sherie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Annie can now know that Sherie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Sherie","Larry","Annie"],"index":887,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6471759677,"difficulty":0.3528240323}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mercedes does not know whether Mercedes's forehead is muddy. It is publicly announced that Lou knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Lou can now know whether Mercedes's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mercedes","Lou"],"index":45991,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995641112,"difficulty":0.0004358888}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paulette does not know whether Paulette's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Katherine can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Paulette","Katherine","John"],"index":18615,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968169332,"difficulty":0.0031830668}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Curtis can now know that Christopher can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Christopher","Curtis","Robert"],"index":28343,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996837378,"difficulty":0.0003162622}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mercedes knows whether or not nobody's forehead is muddy. It is publicly announced that Cicely's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Mercedes can now know whether Mercedes's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cicely","Mercedes"],"index":14173,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995216131,"difficulty":0.0004783869}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"James can now know whether David can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Scott","James"],"index":5105,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996333122,"difficulty":0.0003666878}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gilberto does not know whether Roberta is thirsty. It is publicly announced that Gilberto knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Roberta can now know that Sarah can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roberta","Gilberto","Sarah"],"index":50408,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981938004,"difficulty":0.0018061996}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laraine's card is shown to Beatrice. Thelma's card is shown to Beatrice. Sandra's card is shown to Laraine. Sandra's card is shown to Thelma. Laraine's card is shown to Thelma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know whether Laraine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Beatrice","Laraine","Thelma"],"index":62326,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9900177121,"difficulty":0.0099822879}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kacie's card is shown to Kacie. Alexander's card is shown to Kacie. Eric's card is shown to Anthony. Eric's card is shown to Alexander. It is publicly announced that someone picked a red card. It is publicly announced that Kacie does not know whether Kacie picked a red card. It is publicly announced that Kacie does not know whether Anthony picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Eric can now know that Anthony can know that Alexander picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Kacie","Anthony","Alexander"],"index":33608,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9850357771,"difficulty":0.0149642229}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know whether Norman can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Andrew","Norman","Thomas"],"index":38092,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5702217221,"difficulty":1.5702217221}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to Victoria. Donald's card is shown to Victoria. Frankie's card is shown to Victoria. Donald's card is shown to Elizabeth. Elizabeth's card is shown to Donald. Donald's card is shown to Donald. Victoria's card is shown to Frankie. Elizabeth's card is shown to Frankie. Frankie's card is shown to Frankie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:2,3 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:2,3 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Elizabeth","Donald","Frankie"],"index":293,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976988435,"difficulty":0.0023011565}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether Etta is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Celeste can now know that Etta is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Etta","Margaret","Celeste","Nancy"],"index":12541,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981729984,"difficulty":0.0018270016}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Selina does not know whether Michele is thirsty. It is publicly announced that Michele does not know whether or not everyone is thirsty. It is publicly announced that Selina is thirsty. It is publicly announced that Michele does not know whether Jesse is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Selina can now know that Selina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jesse","William","Selina","Michele"],"index":28224,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9835662246,"difficulty":0.0164337754}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to Craig. Connie's card is shown to Dorothy. Woodrow's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Connie does not know whether Craig picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Connie can now know whether Craig can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Craig","Connie","Dorothy","Woodrow"],"index":48869,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997037053,"difficulty":0.0002962947}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samantha's card is shown to Carolyn. Patricia's card is shown to Carolyn. Carolyn's card is shown to Edna. Samantha's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edna can now know whether Carolyn can know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Samantha","Edna","Patricia"],"index":2558,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986384511,"difficulty":0.0013615489}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether or not everyone's forehead is muddy. It is publicly announced that Stephanie knows whether Jessica's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Jessica can now know that Stephanie can know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jessica","Stephanie"],"index":44249,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8375934958,"difficulty":0.1624065042}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know whether Dodie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Dodie","Robert"],"index":5913,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9921668768,"difficulty":0.0078331232}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Ann is thirsty. It is publicly announced that Johnny is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] 0","hypothesis":"Ann can now know that Johnny can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ann","Mary","Johnny","Brenda"],"index":42013,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.987862587,"difficulty":0.012137413}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kirk knows whether Kirk's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kirk can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christine","Kirk"],"index":14825,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996912479,"difficulty":0.0003087521}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Glenn can now know that Russell can know that Glenn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Russell","Glenn","Michael"],"index":55839,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979263544,"difficulty":0.0020736456}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Alfreda can now know whether Raymond can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Alfreda"],"index":34488,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997282624,"difficulty":0.0002717376}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria knows whether Scott's forehead is muddy. It is publicly announced that Scott knows whether Kirsten's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Victoria can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kirsten","Victoria","Scott"],"index":25307,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984201193,"difficulty":0.0015798807}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Barbara. Barbara's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Eric can now know that Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Barbara","Eric"],"index":47676,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6763072014,"difficulty":0.3236927986}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Alexis. Alexis's card is shown to Cheryl. Cheryl's card is shown to Cheryl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Alexis can now know whether Cheryl can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alexis","Cheryl"],"index":29246,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christine does not know whether Marguerite is thirsty. It is publicly announced that Christine does not know whether or not everyone is thirsty. It is publicly announced that Christine does not know whether Marguerite is thirsty. It is publicly announced that Marguerite knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Christine can now know that Marguerite can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christine","Marguerite"],"index":63355,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997816682,"difficulty":0.0002183318}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerald does not know whether or not everyone is thirsty. It is publicly announced that Gerald does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Wade can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gerald","Wade"],"index":24796,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marilyn's card is shown to Marilyn. Marilyn's card is shown to Tanna. David's card is shown to Tanna. Tanna's card is shown to Tanna. It is publicly announced that someone picked a red card. It is publicly announced that Marilyn does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether Marilyn can know that Tanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marilyn","David","Tanna"],"index":2049,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9699155092,"difficulty":0.0300844908}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that June knows whether Elmer's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Elmer can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["June","Elmer"],"index":52678,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997532964,"difficulty":0.0002467036}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Leona can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Joseph","Leona"],"index":23788,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9878243208,"difficulty":0.0121756792}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Michael's card is shown to Christopher. Christopher's card is shown to Michael. Michael's card is shown to Michael. Ian's card is shown to Michael. Michael's card is shown to Ian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether Michael can know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Michael","Ian"],"index":66881,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7614784241,"difficulty":0.2385215759}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth knows whether Elizabeth is thirsty. It is publicly announced that Brandon does not know whether Francis is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Francis can now know whether Elizabeth can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","Francis","Brandon"],"index":33632,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997753501,"difficulty":0.0002246499}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester knows whether Gale's forehead is muddy. It is publicly announced that Billy does not know whether Billy's forehead is muddy. It is publicly announced that Delilah knows whether Gale's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Gale can now know that Delilah can know whether Gale's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gale","Delilah","Lester","Billy"],"index":7197,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994326234,"difficulty":0.0005673766}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Fredrick can now know that Alfred can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alfred","Dana","Kathleen","Fredrick"],"index":33085,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9927795529,"difficulty":0.0072204471}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virgie knows whether someone is thirsty. It is publicly announced that Kelly does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Kelly can now know that Virgie can know that Kelly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Virgie","Kelly"],"index":36704,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9944486618,"difficulty":0.0055513382}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy does not know whether Heather is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Angel can now know that Amy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amy","Heather","Angel"],"index":45886,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997087121,"difficulty":0.0002912879}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luz does not know whether or not everyone's forehead is muddy. It is publicly announced that Luz does not know whether Luz's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Joe can now know that Margarita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margarita","Joe","George","Luz"],"index":6235,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5928792953,"difficulty":0.4071207047}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lloyd knows whether Lloyd is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carl can now know whether Lloyd can know whether Carl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lloyd","Carl"],"index":28628,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9971733093,"difficulty":1.9971733093}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher knows whether Laura is thirsty. It is publicly announced that Christopher knows whether Laura is thirsty. It is publicly announced that Laura knows whether Christopher is thirsty. It is publicly announced that Christopher knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Christopher can now know whether Laura can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christopher","Laura"],"index":38236,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993988276,"difficulty":0.0006011724}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick knows whether or not nobody's forehead is muddy. It is publicly announced that Brenda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Brenda can now know whether Patrick can know whether Patrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brenda","Patrick"],"index":9311,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995962977,"difficulty":0.0004037023}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leslie can now know whether Elizabeth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Elizabeth","Leslie"],"index":65736,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997182488,"difficulty":0.0002817512}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether Johnnie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Johnnie can now know that Thomas can know whether Johnnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Johnnie","Kimberly","Emilie","Thomas"],"index":28694,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.992618382,"difficulty":0.007381618}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eliza knows whether Eliza's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Patricia can now know that Eliza can know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Ada","Eliza","Albert"],"index":13276,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982676506,"difficulty":0.0017323494}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Melvin can now know that Nancy can know that Brenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Melvin","Brenda"],"index":43854,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9156582355,"difficulty":0.0843417645}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Angel can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Astrid","Angel","Joshua"],"index":2575,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984886646,"difficulty":0.0015113354}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalie's card is shown to Rosalie. Rosalie's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Rosalie can now know that Patricia can know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rosalie","Patricia"],"index":64561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7544292808,"difficulty":0.2455707192}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lloyd can now know whether Frank can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","James","Joan","Lloyd"],"index":38993,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997755885,"difficulty":0.0002244115}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dona does not know whether Dona's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lola can now know whether Frank can know whether Lola's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dona","Lola","Frank"],"index":17836,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99740237,"difficulty":0.00259763}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eduardo does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"David can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Donald","David","Eduardo"],"index":4212,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997156262,"difficulty":0.0002843738}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Consuelo does not know whether Evelyn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Jennifer can now know that Mark is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Evelyn","Jennifer","Consuelo"],"index":66210,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983466864,"difficulty":0.0016533136}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Liliana's card is shown to James. James's card is shown to Liliana. Liliana's card is shown to Liliana. Myron's card is shown to Liliana. Myron's card is shown to Lawrence. James's card is shown to Myron. Lawrence's card is shown to Myron. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Lawrence can know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Liliana","Lawrence","Myron"],"index":35118,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6065781116,"difficulty":0.3934218884}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Tracy can now know that Joy can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tracy","Joy","David","Frank"],"index":29919,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9415768385,"difficulty":0.0584231615}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eva does not know whether or not everyone is thirsty. It is publicly announced that Eva does not know whether David is thirsty. It is publicly announced that Gregory does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Gregory can now know whether David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Eva","David","Karen"],"index":66678,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8570310473,"difficulty":0.1429689527}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Betty can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jewell","Betty","Katrina"],"index":52306,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997414947,"difficulty":0.0002585053}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cinda's card is shown to Cinda. Elizabeth's card is shown to Cinda. Thomas's card is shown to Cinda. Cinda's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Cinda's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cinda can now know that Elizabeth can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Cinda","Elizabeth","Thomas"],"index":38301,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pearl's card is shown to Pearl. Pearl's card is shown to Joshua. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Pearl knows whether someone picked a red card. It is publicly announced that Pearl does not know whether Joshua picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Pearl can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Pearl","Joshua"],"index":901,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Franklin. Corey's card is shown to Bonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bonnie can now know that Corey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Franklin","Bonnie","Corey"],"index":28989,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984049201,"difficulty":0.0015950799}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Aaron can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Willie","Timothy","Aaron"],"index":3333,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981963038,"difficulty":0.0018036962}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Constance can now know that Matthew can know that Jerry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Matthew","Constance","Jerry"],"index":12034,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6192157269,"difficulty":0.3807842731}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather is not thirsty. It is publicly announced that Heather is not thirsty. It is publicly announced that Hazel does not know whether Cheri is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows whether (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Heather can now know whether Viola can know that Heather is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheri","Hazel","Viola","Heather"],"index":20262,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9949329495,"difficulty":0.0050670505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Thomas can now know whether Ernesto can know that Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Brian","Janice","Ernesto"],"index":24197,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9702185988,"difficulty":0.0297814012}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"John can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jean","John"],"index":47891,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9963858128,"difficulty":0.0036141872}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Derrick knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Marie can now know whether Derrick can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Derrick","Marie"],"index":7185,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997790456,"difficulty":0.0002209544}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Jeremy. Jeremy's card is shown to Darrell. Christina's card is shown to Darrell. Darrell's card is shown to Christina. Gonzalo's card is shown to Christina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darrell can now know whether Gonzalo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeremy","Darrell","Christina","Gonzalo"],"index":7356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7722993493,"difficulty":0.2277006507}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Nancy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Nancy","Lashanda"],"index":11467,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983812571,"difficulty":0.0016187429}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Donald can now know that Donald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Betty","Rosanne","Joshua","Donald"],"index":45546,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.996147275,"difficulty":0.003852725}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bridget is thirsty. It is publicly announced that Ian does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"James can now know whether Bridget can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bridget","Ian","James"],"index":38340,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997007847,"difficulty":0.0002992153}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Troy does not know whether Leo is thirsty. It is publicly announced that Leo does not know whether Thelma is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] Agentd knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Thelma can now know that Sara can know whether Leo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leo","Troy","Sara","Thelma"],"index":58611,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9911351204,"difficulty":0.0088648796}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Constance's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Bernadine knows whether Constance's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Constance can now know that Margaret can know that Bernadine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bernadine","Margaret","Constance"],"index":51847,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9741199017,"difficulty":0.0258800983}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether Frank's forehead is muddy. It is publicly announced that Frank does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ashley can now know whether Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Frank","Ashley"],"index":31078,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5895928741,"difficulty":1.5895928741}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ralph knows whether Ralph is thirsty. It is publicly announced that Leon does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Donald can now know that Ralph can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ralph","Leon","Donald"],"index":59047,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997819066,"difficulty":0.0002180934}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Darleen can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julie","Lisa","Darleen"],"index":36449,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977853298,"difficulty":0.0022146702}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chelsea knows whether or not nobody's forehead is muddy. It is publicly announced that Ralph does not know whether or not everyone's forehead is muddy. It is publicly announced that Ralph's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agentb knows that (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Ralph can now know that Chelsea can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Chelsea","Ralph"],"index":27847,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9919365644,"difficulty":1.9919365644}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristen is not thirsty. It is publicly announced that Clarence does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] Agentd knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Joseph can now know that Kristen can know whether Kristen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clarence","Richard","Kristen","Joseph"],"index":23864,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991493225,"difficulty":0.0008506775}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valarie's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Bianca can now know that Valarie can know that Valarie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bianca","Valarie"],"index":39921,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9531354308,"difficulty":0.0468645692}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Ora. Ora's card is shown to Cesar. Dorothy's card is shown to Cesar. Ora's card is shown to Dorothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sherry can now know whether Cesar can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ora","Sherry","Cesar","Dorothy"],"index":33792,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8966835141,"difficulty":1.8966835141}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Dorothy can now know that Timothy can know that Mark is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jill","Dorothy","Timothy","Mark"],"index":38615,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985771179,"difficulty":0.0014228821}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tessa knows whether or not nobody's forehead is muddy. It is publicly announced that Tessa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Tessa can now know whether Christine can know that Tessa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tessa","Christine"],"index":50799,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6692584157,"difficulty":0.3307415843}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Melissa can now know whether Christopher can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Melissa","Richard"],"index":17963,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.995296061,"difficulty":0.004703939}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Chi can now know that Chi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wendy","George","Rose","Chi"],"index":67361,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.994983077,"difficulty":0.005016923}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know that Bobbie can know whether Bobbie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Bobbie","Michael"],"index":8012,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9860681295,"difficulty":0.0139318705}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Monica is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Marcia can now know that Jennifer can know that Marcia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Monica","Marcia","Daniel"],"index":25222,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971303344,"difficulty":0.0028696656}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Sherrie can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sherrie","Susan","James","Robyn"],"index":51880,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99975425,"difficulty":0.00024575}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis knows whether James's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"James can now know that Francis can know that Francis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Francis"],"index":25183,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979059696,"difficulty":0.0020940304}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christie does not know whether Francis is thirsty. It is publicly announced that Christie is not thirsty. It is publicly announced that Ruth knows whether Christie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Francis can now know that Sheena can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christie","Sheena","Ruth","Francis"],"index":48388,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985650182,"difficulty":0.0014349818}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cari's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"James can now know that Jacqui can know whether Charis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cari","Charis","James","Jacqui"],"index":54222,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997063279,"difficulty":0.0002936721}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Velma can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Velma"],"index":13844,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999778688,"difficulty":0.000221312}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley's forehead is not muddy. It is publicly announced that Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Shirley can now know that Shirley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Raymond","Shirley"],"index":49981,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.696195364,"difficulty":0.303804636}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ward is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Ward can now know that Kent can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kent","Ward"],"index":24715,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997282624,"difficulty":0.0002717376}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy. It is publicly announced that Emily knows whether someone's forehead is muddy. It is publicly announced that James knows whether Emily's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Emily can now know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Gabriella","Richard","Emily"],"index":21642,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979332685,"difficulty":0.0020667315}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is muddy. It is publicly announced that Edward knows whether someone's forehead is muddy. It is publicly announced that Gerardo knows whether Conrad's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Conrad can now know that Robert can know that Conrad's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Conrad","Gerardo","Robert","Edward"],"index":66123,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9376573563,"difficulty":0.0623426437}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Alan can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","David","Alan","Kathy"],"index":64169,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995933175,"difficulty":0.0004066825}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Margaret knows whether Margaret is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"William can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","William","Clyde"],"index":3969,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983581901,"difficulty":0.0016418099}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jason can now know that Helena can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Helena","Jason"],"index":36713,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984601736,"difficulty":0.0015398264}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Sabina. Rene's card is shown to Rene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Sabina can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sabina","William","Rene"],"index":59264,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995469451,"difficulty":0.0004530549}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Casey can now know that Amanda can know that Casey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Casey","Angela","Amanda"],"index":48959,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9767314196,"difficulty":0.0232685804}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Craig knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Craig can now know whether Albert can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Glenn","Albert","Craig","Marie"],"index":62863,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Marjorie. Marjorie's card is shown to Jean. Jean's card is shown to Jean. Marjorie's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jean can now know whether Marjorie can know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marjorie","Jean","Elizabeth"],"index":57917,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982964396,"difficulty":0.0017035604}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Mary can now know whether Sara can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sara","Margaret","Mary"],"index":39024,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997835755,"difficulty":0.0002164245}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Earl's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Willis can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willis","William","Earl","Catrina"],"index":41116,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979962707,"difficulty":0.0020037293}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Wendy. Jennifer's card is shown to Wendy. Mary's card is shown to Christopher. Christopher's card is shown to Mary. Jennifer's card is shown to Mary. Christopher's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Mary picked a red card. It is publicly announced that Christopher knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Wendy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wendy","Christopher","Mary","Jennifer"],"index":21964,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998472631,"difficulty":0.001527369}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Yvonne's card is shown to Dorothy. Dorothy's card is shown to Yvonne. It is publicly announced that someone picked a red card. It is publicly announced that Yvonne does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Yvonne can now know that Dorothy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Yvonne"],"index":41195,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Germaine can now know that Stephen can know whether Germaine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephen","Germaine","Jimmy"],"index":49134,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9898061156,"difficulty":0.0101938844}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denice's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Denice can now know whether Harold can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Denice","Harold","Regina"],"index":23858,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995875955,"difficulty":0.0004124045}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina knows whether someone's forehead is muddy. It is publicly announced that Heriberto knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Tina can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Joseph","Heriberto","Tina"],"index":35729,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976684451,"difficulty":0.0023315549}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Craig. Clifton's card is shown to Craig. Suzi's card is shown to Craig. Timothy's card is shown to Clifton. Timothy's card is shown to Suzi. Suzi's card is shown to Suzi. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clifton can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Craig","Clifton","Timothy","Suzi"],"index":65236,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether or not everyone's forehead is muddy. It is publicly announced that Kenneth knows whether Walter's forehead is muddy. It is publicly announced that Kenneth's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Walter can now know whether Kenneth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenneth","Walter"],"index":34686,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995800853,"difficulty":0.0004199147}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nelson knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Melissa can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Melissa","Nelson","Rickey","John"],"index":228,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994322658,"difficulty":0.0005677342}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy. It is publicly announced that Jamie does not know whether Jamie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Shirley can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Jack","Shirley","Jamie"],"index":29889,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lillian's card is shown to Beatrice. Patsy's card is shown to Patsy. Beatrice's card is shown to Lillian. It is publicly announced that someone picked a red card. It is publicly announced that Lillian does not know whether Lillian picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Beatrice can now know that Lillian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Beatrice","Patsy","Lillian"],"index":56825,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954571724,"difficulty":0.0045428276}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacob knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Andrea can now know whether Jacob can know whether Jacob is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrea","Mario","Jacob"],"index":48240,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986246824,"difficulty":0.0013753176}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Claudia does not know whether Claudia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Leonard can now know whether David can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Claudia","Leonard"],"index":51563,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997152686,"difficulty":0.0002847314}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leo does not know whether Marie is thirsty. It is publicly announced that Leo does not know whether Katherine is thirsty. It is publicly announced that Marie is thirsty. It is publicly announced that Katherine does not know whether Leo is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Leo can now know whether Katherine can know that Katherine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marie","Katherine","Leo"],"index":40096,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9441597462,"difficulty":1.9441597462}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Benito's card is shown to Anita. Joshua's card is shown to John. Joshua's card is shown to Joshua. Anita's card is shown to Benito. John's card is shown to Benito. It is publicly announced that someone picked a red card. It is publicly announced that Joshua does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Benito can now know that Joshua can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anita","John","Joshua","Benito"],"index":49612,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997714162,"difficulty":0.0002285838}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randall knows whether Randall is thirsty. It is publicly announced that Barbara knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Clare can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Clare","Randall"],"index":5700,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986880422,"difficulty":0.0013119578}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Mary does not know whether Elwood is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Colin can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elwood","Mary","Colin","Harry"],"index":5936,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Renee does not know whether Shannon is thirsty. It is publicly announced that Renee does not know whether Paul is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Renee can now know that Shannon can know that Shannon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shannon","Paul","Renee"],"index":2378,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9424911141,"difficulty":0.0575088859}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy. It is publicly announced that Charles's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Rodney can now know that Gracie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Rodney","Gracie","Hannah"],"index":45680,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985634685,"difficulty":0.0014365315}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jefferson can now know that Carlos can know that Diane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jefferson","Carlos","Diane","Clark"],"index":14000,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986542463,"difficulty":0.0013457537}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Robert. Robert's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Shannon can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Robert","Shannon","Cynthia"],"index":43579,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.973050952,"difficulty":0.026949048}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Wendell knows whether Carlos is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Wendell can now know that Carlos is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Carlos","Wendell"],"index":15687,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9927937984,"difficulty":0.0072062016}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Noel can now know whether Noel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Sarah","Noel","Michelle"],"index":7005,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.966809094,"difficulty":0.033190906}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"James can now know whether Sheila can know whether Martin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Martin","Sheila","Shari"],"index":38233,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993523955,"difficulty":0.0006476045}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katharine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Catherine can now know that Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Luis","Katharine","Terry","Catherine"],"index":28151,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984387755,"difficulty":0.0015612245}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Michael can now know that Robert can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Alfred","Michael"],"index":33328,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997677207,"difficulty":0.0002322793}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Donald. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Donald can now know whether Alexis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Raymond","Alexis"],"index":51945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8942732811,"difficulty":0.1057267189}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to John. John's card is shown to Jeffrey. John's card is shown to Doris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Doris can now know that Jeffrey can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Jeffrey","Doris"],"index":4742,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984331727,"difficulty":0.0015668273}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret does not know whether Margaret's forehead is muddy. It is publicly announced that Leonora knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Leonora can now know that Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leonora","Robert","Margaret"],"index":61778,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5471736789,"difficulty":1.5471736789}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene knows whether someone's forehead is muddy. It is publicly announced that Bryan knows whether Bryan's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Arlene knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Bryan can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bryan","Arlene"],"index":28163,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997566342,"difficulty":0.0002433658}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danny's card is shown to Danny. Janice's card is shown to Danny. Danny's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Danny's card is shown to Mario. Danny's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mario can now know whether Danny can know whether Mario picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danny","Carolyn","Mario","Janice"],"index":9899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997721374,"difficulty":0.002278626}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Teresa can now know whether Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debra","Hwa","Teresa"],"index":63771,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995274544,"difficulty":0.0004725456}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cecilia does not know whether or not everyone is thirsty. It is publicly announced that Cecilia does not know whether or not everyone is thirsty. It is publicly announced that Cecilia does not know whether Marty is thirsty. It is publicly announced that Cecilia knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Cecilia can now know that Cecilia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marty","Cecilia"],"index":28033,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9920617342,"difficulty":0.0079382658}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cecil does not know whether or not everyone is thirsty. It is publicly announced that Robert does not know whether Nancy is thirsty. It is publicly announced that Nancy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Nancy can now know that Nancy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cecil","Nancy","Robert"],"index":51078,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9288054705,"difficulty":1.9288054705}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether someone's forehead is muddy. It is publicly announced that Angel knows whether Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Nancy can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jillian","Angel","Nancy"],"index":30175,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996857643,"difficulty":0.0003142357}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle knows whether or not everyone's forehead is muddy. It is publicly announced that Danielle does not know whether Danielle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Carrie can now know that Carrie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Carrie","Danielle"],"index":4555,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8479830623,"difficulty":0.1520169377}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christina knows whether someone is thirsty. It is publicly announced that Daniel does not know whether Terry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Christina can now know whether Terry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christina","Daniel","Michael","Terry"],"index":55696,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9930968881,"difficulty":0.0069031119}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samantha's card is shown to Dan. John's card is shown to Janet. Samantha's card is shown to Samantha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dan can now know that Samantha can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dan","Janet","Samantha","John"],"index":23424,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980911613,"difficulty":0.0019088387}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Harold can now know that Leslie can know whether Leslie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tanya","Leslie","Simone","Harold"],"index":7808,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996125102,"difficulty":0.0003874898}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clinton does not know whether Clinton's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Clifford can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clinton","Clifford","Nicole"],"index":48631,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997602105,"difficulty":0.0002397895}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jana's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Linda can now know that Christina can know that Jana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christina","Linda","Jana"],"index":25144,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9695525169,"difficulty":0.0304474831}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jorge can now know that Rosa can know that Katherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jorge","Rosa","Eldon","Katherine"],"index":28255,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966195822,"difficulty":0.0033804178}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Simone knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Rosa can now know that Rosa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rosa","Sharon","Lori","Simone"],"index":9421,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9527847171,"difficulty":0.0472152829}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence's forehead is not muddy. It is publicly announced that Timothy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Teresita can now know that Lawrence's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Todd","Lawrence","Timothy","Teresita"],"index":7612,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9861126542,"difficulty":0.0138873458}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Taylor's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Elsie can now know whether David can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elsie","David","Taylor"],"index":51467,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996920824,"difficulty":0.0003079176}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Debbi can now know that Noelle can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Noelle","Geraldine","David","Debbi"],"index":21785,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984663725,"difficulty":0.0015336275}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dante does not know whether or not everyone is thirsty. It is publicly announced that Dante does not know whether Barbara is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Eula knows whether Eula is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dante can now know whether Barbara can know that Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eula","Barbara","Dante"],"index":53381,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9052246213,"difficulty":1.9052246213}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Imelda's card is shown to Jacques. Imelda's card is shown to Imelda. Jesus's card is shown to Imelda. Imelda's card is shown to Jesus. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jacques can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacques","Frank","Imelda","Jesus"],"index":18465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997710586,"difficulty":0.0002289414}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paulette's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Barry can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Barry","Paulette"],"index":39551,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985793829,"difficulty":0.0014206171}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aaron knows whether Aaron is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mai can now know that Aaron is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mai","Aaron","Logan"],"index":59446,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997610569,"difficulty":0.002389431}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Juliette. Juliette's card is shown to Marie. Marie's card is shown to William. Joseph's card is shown to William. William's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Marie knows whether Juliette picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Juliette can now know that Marie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Juliette","Marie","William","Joseph"],"index":7452,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969305396,"difficulty":0.0030694604}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dian knows whether Dian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Dian can now know that Dian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","John","Dian","Julia"],"index":5235,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9971005321,"difficulty":1.9971005321}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene knows whether Irene's forehead is muddy. It is publicly announced that Irene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Irene can now know that Thomas can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irene","Brenda","Thomas","Tanya"],"index":50932,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998393476,"difficulty":0.001606524}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to Connie. Barbara's card is shown to Connie. Connie's card is shown to Barbara. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Connie knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Irvin can now know that Connie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Irvin","Connie","Barbara"],"index":52109,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986114502,"difficulty":0.0013885498}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Kim. Renee's card is shown to Kim. Kim's card is shown to Renee. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Renee can now know that Kim can know whether Renee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kim","Renee"],"index":16212,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8366023898,"difficulty":1.8366023898}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Hue is thirsty. It is publicly announced that Hue knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Charles can now know that Hue is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beatrice","Charles","Hue","William"],"index":3688,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973315001,"difficulty":0.0026684999}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrea does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Andrea can now know whether Charlene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Reginald","Charlene","Andrea","Shona"],"index":62493,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6721410155,"difficulty":0.3278589845}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melvin does not know whether Galen is thirsty. It is publicly announced that Alan does not know whether Melvin is thirsty. It is publicly announced that Alan knows whether or not nobody is thirsty. It is publicly announced that Galen does not know whether Donald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Alan can now know whether Galen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Galen","Alan","Donald","Melvin"],"index":29864,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9853628874,"difficulty":0.0146371126}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Todd can now know that Charles can know whether Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Todd","Christopher","Bernie"],"index":35370,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997246861,"difficulty":0.0002753139}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Marion can now know that Leslie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Simone","Marion","Leslie"],"index":16336,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984413981,"difficulty":0.0015586019}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Micheline knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Imelda can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Imelda","Micheline","Wendell"],"index":20528,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brooke's card is shown to Brooke. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Brooke picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that Brooke can know whether Brooke picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brooke","Robert"],"index":59646,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9927152991,"difficulty":0.0072847009}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heidi knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Chris can now know that Heidi can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Chris","Heidi"],"index":1115,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983696342,"difficulty":0.0016303658}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sammie's card is shown to David. Tracy's card is shown to Sammie. John's card is shown to Sammie. Sammie's card is shown to Tracy. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tracy can now know whether David can know whether Sammie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Sammie","Tracy","John"],"index":60874,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989142418,"difficulty":0.0010857582}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Colleen knows whether or not everyone's forehead is muddy. It is publicly announced that Colleen knows whether someone's forehead is muddy. It is publicly announced that Colleen knows whether Colleen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Stacy can now know whether Colleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Colleen","Stacy"],"index":22960,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997311234,"difficulty":0.0002688766}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Ronald can now know that Barbara can know whether Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronald","Barbara"],"index":21517,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9654383659,"difficulty":1.9654383659}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Jamie can now know that Edna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edna","Jamie","Pierre","James"],"index":6468,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9458946586,"difficulty":0.0541053414}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Candy's forehead is muddy. It is publicly announced that Elizabeth knows whether Candy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Candy can now know that Elizabeth can know that Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Elizabeth","Candy"],"index":14606,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966338277,"difficulty":0.0033661723}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnetta's card is shown to Tammy. Lisa's card is shown to Tammy. Johnetta's card is shown to Johnetta. Lisa's card is shown to Johnetta. Lisa's card is shown to Lisa. Anna's card is shown to Lisa. Anna's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Johnetta can now know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tammy","Johnetta","Lisa","Anna"],"index":29035,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9783859849,"difficulty":0.0216140151}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cora knows whether or not nobody's forehead is muddy. It is publicly announced that Katherine knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Cora can now know that Katherine can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Katherine","Cora"],"index":63796,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973857999,"difficulty":0.0026142001}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Christopher's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Christopher can now know whether John can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Christopher"],"index":61709,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.877900064,"difficulty":0.122099936}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Helen can now know that Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bobby","Anna","Helen"],"index":36239,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971354008,"difficulty":0.0028645992}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Edna can now know that Michael can know that Edna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Edna"],"index":46136,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99702245,"difficulty":0.00297755}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Herbert does not know whether Arthur is thirsty. It is publicly announced that Christine does not know whether Theodore is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know that Herbert can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Arthur","Herbert","Theodore"],"index":66793,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984411597,"difficulty":0.0015588403}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yetta does not know whether Yetta's forehead is muddy. It is publicly announced that Isidro's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Anthony can now know that Yetta can know that Yetta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Yetta","Anthony","Isidro"],"index":29685,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8965849876,"difficulty":0.1034150124}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly's forehead is muddy. It is publicly announced that Vickie knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Vickie can now know that Geraldine can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geraldine","Vanessa","Kimberly","Vickie"],"index":5861,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997845292,"difficulty":0.0002154708}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francisco knows whether or not nobody is thirsty. It is publicly announced that Rose does not know whether Damon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rose can now know that Damon can know whether Rose is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leonard","Rose","Damon","Francisco"],"index":246,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9914958477,"difficulty":0.0085041523}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Terra is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Erik can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erik","Terra","Joseph","Theresa"],"index":49363,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951840043,"difficulty":0.0048159957}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Otha can now know whether Mary can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Otha","Keith","Mary"],"index":22222,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lonnie knows whether Michael's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy. It is publicly announced that Lonnie knows whether Lonnie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lonnie can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lonnie","Michael"],"index":54214,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996234179,"difficulty":0.0003765821}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Brian can now know that Jean can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Brian","Jean","George"],"index":13856,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975863695,"difficulty":0.0024136305}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Valorie does not know whether Lorraine is thirsty. It is publicly announced that Lorraine does not know whether Fernando is thirsty. It is publicly announced that Lester knows whether Lester is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lester can now know whether Fernando is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorraine","Valorie","Lester","Fernando"],"index":21162,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9885649085,"difficulty":0.0114350915}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Gary. Gary's card is shown to Valerie. Melvin's card is shown to Helen. Gary's card is shown to Melvin. Helen's card is shown to Melvin. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card. It is publicly announced that Gary picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Helen can now know that Valerie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Valerie","Helen","Melvin"],"index":46288,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7872343659,"difficulty":0.2127656341}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shalon's forehead is not muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy. It is publicly announced that Kenneth knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know that Shalon can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shalon","Kenneth","Lori"],"index":55873,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9032426476,"difficulty":0.0967573524}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Anthony can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Gayle","Ronald","Anthony"],"index":914,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.981480062,"difficulty":0.018519938}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ethel's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Diane can now know that Ethel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ethel","Diane"],"index":40515,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983545542,"difficulty":0.0016454458}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"James can now know that George can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","David","George","Wanda"],"index":4095,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997829795,"difficulty":0.0002170205}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy. It is publicly announced that Eva knows whether Eva's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Travis can now know that Danny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eva","Travis","Robert","Danny"],"index":36562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982682467,"difficulty":0.0017317533}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ruth can now know that Donald can know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ruth","Donald"],"index":3786,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9589896798,"difficulty":0.0410103202}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilma does not know whether Wilma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gertie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wilma","Francisco","Ronald","Gertie"],"index":19264,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986176491,"difficulty":0.0013823509}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether Carmel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Carmel can now know that Lori can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","John","Carmel","Lori"],"index":12626,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997130036,"difficulty":0.0002869964}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sandra can now know that Colleen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Sandra","Minnie","Colleen"],"index":44839,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984696507,"difficulty":0.0015303493}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alana knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Rosemary can now know whether Samuel can know whether Samuel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Samuel","Gloria","Rosemary","Alana"],"index":61818,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9898404479,"difficulty":0.0101595521}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Bruce. Bruce's card is shown to Paul. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Bruce can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bruce","Paul"],"index":13278,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984930754,"difficulty":0.0015069246}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dan knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Dan can now know whether Kenneth can know that Marvin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marvin","Dan","Kenneth"],"index":44165,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9898825288,"difficulty":0.0101174712}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Dale. Pablo's card is shown to Douglas. Dale's card is shown to Pablo. Pablo's card is shown to Pablo. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Douglas can now know whether Pablo can know whether Dale picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dale","Douglas","Pablo"],"index":49685,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982275367,"difficulty":0.0017724633}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Veronica. Frances's card is shown to Norman. Norman's card is shown to Len. Veronica's card is shown to Frances. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Veronica can now know whether Len picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Veronica","Norman","Len","Frances"],"index":18456,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9414410591,"difficulty":0.0585589409}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ginger knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Diane can now know that Ginger can know whether Diane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ginger","Deborah","Latoya","Diane"],"index":40134,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997430444,"difficulty":0.0002569556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Arthur knows whether Patricia's forehead is muddy. It is publicly announced that Ivette's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Arthur can now know that Arthur's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Ivette","Patricia","Samantha"],"index":3176,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9883131385,"difficulty":0.0116868615}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Eric can now know whether Anthony can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Anthony","Dwight"],"index":39956,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997592568,"difficulty":0.0002407432}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Gerald can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sherry","Gerald","James","Daniel"],"index":55485,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983133078,"difficulty":0.0016866922}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. John's card is shown to Anthony. Gregory's card is shown to Anthony. John's card is shown to Jose. Gregory's card is shown to Jose. John's card is shown to John. Gregory's card is shown to John. Anthony's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Jose knows whether or not everyone picked a red card. It is publicly announced that Gregory picked a black card. It is publicly announced that Anthony picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Anthony can now know that John can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Jose","John","Gregory"],"index":15928,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8031829596,"difficulty":0.1968170404}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Levi is not thirsty. It is publicly announced that Regina does not know whether Katherine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Katherine can now know that Regina can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Regina","Katherine","Levi","Margaret"],"index":34432,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983206391,"difficulty":0.0016793609}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad knows whether someone's forehead is muddy. It is publicly announced that Jeannette knows whether Greta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jeannette can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Greta","Jeannette","Chad"],"index":31466,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997547269,"difficulty":0.0002452731}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Thomas's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Thomas knows whether someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card. It is publicly announced that Thomas does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Joseph can now know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thomas","Joseph"],"index":42430,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.77985394,"difficulty":0.22014606}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dolores knows whether someone is thirsty. It is publicly announced that Gregg knows whether Dolores is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Dolores can now know that Gregg is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dolores","Gregg"],"index":8246,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973100424,"difficulty":0.0026899576}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Colleen does not know whether Lila is thirsty. It is publicly announced that Colleen does not know whether Lila is thirsty. It is publicly announced that Colleen knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Lila can now know whether Lila is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Lila","Colleen"],"index":51107,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988105297,"difficulty":0.0011894703}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Phillip can now know whether Catherine can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Catherine","Linda","Phillip","Francis"],"index":27244,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995756745,"difficulty":0.0004243255}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Royal. Royal's card is shown to Frances. It is publicly announced that someone picked a red card. It is publicly announced that Royal does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Frances can now know whether Royal can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Royal","Frances"],"index":18389,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.994099021,"difficulty":0.005900979}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Orlando. Orlando's card is shown to Glen. Glen's card is shown to Glen. Jesus's card is shown to Glen. Thomas's card is shown to Glen. Glen's card is shown to Jesus. Orlando's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Jesus does not know whether Orlando picked a red card. It is publicly announced that Orlando knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Orlando can now know whether Glen can know that Glen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Orlando","Glen","Jesus","Thomas"],"index":51006,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8918110132,"difficulty":1.8918110132}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kylie does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Kylie can now know that Matthew can know that Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Thomas","Kylie"],"index":44651,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5228434205,"difficulty":1.5228434205}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dallas knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Joesph can now know whether Michael can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arthur","Michael","Dallas","Joesph"],"index":20344,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996052384,"difficulty":0.0003947616}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark knows whether someone is thirsty. It is publicly announced that Tricia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] Agenta knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Shana can now know that Tricia can know whether Shana is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shana","Mark","Tricia"],"index":3817,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9771004915,"difficulty":0.0228995085}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Colleen is thirsty. It is publicly announced that Mark does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Mary can now know that Susan can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Susan","Colleen","Mary"],"index":30646,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.966113627,"difficulty":0.033886373}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry knows whether or not nobody's forehead is muddy. It is publicly announced that Melanie's forehead is not muddy. It is publicly announced that Wm does not know whether Wm's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Harry can now know whether Wm can know that Wm's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wm","Melanie","Harry"],"index":62550,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8523618579,"difficulty":0.1476381421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gertrude does not know whether Joaquina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gertrude can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gertrude","Joaquina","Donald"],"index":35382,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957392216,"difficulty":0.0042607784}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula knows whether or not nobody is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Tim can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paula","Tim","James"],"index":22649,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983312488,"difficulty":0.0016687512}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Martin can now know that Jill can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martin","Jill","Wayne"],"index":66125,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976611137,"difficulty":0.0023388863}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Thomas can now know whether Shelly can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Thomas","Shelly"],"index":59602,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9398383498,"difficulty":0.0601616502}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sophia knows whether Jill's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentd knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Terrence can now know that Sophia can know that Jill's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sophia","Jill","Tristan","Terrence"],"index":41474,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998005569,"difficulty":0.001994431}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Michael. Michael's card is shown to Edith. Barbara's card is shown to Mary. Michael's card is shown to Barbara. Edith's card is shown to Barbara. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Edith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Edith","Mary","Barbara"],"index":50511,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7629131079,"difficulty":0.2370868921}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erica does not know whether Vincent is thirsty. It is publicly announced that Selene does not know whether Erica is thirsty. It is publicly announced that Selene does not know whether Vincent is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Erica can now know whether Selene can know whether Erica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erica","Selene","Vincent"],"index":12465,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980450869,"difficulty":0.0019549131}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether or not everyone is thirsty. It is publicly announced that Lisa does not know whether or not everyone is thirsty. It is publicly announced that John knows whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know whether Salvador is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Salvador","John","Lisa","Elizabeth"],"index":803,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6357010603,"difficulty":0.3642989397}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Georgia can now know that David can know that Georgia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Georgia","Linda"],"index":7222,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.925485909,"difficulty":0.074514091}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Janice can now know whether Robert can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Charles","Janice"],"index":35902,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997547269,"difficulty":0.0002452731}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clare can now know that George can know whether Flossie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clare","George","Edwin","Flossie"],"index":21637,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997412562,"difficulty":0.0002587438}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Tina is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Tina can now know that Gerald can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Tina","John","Gerald"],"index":8741,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941672087,"difficulty":0.0058327913}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Chester can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Paul","Sherry","Chester"],"index":22964,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983882904,"difficulty":0.0016117096}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether or not nobody's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"David can now know whether Patricia can know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Patricia"],"index":7870,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996311665,"difficulty":0.0003688335}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Christopher. Debra's card is shown to Debra. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Debra can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Debra","Richard"],"index":67079,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983065128,"difficulty":0.0016934872}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Van's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Donald can now know that Tyler can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tyler","Robert","Van","Donald"],"index":17862,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9752667546,"difficulty":0.0247332454}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Larry knows whether Dale's forehead is muddy. It is publicly announced that Larry knows whether someone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentd knows that (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Dale can now know that Larry can know whether Charlotte's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tad","Larry","Charlotte","Dale"],"index":48874,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994466901,"difficulty":0.0005533099}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jessica can now know that Matthew can know that Jessica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jessica","Matthew","Dean"],"index":30992,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.960087955,"difficulty":0.039912045}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Priscilla knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Priscilla can now know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Dana","Priscilla"],"index":6381,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8907474875,"difficulty":0.1092525125}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Terri can now know whether Donald can know that Terri's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Terri","Donald"],"index":22914,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9229231477,"difficulty":1.9229231477}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lydia knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kathleen can now know that Donald can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Donald","Lydia"],"index":17995,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997652173,"difficulty":0.0002347827}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Mary. Alejandra's card is shown to Alejandra. Susan's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Susan picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Alejandra","Susan"],"index":40442,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9481422305,"difficulty":1.9481422305}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda knows whether or not everyone's forehead is muddy. It is publicly announced that Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Margaret can now know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Amanda","Margaret"],"index":50687,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8501531482,"difficulty":0.1498468518}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Curtis can now know whether Keith can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Curtis","Robert","Keith"],"index":29814,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995686412,"difficulty":0.0004313588}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether or not nobody's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Cynthia can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cynthia","Michael","Susan"],"index":60010,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997195601,"difficulty":0.0002804399}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raphael knows whether or not everyone's forehead is muddy. It is publicly announced that Nina's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Dawn can now know that Nina can know that Dawn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raphael","Nina","Dawn"],"index":15911,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9346798062,"difficulty":0.0653201938}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerome knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Spencer can now know that Fred can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerome","Angelo","Spencer","Fred"],"index":14763,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982860684,"difficulty":0.0017139316}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Sherry. Sherry's card is shown to Maurice. Maurice's card is shown to Maurice. It is publicly announced that someone picked a red card. It is publicly announced that Maurice knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Maurice can now know whether Sherry can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sherry","Maurice"],"index":29603,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997677207,"difficulty":0.0002322793}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Elizabeth. Elizabeth's card is shown to Sue. Sue's card is shown to Sue. Elizabeth's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know that Sue can know that Sue picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","Sue","Michael"],"index":1047,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949285984,"difficulty":0.0050714016}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maryann can now know whether Lawrence can know that Lawrence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Teresita","Maryann","Lawrence"],"index":64363,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996429682,"difficulty":0.0003570318}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Roger can now know that Joseph can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Michael","Joseph","Naomi"],"index":53265,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998283267,"difficulty":0.001716733}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Herman. Herman's card is shown to Jerry. Jerry's card is shown to Jerry. Herman's card is shown to James. Jerry's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know whether Jesus picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Herman","Jerry","Jesus","James"],"index":56950,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.856844306,"difficulty":0.143155694}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Evelyn. Evelyn's card is shown to John. Amy's card is shown to John. Vivian's card is shown to Vivian. John's card is shown to Amy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vivian can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","John","Vivian","Amy"],"index":17487,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985175729,"difficulty":0.0014824271}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Emily's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Emily can now know whether Kevin can know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emily","Nick","Kevin","Francis"],"index":2901,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996371269,"difficulty":0.0003628731}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Crystal. Crystal's card is shown to Joe. John's card is shown to Joe. Crystal's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joe can now know that John can know whether Crystal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Joe","John"],"index":31903,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5776020288,"difficulty":1.5776020288}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know whether Chris can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eldon","Chris","Michael"],"index":63772,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5335063934,"difficulty":1.5335063934}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not nobody's forehead is muddy. It is publicly announced that Karen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know whether Kristy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Virginia","Kristy","Karen"],"index":52290,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elaine knows whether or not everyone's forehead is muddy. It is publicly announced that Elaine does not know whether Elaine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Elaine can now know whether Elaine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Belinda","Elaine","Matthew","William"],"index":9437,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6067538857,"difficulty":1.6067538857}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Susan can now know that Cynthia can know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cynthia","Susan"],"index":32928,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.979714334,"difficulty":0.020285666}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isabelle does not know whether Paul is thirsty. It is publicly announced that Ralph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Ralph can now know whether Isabelle can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Isabelle","Ralph","Paul","Janet"],"index":20809,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9972471595,"difficulty":0.0027528405}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Lauri's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! 1 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! 1 ] 0","hypothesis":"Sheryl can now know that Lauri's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lauri","Sheryl"],"index":7952,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.6410716176,"difficulty":0.3589283824}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Travis does not know whether or not everyone is thirsty. It is publicly announced that Travis does not know whether Maurice is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Grace can now know whether Maurice can know that Maurice is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Travis","Maurice","Grace"],"index":58039,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9113295674,"difficulty":1.9113295674}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrea does not know whether Jay is thirsty. It is publicly announced that Jay is not thirsty. It is publicly announced that Andrea is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] 0","hypothesis":"Jay can now know whether Michelle can know whether Andrea is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jay","Andrea","Clark","Michelle"],"index":25537,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987989664,"difficulty":0.0012010336}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karl does not know whether Jessica is thirsty. It is publicly announced that Carman is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] Agentd knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] 0","hypothesis":"Joshua can now know that Carman can know that Karl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessica","Karl","Carman","Joshua"],"index":5592,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9840381145,"difficulty":0.0159618855}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Sonia can now know that Frank can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nichole","Marvin","Frank","Sonia"],"index":53758,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985200763,"difficulty":0.0014799237}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Freda can now know whether Noelle can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cindy","Andrew","Noelle","Freda"],"index":35025,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shaun's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Sidney can now know that Laura's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Tiffany","Shaun","Sidney"],"index":6522,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9784346819,"difficulty":0.0215653181}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Michael. Margaret's card is shown to Aaron. Aaron's card is shown to Aaron. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Charles can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Charles","Margaret","Aaron"],"index":47296,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997121692,"difficulty":0.0002878308}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rosanna","Robert","Justin"],"index":56865,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984999895,"difficulty":0.0015000105}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracie's card is shown to Tracie. Scott's card is shown to Roberto. Roberto's card is shown to Scott. Scott's card is shown to Scott. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Scott can now know whether Tracie can know whether Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracie","Roberto","Scott"],"index":58174,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982103109,"difficulty":0.0017896891}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julius's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Michael can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Penny","Michael","Julius"],"index":6596,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983872175,"difficulty":0.0016127825}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kasie knows whether Kasie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carmen can now know whether Kasie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kasie","Lisa","Tara","Carmen"],"index":20834,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996802807,"difficulty":0.0003197193}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence knows whether Judy's forehead is muddy. It is publicly announced that Florence knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Chad can now know that Ella can know that Florence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florence","Judy","Chad","Ella"],"index":2632,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978298545,"difficulty":0.0021701455}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Sharon. Sharon's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sharon can now know that John can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","John","James"],"index":28517,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983631968,"difficulty":0.0016368032}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Katherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Deborah can now know whether Deborah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Deborah","Katherine"],"index":67318,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990334511,"difficulty":0.0009665489}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Ronald. Ronald's card is shown to Brooke. Raymond's card is shown to Brooke. Cleo's card is shown to Cleo. Raymond's card is shown to Cleo. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know whether Brooke can know that Raymond picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Brooke","Cleo","Raymond"],"index":27580,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.886687696,"difficulty":1.886687696}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandi's card is shown to Carol. Karisa's card is shown to Carol. Carolyn's card is shown to Carol. Carolyn's card is shown to Brandi. Carol's card is shown to Karisa. Karisa's card is shown to Carolyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Brandi can know whether Karisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Brandi","Karisa","Carolyn"],"index":30254,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6032894254,"difficulty":0.3967105746}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Robert can now know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Katrina","Michael","John"],"index":961,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996460676,"difficulty":0.0003539324}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heather's card is shown to Heather. Elda's card is shown to Elda. Heather's card is shown to Allen. It is publicly announced that someone picked a red card. It is publicly announced that Heather picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Allen can now know that Elda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Heather","Elda","Allen","Mark"],"index":46395,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9514104724,"difficulty":0.0485895276}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether Amy is thirsty. It is publicly announced that Darryl knows whether or not everyone is thirsty. It is publicly announced that Darryl does not know whether Stephen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Amy can now know whether Darryl can know whether Darryl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amy","Stephen","Darryl"],"index":5899,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979624748,"difficulty":0.0020375252}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Corinne does not know whether Floyd is thirsty. It is publicly announced that Corinne knows whether someone is thirsty. It is publicly announced that Sandy does not know whether Floyd is thirsty. It is publicly announced that Floyd does not know whether Corinne is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Sandy can now know that Sandy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Corinne","Floyd","Sandy"],"index":19026,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.94811064,"difficulty":0.05188936}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilfred's card is shown to James. James's card is shown to James. Foster's card is shown to Stanley. Wilfred's card is shown to Foster. James's card is shown to Foster. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilfred can now know that Stanley can know that Wilfred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wilfred","James","Stanley","Foster"],"index":53679,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956464171,"difficulty":0.0043535829}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric does not know whether or not everyone's forehead is muddy. It is publicly announced that Becky knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Eric can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Fred","Becky"],"index":47147,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9946919084,"difficulty":0.0053080916}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise's forehead is muddy. It is publicly announced that Louise knows whether Johnny's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Johnny can now know whether Charles can know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louise","Johnny","Charles"],"index":15608,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6100612283,"difficulty":0.3899387717}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Desmond does not know whether Tammy is thirsty. It is publicly announced that Russell is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! (1|2|3) ] 0","hypothesis":"Desmond can now know whether Tammy can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Desmond","Russell","Tammy"],"index":48100,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know that Ora is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ora","Kenneth","Jennifer"],"index":31649,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984464049,"difficulty":0.0015535951}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Grover can now know whether Emily can know whether Grover's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Grover","Emily","Kathy"],"index":38357,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997009039,"difficulty":0.0002990961}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie does not know whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Eric can now know whether Kathy can know that Kathy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Willie","Eric","Kathy"],"index":36588,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7827678919,"difficulty":0.2172321081}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lavonda does not know whether Albert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lavonda can now know whether Albert can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lavonda","James","Albert","Arnold"],"index":42910,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997054935,"difficulty":0.0002945065}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danika's card is shown to Brandon. Danika's card is shown to Danika. Rogelio's card is shown to Allen. Brandon's card is shown to Rogelio. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rogelio can now know whether Brandon can know that Allen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandon","Danika","Allen","Rogelio"],"index":25385,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8469743133,"difficulty":0.1530256867}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annette's card is shown to Annette. Stephen's card is shown to Annette. Annette's card is shown to David. Susannah's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Annette does not know whether David picked a red card. It is publicly announced that David does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Susannah can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Annette","Susannah","David","Stephen"],"index":55879,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986067414,"difficulty":0.0013932586}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Jeremy. James's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether John picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Jeremy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeremy","James","John"],"index":15615,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984402061,"difficulty":0.0015597939}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Sharon. Sharon's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether Rosa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Sharon can now know whether Rosa can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosa","Sharon","Gary"],"index":17949,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5634890199,"difficulty":1.5634890199}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Renita's card is shown to Renita. Barbara's card is shown to Renita. Renita's card is shown to Barbara. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Barbara knows whether or not nobody picked a red card. It is publicly announced that Barbara picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 2 ] 0","hypothesis":"Renita can now know whether Barbara can know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Renita","Barbara"],"index":13874,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9965002537,"difficulty":0.0034997463}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruben's card is shown to Ruben. Sara's card is shown to Ruben. Don's card is shown to Don. Sara's card is shown to Don. Ruben's card is shown to Sara. Sara's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ruben can now know whether Don can know whether Don picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruben","Don","Sara"],"index":60051,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9949382544,"difficulty":0.0050617456}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wayne is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Wayne can now know whether Walter is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Wayne","Walter"],"index":44584,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9860659242,"difficulty":0.0139340758}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Sharon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Angela can now know whether Sharon can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Mary","Rosie","Angela"],"index":54082,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9903718233,"difficulty":0.0096281767}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Alton. Denny's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Maria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Maria can now know that Alton can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alton","Maria","Richard","Denny"],"index":18512,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary is thirsty. It is publicly announced that Josh knows whether Josh is thirsty. It is publicly announced that Gary does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kelly can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josh","Gary","Kelly","Natalie"],"index":23513,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether or not nobody's forehead is muddy. It is publicly announced that Alissa knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Douglas can now know whether Alissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Douglas","Alissa"],"index":53001,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997406602,"difficulty":0.0002593398}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darnell knows whether someone's forehead is muddy. It is publicly announced that Darnell knows whether Trudy's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Trudy can now know whether Darnell can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olga","Ralph","Trudy","Darnell"],"index":65289,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9941208959,"difficulty":0.0058791041}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Melissa. Leila's card is shown to Melissa. Leila's card is shown to Nicholas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Melissa can now know whether Melissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melissa","Nicholas","Leila"],"index":51395,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.671191752,"difficulty":0.328808248}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Marie. Alexandria's card is shown to Paul. Paul's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marie can now know that Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Anthony","Alexandria","Paul"],"index":21066,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979779124,"difficulty":0.0020220876}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Selena. Selena's card is shown to Nancy. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that Selena can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Selena","Nancy","Mary"],"index":4519,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999776423,"difficulty":0.000223577}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Henry can now know whether Phillip can know whether Phillip's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phillip","Henry","Matthew"],"index":41359,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996140599,"difficulty":0.0003859401}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Mark's card is shown to Louise. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Louise can now know whether Mark can know that Lester picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Louise","Lester"],"index":53052,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9833292961,"difficulty":0.0166707039}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Frank can now know whether Eva is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Frank","Ira","Eva"],"index":42283,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9665012956,"difficulty":0.0334987044}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. Miguel's card is shown to Curtis. Kay's card is shown to Curtis. Curtis's card is shown to Kay. Kay's card is shown to Kay. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Curtis can now know whether Miguel can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Curtis","Miguel","Kay"],"index":9198,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9916759729,"difficulty":0.0083240271}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julio knows whether Julio is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Garry can now know that Julio is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julio","Johanna","Garry"],"index":44806,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978340268,"difficulty":0.0021659732}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Derrick does not know whether or not everyone is thirsty. It is publicly announced that Joann is not thirsty. It is publicly announced that Joann knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Derrick can now know that Joann can know whether Joann is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Derrick","Joann"],"index":7354,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990573525,"difficulty":0.0009426475}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sherman knows whether or not nobody is thirsty. It is publicly announced that Joan does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Charles can now know whether Cecilia can know whether Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cecilia","Joan","Charles","Sherman"],"index":56668,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989443421,"difficulty":0.0010556579}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adriana's card is shown to Jacqueline. Julie's card is shown to Jacqueline. Julie's card is shown to Sandy. Jacqueline's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Jacqueline does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jacqueline can now know whether Jacqueline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adriana","Jacqueline","Sandy","Julie"],"index":63765,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9948164821,"difficulty":1.9948164821}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willis's card is shown to Linda. Kyle's card is shown to Linda. Willis's card is shown to Jason. Jason's card is shown to Jason. Jason's card is shown to Kyle. Kyle's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that Willis does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Willis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Willis","Jason","Kyle"],"index":8912,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9942212105,"difficulty":0.0057787895}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra does not know whether Debra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Debra can now know that Chester can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Chester","Debra","Elizabeth"],"index":5223,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984219074,"difficulty":0.0015780926}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Cynthia knows whether Cynthia's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Carma can now know whether Cynthia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucinda","Cynthia","Carma"],"index":6482,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995377064,"difficulty":0.0004622936}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Fred can now know whether Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Timothy","Fred"],"index":41664,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995841384,"difficulty":0.0004158616}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ralph does not know whether Kelli is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Ralph can now know that Milton is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Milton","Zulma","Kelli","Ralph"],"index":6162,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983397722,"difficulty":0.0016602278}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Naomi does not know whether or not everyone is thirsty. It is publicly announced that George is thirsty. It is publicly announced that George is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! 3 ] Agenta knows whether (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Matthew can now know whether George can know whether George is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Joann","George","Naomi"],"index":52701,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988040924,"difficulty":0.0011959076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steve does not know whether Helen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Robert can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Susan","Steve","Helen"],"index":36415,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997145534,"difficulty":0.0002854466}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Leona can now know that Ron's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ron","Leona","Robert","Laura"],"index":13535,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6635322571,"difficulty":0.3364677429}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kevin can now know that Helen can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Brad","Judith","Helen"],"index":57095,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997586608,"difficulty":0.0002413392}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angelia knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Mark can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Angelia","Leonard","Mark"],"index":6370,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981122017,"difficulty":0.0018877983}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth does not know whether or not everyone's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy. It is publicly announced that Elizabeth knows whether Denise's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Elizabeth can now know whether Denise can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elizabeth","Denise"],"index":66085,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994074106,"difficulty":0.0005925894}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paul can now know that Steven can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Paul","David","Mary"],"index":3028,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997672439,"difficulty":0.0002327561}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loriann knows whether Sharon's forehead is muddy. It is publicly announced that Greg does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Loriann can now know whether Greg can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Loriann","King","Sharon","Greg"],"index":21576,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997727275,"difficulty":0.0002272725}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Gregory knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Gregory can now know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gregory","William"],"index":22897,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8983597755,"difficulty":1.8983597755}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Edward can now know that Sharon can know that Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Phyllis","Sharon","Hannah","Edward"],"index":28979,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980577826,"difficulty":0.0019422174}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathryn's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Carlos can now know that Carlos's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathryn","Martha","Carlos"],"index":55719,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9905503988,"difficulty":0.0094496012}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Scott. Teresa's card is shown to Betty. James's card is shown to Teresa. Teresa's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Teresa can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Scott","Betty","Teresa","James"],"index":51211,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997215867,"difficulty":0.0002784133}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime's forehead is muddy. It is publicly announced that Jaime knows whether Christian's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Christian can now know that Jaime can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jaime","Christian","Martha"],"index":43435,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980717301,"difficulty":0.0019282699}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pedro knows whether someone is thirsty. It is publicly announced that Henry does not know whether Pedro is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Pedro can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Henry","Roberto","Pedro","Willie"],"index":59041,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983507395,"difficulty":0.0016492605}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theresa does not know whether Amanda is thirsty. It is publicly announced that Theresa does not know whether or not everyone is thirsty. It is publicly announced that Theresa does not know whether Amanda is thirsty. It is publicly announced that Amanda knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Theresa can now know that Amanda can know that Amanda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Theresa","Amanda"],"index":46815,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9384427071,"difficulty":1.9384427071}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edgar's card is shown to Edgar. Christine's card is shown to Edgar. Richard's card is shown to Richard. Richard's card is shown to James. Christine's card is shown to James. Christine's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Edgar does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know whether Richard can know that Edgar picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edgar","Richard","James","Christine"],"index":11823,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9356552958,"difficulty":0.0643447042}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether Kristen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kristen can now know whether Jane can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edwin","Kristen","Jane"],"index":22424,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997425675,"difficulty":0.0002574325}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diane does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Carmen can now know whether Robert can know whether Carmen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Carmen","Robert"],"index":61399,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9970455766,"difficulty":0.0029544234}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell does not know whether Darrell's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Darrell can now know whether Darrell's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Ray","Darrell"],"index":14373,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9719364047,"difficulty":0.0280635953}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia knows whether or not nobody's forehead is muddy. It is publicly announced that Virginia knows whether Virginia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Virginia can now know that Richard can know whether Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Virginia","Richard"],"index":20408,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995445609,"difficulty":0.0004554391}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Nolan can now know whether Lacy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cindy","Lacy","Nolan","David"],"index":53213,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997380376,"difficulty":0.0002619624}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Kenny can now know whether George can know that Jaime's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Kenny","George","Jaime"],"index":20629,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996629953,"difficulty":0.0003370047}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helene's card is shown to Helene. Michael's card is shown to Michael. Michael's card is shown to Amanda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helene","Tanya","Michael","Amanda"],"index":27864,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997214675,"difficulty":0.0002785325}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"William can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marvin","James","William","Stephen"],"index":52080,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9916040301,"difficulty":0.0083959699}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann knows whether Marvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Jean can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jean","Alexander","Ann","Marvin"],"index":6156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985073209,"difficulty":0.0014926791}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Brian's card is shown to Mary. Joseph's card is shown to Mary. Mary's card is shown to Tracy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know whether Mary can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Joseph","Mary","Tracy"],"index":67247,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995889068,"difficulty":0.0004110932}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know that Sylvia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sylvia","Rachel","Alton","James"],"index":32911,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980365634,"difficulty":0.0019634366}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joyce does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Joyce can now know whether Amanda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amanda","Brendan","Todd","Joyce"],"index":34189,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8644359112,"difficulty":0.1355640888}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danny's card is shown to Esther. Kathy's card is shown to Esther. Sadie's card is shown to Sadie. Kathy's card is shown to Sadie. Esther's card is shown to Danny. Sadie's card is shown to Kathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sadie can now know that Kathy can know whether Esther picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Esther","Sadie","Danny","Kathy"],"index":21872,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6756051183,"difficulty":0.3243948817}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Micheal. Jesse's card is shown to Robert. Jesse's card is shown to Jesse. It is publicly announced that someone picked a red card. It is publicly announced that Jesse does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Micheal can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Micheal","Robert","Jesse"],"index":17850,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978823066,"difficulty":0.0021176934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether or not everyone's forehead is muddy. It is publicly announced that Gary does not know whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Salvador can now know whether Salvador's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brett","Gary","Hazel","Salvador"],"index":43526,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7710533142,"difficulty":0.2289466858}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Terri can now know that David can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","John","Terri"],"index":15955,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984057546,"difficulty":0.0015942454}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pauline does not know whether Jerry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Pauline can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Jacqueline","Rebecca","Pauline"],"index":65627,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998229444,"difficulty":0.001770556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Almeda can now know whether Brendan can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dena","Brendan","Tammy","Almeda"],"index":48474,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997605681,"difficulty":0.0002394319}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Larry can now know whether Barbara can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Barbara","Karyn"],"index":19338,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald's forehead is not muddy. It is publicly announced that Loreta knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Vicky can now know that Ronald can know that Vicky's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Loreta","Michael","Ronald","Vicky"],"index":47187,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8956383467,"difficulty":0.1043616533}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glenn's card is shown to Glenn. Inga's card is shown to Glenn. Inga's card is shown to Mable. Inga's card is shown to Inga. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Inga can now know that Mable picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glenn","Mable","Inga"],"index":60112,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982631803,"difficulty":0.0017368197}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfred knows whether Joshua's forehead is muddy. It is publicly announced that Alfred knows whether Joshua's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Alfred can now know whether Denise can know whether Joshua's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfred","Joshua","Denise","Frances"],"index":1815,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997324347,"difficulty":0.0002675653}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jody's card is shown to Jody. William's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether Jody picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"William can now know whether Jody can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jody","William"],"index":52726,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9942147136,"difficulty":0.0057852864}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dora knows whether someone's forehead is muddy. It is publicly announced that Clarence knows whether or not nobody's forehead is muddy. It is publicly announced that Clarence knows whether Dora's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Clarence can now know that Joseph can know that Clarence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dora","Joseph","Clarence"],"index":43253,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970658422,"difficulty":0.0029341578}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ali's card is shown to Patricia. Ronnie's card is shown to Mary. Ali's card is shown to Mary. Ali's card is shown to Ronnie. Ronnie's card is shown to Ali. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Mary","Ronnie","Ali"],"index":30856,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985192418,"difficulty":0.0014807582}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Laura. Laura's card is shown to Jonathan. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan knows whether Jonathan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jonathan can now know that Laura picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Laura","Jonathan"],"index":64639,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99590379,"difficulty":0.00409621}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Victor is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Victor can now know that Victor is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sophie","Victor","Mark"],"index":6878,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7866265774,"difficulty":1.7866265774}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lula's card is shown to Elsy. Janet's card is shown to Elsy. Lula's card is shown to Lula. Harold's card is shown to Lula. Janet's card is shown to Harold. Harold's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Lula picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agenta knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Elsy can now know that Janet can know whether Elsy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elsy","Lula","Harold","Janet"],"index":61512,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9182085395,"difficulty":0.0817914605}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth is not thirsty. It is publicly announced that Virginia knows whether Elizabeth is thirsty. It is publicly announced that Elizabeth does not know whether Armando is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Lee can now know that Virginia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Lee","Armando","Elizabeth"],"index":20881,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9903641343,"difficulty":0.0096358657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Joe can now know whether Shirley can know whether Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","James","Joe","Shirley"],"index":66807,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9917603731,"difficulty":0.0082396269}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jess can now know whether Lisa can know that Lisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sheridan","Michael","Lisa","Jess"],"index":42878,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999574244,"difficulty":0.000425756}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. Paul's card is shown to Ruth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that Ruth can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Ruth","Dessie"],"index":28016,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997702241,"difficulty":0.0002297759}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Billy does not know whether Wayne is thirsty. It is publicly announced that Teresita does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Wayne can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wayne","Teresita","William","Billy"],"index":49874,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6793031693,"difficulty":0.3206968307}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Audra is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty. It is publicly announced that John does not know whether Michelle is thirsty. It is publicly announced that Audra does not know whether Michelle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"John can now know that Audra can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Patricia","Audra","John"],"index":11837,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Charles. Albert's card is shown to Albert. Albert's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether Charles can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Albert","Joseph"],"index":48837,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6459270716,"difficulty":1.6459270716}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brett's card is shown to Robin. Regina's card is shown to Robin. Robin's card is shown to Brett. Regina's card is shown to Brett. Regina's card is shown to Homer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robin can now know whether Regina can know whether Homer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Brett","Regina","Homer"],"index":40121,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985521436,"difficulty":0.0014478564}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mindy's card is shown to Mindy. William's card is shown to William. Eric's card is shown to William. Eric's card is shown to Eric. Mindy's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mindy","William","Eric","Robert"],"index":6163,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7314906716,"difficulty":1.7314906716}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to David. David's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether Michael picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Michael"],"index":45664,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952716231,"difficulty":0.0047283769}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to Ben. Andrew's card is shown to Ben. Cheryl's card is shown to Cheryl. Cheryl's card is shown to Jesus. Jesus's card is shown to Jesus. Andrew's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Jesus knows whether Jesus picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ben can now know that Jesus picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ben","Cheryl","Jesus","Andrew"],"index":47901,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9926233292,"difficulty":0.0073766708}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin does not know whether or not everyone's forehead is muddy. It is publicly announced that Beatrice knows whether or not nobody's forehead is muddy. It is publicly announced that Benjamin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Beatrice can now know whether Beatrice's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alyce","Benjamin","Beatrice"],"index":47982,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.517958045,"difficulty":0.482041955}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy does not know whether Tracy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Tracy can now know that Elsie can know whether Elsie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edith","Elsie","Dianna","Tracy"],"index":67283,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9763693213,"difficulty":0.0236306787}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristi's card is shown to Jackie. Gary's card is shown to Jackie. Jackie's card is shown to Kristi. Kristi's card is shown to Kristi. Gary's card is shown to Kristi. Jackie's card is shown to Gary. Raymond's card is shown to Gary. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Raymond does not know whether Gary picked a red card. It is publicly announced that Raymond does not know whether Kristi picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Gary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jackie","Kristi","Gary","Raymond"],"index":63897,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Pamela. Jefferson's card is shown to Pamela. Vito's card is shown to Pamela. Pamela's card is shown to Jefferson. Jefferson's card is shown to Jefferson. Jefferson's card is shown to Vito. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bruce can now know that Bruce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pamela","Bruce","Jefferson","Vito"],"index":37796,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974927902,"difficulty":0.0025072098}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanna's card is shown to Joanna. Donald's card is shown to Joanna. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether Joanna picked a red card. It is publicly announced that Donald does not know whether or not everyone picked a red card. It is publicly announced that Donald does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Donald can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joanna","Donald"],"index":34365,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Jose can now know whether Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Jose"],"index":65026,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6150773168,"difficulty":1.6150773168}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isabel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Isabel can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Glennis","Jane","Gretchen","Isabel"],"index":57604,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Irene can now know whether Bonnie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Irene","Bonnie","Terry","Cheryl"],"index":3947,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995725751,"difficulty":0.0004274249}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Isreal can now know whether Glenda can know whether Glenda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Isreal","Sergio","Glenda","Amanda"],"index":58050,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9894531965,"difficulty":0.0105468035}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Warren knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Warren can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Warren","Charles","Robert"],"index":36547,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994627833,"difficulty":0.0005372167}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delilah's card is shown to Carole. Carole's card is shown to Delilah. Richard's card is shown to Delilah. Howard's card is shown to Howard. Richard's card is shown to Howard. Carole's card is shown to Richard. Howard's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Howard can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carole","Delilah","Howard","Richard"],"index":45967,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9859653711,"difficulty":0.0140346289}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Debra can now know that Kevin can know whether Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Debra"],"index":55259,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989058971,"difficulty":0.0010941029}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Elizebeth knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Boris can now know that Kevin can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Boris","Elizebeth","William"],"index":24370,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984815717,"difficulty":0.0015184283}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Norma can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Wendy","Elizabeth","Norma"],"index":10162,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983556867,"difficulty":0.0016443133}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa does not know whether Teresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Teresa can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sherri","Teresa","Kevin"],"index":3712,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997556806,"difficulty":0.0002443194}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kent can now know whether Kent's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kent","Suzanne","Walter","Sara"],"index":18719,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994738698,"difficulty":0.0005261302}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria is thirsty. It is publicly announced that Maria knows whether Maria is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Orlando can now know that Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Maria","Orlando"],"index":11946,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9679675102,"difficulty":0.0320324898}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Vincent. It is publicly announced that someone picked a red card. It is publicly announced that Vincent picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Vincent can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vincent","John"],"index":14106,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6373462081,"difficulty":1.6373462081}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby knows whether Charles's forehead is muddy. It is publicly announced that Bobby does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Charles can now know whether Bobby can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bobby","Charles"],"index":22008,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997809529,"difficulty":0.0002190471}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Carlos can now know that Robert can know that Carlos's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Anna","Roberto","Carlos"],"index":21651,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9964046478,"difficulty":0.0035953522}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lowell's card is shown to Anna. Anna's card is shown to Lowell. Joseph's card is shown to Lowell. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Anna picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Lowell can now know whether Joseph can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anna","Lowell","Joseph"],"index":12755,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9960091114,"difficulty":0.0039908886}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew knows whether Andrew is thirsty. It is publicly announced that Andrew is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Andrew can now know that Clifford is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clifford","Eric","Andrew"],"index":6179,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9854202867,"difficulty":0.0145797133}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Amy's card is shown to Robert. Amy's card is shown to Alfonso. Robert's card is shown to Donovan. It is publicly announced that someone picked a red card. It is publicly announced that Alfonso does not know whether Alfonso picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Donovan can now know whether Amy can know whether Amy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amy","Robert","Alfonso","Donovan"],"index":49847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9947675467,"difficulty":0.0052324533}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eddie knows whether or not everyone's forehead is muddy. It is publicly announced that Eddie knows whether someone's forehead is muddy. It is publicly announced that Eddie knows whether Eddie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Eddie can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Eddie","Rebecca"],"index":7647,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997778535,"difficulty":0.0002221465}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"James can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Natasha","James","Linda"],"index":60100,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998678863,"difficulty":0.001321137}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chanda's card is shown to Robert. Jose's card is shown to Karl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Karl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Jose","Karl","Chanda"],"index":2050,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985132813,"difficulty":0.0014867187}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Timothy can now know that Trinidad can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Jaime","Trinidad","Timothy"],"index":34015,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louis's card is shown to Clara. John's card is shown to Clara. Cory's card is shown to Cory. Clara's card is shown to John. Louis's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Cory picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Cory can now know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clara","Cory","Louis","John"],"index":55492,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7247586846,"difficulty":1.7247586846}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Pamela. Pamela's card is shown to Christopher. Irma's card is shown to Christopher. Christopher's card is shown to Irma. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card. It is publicly announced that Irma does not know whether Pamela picked a red card. It is publicly announced that Pamela does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Irma can now know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pamela","Christopher","Irma"],"index":36808,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6103951335,"difficulty":0.3896048665}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy. It is publicly announced that Jennifer knows whether Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Barbara can now know that Martha can know whether Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martha","Barbara","Jennifer"],"index":6170,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997416139,"difficulty":0.0002583861}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Elizabeth can now know whether Robert can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Jose","Robert","John"],"index":41960,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9928556681,"difficulty":0.0071443319}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Percy. Ola's card is shown to Carl. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Carl can now know that Carl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Percy","Carl","Charles","Ola"],"index":8743,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8625539541,"difficulty":0.1374460459}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann does not know whether Lisa is thirsty. It is publicly announced that Ann does not know whether or not everyone is thirsty. It is publicly announced that Chung knows whether Ann is thirsty. It is publicly announced that Lisa does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ann can now know whether Chung can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chung","Ann","Lisa"],"index":41761,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996843338,"difficulty":0.0003156662}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tomasa does not know whether Tomasa's forehead is muddy. It is publicly announced that Helen does not know whether Helen's forehead is muddy. It is publicly announced that Tomasa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Stella can now know whether Helen can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Roger","Tomasa","Stella"],"index":50075,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9962332845,"difficulty":0.0037667155}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alfonzo can now know that Edward can know whether Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alfonzo","Jayne","Edward"],"index":51165,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9941611886,"difficulty":0.0058388114}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Jean can now know that Joshua can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jean","James","Joshua"],"index":34430,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940367937,"difficulty":0.0059632063}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether Maria's forehead is muddy. It is publicly announced that Matthew knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jerry can now know that Maria can know whether Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Jerry","Matthew"],"index":41012,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994244576,"difficulty":0.0005755424}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Colin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Sherry can now know whether Sherry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tina","Colin","Sherry","Jessica"],"index":30371,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9983647466,"difficulty":0.0016352534}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mac knows whether Mac's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Beverly can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mac","Melissa","Michael","Beverly"],"index":56275,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983079433,"difficulty":0.0016920567}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Billy can now know that Joseph can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Billy","Judy","Rose"],"index":66314,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984223843,"difficulty":0.0015776157}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maxine's card is shown to Lacy. Lacy's card is shown to Wilma. Maxine's card is shown to Paula. It is publicly announced that someone picked a red card. It is publicly announced that Lacy picked a red card. It is publicly announced that Lacy does not know whether Wilma picked a red card. It is publicly announced that Wilma does not know whether Paula picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Wilma can now know whether Lacy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maxine","Lacy","Wilma","Paula"],"index":50410,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Tyler knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Wilma can now know whether Tyler can know whether Wilma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tyler","Wilma"],"index":54070,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989187717,"difficulty":0.0010812283}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Jose is thirsty. It is publicly announced that Carrie does not know whether Jose is thirsty. It is publicly announced that Carrie does not know whether Jose is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Carrie can now know whether Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Jose","Carrie"],"index":9064,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9477061033,"difficulty":0.0522938967}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Greg does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know that Thomas can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Crystal","John","Thomas","Greg"],"index":20945,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997184873,"difficulty":0.0002815127}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachel's card is shown to Kendall. Rachel's card is shown to Rachel. Robert's card is shown to Rachel. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Rachel can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kendall","Rachel","Robert"],"index":30087,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985773563,"difficulty":0.0014226437}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tina's card is shown to Carlene. Scott's card is shown to Scott. Tina's card is shown to Scott. Scott's card is shown to Tina. Tina's card is shown to Tina. It is publicly announced that someone picked a red card. It is publicly announced that Tina picked a red card. It is publicly announced that Tina does not know whether Carlene picked a red card. It is publicly announced that Tina knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Tina can now know that Scott picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carlene","Scott","Tina"],"index":59279,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.573720634,"difficulty":0.426279366}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lucinda can now know whether James can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Lucinda","Michelle","William"],"index":51179,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994778037,"difficulty":0.0005221963}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynette's card is shown to Alma. Christopher's card is shown to Alma. Alma's card is shown to Lynette. Alma's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Lynette picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Christopher can now know whether Lynette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alma","Lynette","Christopher"],"index":13352,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8028267026,"difficulty":0.1971732974}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yvonne's card is shown to Michael. Michael's card is shown to Yvonne. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Nellie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Yvonne can now know that Michael can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Yvonne","Elizabeth","Nellie"],"index":15433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982084036,"difficulty":0.0017915964}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pei knows whether Pei's forehead is muddy. It is publicly announced that Billy knows whether or not everyone's forehead is muddy. It is publicly announced that Dalila knows whether Pei's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Dalila can now know whether Billy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Billy","Pei","Dalila","Miles"],"index":62253,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997004271,"difficulty":0.0002995729}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jane does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jane can now know whether Carol can know that Jane is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jane","Anthony","Carol","William"],"index":66434,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9957143664,"difficulty":0.0042856336}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Andrew can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debra","Thomas","Andrew"],"index":53511,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981404543,"difficulty":0.0018595457}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl does not know whether Christopher is thirsty. It is publicly announced that Carl is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(3) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Erin can now know whether Olivia can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olivia","Erin","Carl","Christopher"],"index":29702,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Christopher's forehead is muddy. It is publicly announced that Christopher does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Patricia can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","John","Christopher"],"index":34329,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Peter does not know whether Andres is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"James can now know that Andres can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Andres","Peter"],"index":63030,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984824061,"difficulty":0.0015175939}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Mary can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Mary","Walter","Lisa"],"index":15309,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994952679,"difficulty":0.0005047321}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Nathaniel knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Alta can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alta","Rachel","Nathaniel","James"],"index":9525,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997842908,"difficulty":0.0002157092}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth knows whether or not everyone is thirsty. It is publicly announced that Miranda knows whether Miranda is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Miranda can now know that Ruth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Miranda","Ruth"],"index":4334,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9688842893,"difficulty":0.0311157107}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Wayne is thirsty. It is publicly announced that John does not know whether Amanda is thirsty. It is publicly announced that Wayne is thirsty. It is publicly announced that Amanda does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"John can now know that Wayne can know that Wayne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wayne","Amanda","John"],"index":11083,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8524258733,"difficulty":0.1475741267}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Greg's card is shown to Greg. Shirley's card is shown to Greg. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Greg can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Greg","Shirley"],"index":67684,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997208714,"difficulty":0.0002791286}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Bradley can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bradley","William","Robert","Laura"],"index":9948,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984104633,"difficulty":0.0015895367}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Alease can now know that Ashley can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alease","Luke","Ashley","Tina"],"index":67098,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984952211,"difficulty":0.0015047789}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Albert can now know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Veronica","David","Albert","Eric"],"index":48543,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984881878,"difficulty":0.0015118122}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rick does not know whether Rick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Rick can now know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Betty","Rick","David","Veronica"],"index":33784,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994320273,"difficulty":0.0005679727}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Shawnda is thirsty. It is publicly announced that Shawnda does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"William can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Shawnda","William"],"index":26424,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986150265,"difficulty":0.0013849735}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jacqueline can now know that Kenneth can know that Jacqueline's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Jacqueline","Kenneth"],"index":53900,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974368215,"difficulty":0.0025631785}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rena's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Richard can now know that Rena can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Torri","Rena","Richard","Velma"],"index":52210,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998431623,"difficulty":0.001568377}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Brian can now know that William can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Brian","William"],"index":49746,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983379841,"difficulty":0.0016620159}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Curtis's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Curtis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janet","David","Susan","Curtis"],"index":56979,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984153509,"difficulty":0.0015846491}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Sara. Dianna's card is shown to Dianna. Sulema's card is shown to Bonnie. Bonnie's card is shown to Bonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dianna can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sulema","Sara","Dianna","Bonnie"],"index":67651,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abraham's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Shirley can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Abraham","Shirley"],"index":48754,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998385787,"difficulty":0.001614213}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina does not know whether or not everyone's forehead is muddy. It is publicly announced that Christina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Mary can now know that Nellie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jane","Mary","Christina","Nellie"],"index":5602,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6235466599,"difficulty":0.3764533401}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billy does not know whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mary can now know that Jose can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Mary","Billy"],"index":1593,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979617596,"difficulty":0.0020382404}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ethel does not know whether or not everyone is thirsty. It is publicly announced that Ethel knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Melba can now know that Ethel can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melba","Ethel"],"index":56344,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997819066,"difficulty":0.0002180934}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Carl is thirsty. It is publicly announced that Carl does not know whether or not everyone is thirsty. It is publicly announced that Carl does not know whether Marcus is thirsty. It is publicly announced that Carl does not know whether Marcus is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Carl can now know whether Marcus can know that Marcus is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Carl","Marcus"],"index":3869,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9532093406,"difficulty":1.9532093406}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kirk does not know whether or not everyone's forehead is muddy. It is publicly announced that Frances's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Kirk can now know whether Frances's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kirk","Frances"],"index":6757,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994694591,"difficulty":0.0005305409}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Grace does not know whether Karl is thirsty. It is publicly announced that Grace does not know whether Karl is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Grace can now know whether Karl is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Karl","Grace"],"index":66057,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9390120506,"difficulty":0.0609879494}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether Gary's forehead is muddy. It is publicly announced that Norman's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] 0","hypothesis":"Kathleen can now know whether Gary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathleen","Albert","Norman","Gary"],"index":34124,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995673299,"difficulty":0.0004326701}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether Davis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Frank can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marjorie","Frank","Davis","Dorothy"],"index":7191,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982551932,"difficulty":0.0017448068}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Nathaniel can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Nancy","Nathaniel"],"index":66851,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982106686,"difficulty":0.0017893314}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Dacia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"David can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dacia","David","Grace","Karen"],"index":39506,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996046424,"difficulty":0.0003953576}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Patrick. Michael's card is shown to Patrick. Patrick's card is shown to Suzanne. Suzanne's card is shown to Suzanne. Patrick's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Suzanne","Michael"],"index":58458,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997273088,"difficulty":0.0002726912}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria does not know whether Victoria's forehead is muddy. It is publicly announced that Donn does not know whether Donn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Donn can now know that Victoria can know whether Victoria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Victoria","Carolyn","Donn"],"index":37876,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8306791782,"difficulty":0.1693208218}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Dan can now know whether Marina can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","Dan","Roy","Marina"],"index":15294,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973166585,"difficulty":0.0026833415}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether Jeffrey picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jeffrey can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jeffrey","Larry"],"index":22080,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9064131379,"difficulty":0.0935868621}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gail does not know whether Gail's forehead is muddy. It is publicly announced that Gail does not know whether Gail's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ronald can now know that Gail can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ronald","Gail"],"index":10445,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982497096,"difficulty":0.0017502904}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Frank","Patricia","Chris"],"index":61651,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997695088,"difficulty":0.0002304912}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiffany knows whether Terry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Max can now know that Max's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Max","Herbert","Tiffany","Terry"],"index":11730,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998016715,"difficulty":0.001983285}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Derrick does not know whether or not everyone is thirsty. It is publicly announced that Derrick does not know whether Angela is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Angela can now know that Roberta can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Derrick","Angela","Roberta"],"index":63298,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9933828115,"difficulty":0.0066171885}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Charles can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Robert"],"index":35471,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9971691966,"difficulty":0.0028308034}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Patricia can now know that Carolyn can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Alan","Carolyn"],"index":67537,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983139038,"difficulty":0.0016860962}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl does not know whether Cheryl's forehead is muddy. It is publicly announced that Cheryl does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Cheryl can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sue","Maria","Cheryl"],"index":6528,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pearl knows whether Joshua's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Joshua can now know that Daisy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Pearl","Joshua","Daisy"],"index":14819,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984431863,"difficulty":0.0015568137}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catherine knows whether or not nobody is thirsty. It is publicly announced that Catherine does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Catherine can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Catherine","Linda","Derrick"],"index":8672,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981848598,"difficulty":0.0018151402}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Kimberly is thirsty. It is publicly announced that Kimberly does not know whether Burton is thirsty. It is publicly announced that Maria does not know whether Kimberly is thirsty. It is publicly announced that Maria does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentb knows whether (Agentd knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Kimberly can now know whether Maria can know that Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Kimberly","Burton","Maria"],"index":61613,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9871539474,"difficulty":1.9871539474}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Veronica knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Ernestina can now know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ernestina","Scott","Veronica"],"index":7610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978990555,"difficulty":0.0021009445}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barry does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Barry can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marc","Geraldine","Barry"],"index":67255,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962879419,"difficulty":0.0037120581}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Margaret's card is shown to Joan. Jason's card is shown to Jason. Jason's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether Joan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Margaret can now know that Joan can know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joan","Jason","Margaret"],"index":37704,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9393963218,"difficulty":1.9393963218}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Ada can now know that Mary can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Ada"],"index":7047,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8723322749,"difficulty":1.8723322749}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dixie's card is shown to Mark. Randall's card is shown to Mark. Randall's card is shown to Randall. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dixie can now know whether Mark can know that Randall picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dixie","Mark","Randall"],"index":16668,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9383004904,"difficulty":0.0616995096}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry knows whether Harry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Larry can now know that Jane's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harry","Jane","Catherine","Larry"],"index":46115,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983648658,"difficulty":0.0016351342}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Connie can now know that Maria can know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lee","Connie","Maria","Tameka"],"index":55538,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7322764993,"difficulty":0.2677235007}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renata's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Derek can now know that Renata can know that Derek's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lloyd","Renata","Derek","Austin"],"index":20084,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9743518233,"difficulty":0.0256481767}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Diane. Joseph's card is shown to Ruth. Richard's card is shown to Ruth. Diane's card is shown to Joseph. Ruth's card is shown to Joseph. Ruth's card is shown to Richard. Joseph's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Diane can now know whether Ruth can know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Diane","Ruth","Joseph","Richard"],"index":18576,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8817247152,"difficulty":0.1182752848}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jewel's card is shown to Beverly. Don's card is shown to Don. Beverly's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Don picked a red card. It is publicly announced that Jewel knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Jewel can now know whether Beverly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jewel","Beverly","Don","Mary"],"index":49646,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6442716122,"difficulty":1.6442716122}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan's forehead is muddy. It is publicly announced that James knows whether Dorothea's forehead is muddy. It is publicly announced that Jacqueline knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Susan can now know whether Jacqueline can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Jacqueline","James","Dorothea"],"index":59044,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996722937,"difficulty":0.0003277063}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Erin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Dionne can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cathy","Erin","Dionne","Brian"],"index":20159,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997679591,"difficulty":0.0002320409}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Dorris's card is shown to Angela. Darryl's card is shown to Dorris. Darryl's card is shown to Darryl. Darryl's card is shown to Violet. It is publicly announced that someone picked a red card. It is publicly announced that Darryl picked a red card. It is publicly announced that Angela picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(1) ] 0","hypothesis":"Angela can now know that Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Dorris","Darryl","Violet"],"index":50142,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5390664339,"difficulty":0.4609335661}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Darren can now know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Darren","Patricia","Kellie","Kelli"],"index":49996,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.998077631,"difficulty":0.001922369}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Della knows whether Della's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Charles can now know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Della","Charles","Dolores","Gloria"],"index":61113,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998270154,"difficulty":0.001729846}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin knows whether Rosalie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ronnie can now know that Justin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Justin","Rosalie","Ronnie"],"index":67267,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983382225,"difficulty":0.0016617775}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leola knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Nancy can now know whether Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leola","Nancy","Daniel","Arnoldo"],"index":30083,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9988601208,"difficulty":0.0011398792}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terrie can now know that Sherry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jill","Micah","Sherry","Terrie"],"index":42252,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986351132,"difficulty":0.0013648868}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances's forehead is muddy. It is publicly announced that Frances's forehead is muddy. It is publicly announced that Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agentc knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Laila can now know whether Paola can know whether Frances's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","Paola","Laila","Sally"],"index":13187,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993931055,"difficulty":0.0006068945}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Kim's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Christopher can now know whether Kim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Susan","Christopher","Edwin","Kim"],"index":20473,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997543693,"difficulty":0.0002456307}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aaron's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Dudley can now know whether Aaron can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dudley","Aaron"],"index":53198,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995525479,"difficulty":0.0004474521}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Tonya. Tonya's card is shown to Glen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Tonya can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tonya","Mary","Jonathan","Glen"],"index":65934,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9447656274,"difficulty":0.0552343726}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Robert's forehead is muddy. It is publicly announced that Madelyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Joseph can now know whether Thomas can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Madelyn","Joseph","Robert","Thomas"],"index":35093,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995978475,"difficulty":0.0004021525}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Margaret can now know that Nadine can know whether Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Nadine","Bessie","Margaret"],"index":51082,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990651011,"difficulty":0.0009348989}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Brandon can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Roger","James","Brandon"],"index":53257,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997377992,"difficulty":0.0002622008}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Gregorio can now know that Jarrett's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danilo","Jarrett","Gregorio","Paul"],"index":32408,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984369874,"difficulty":0.0015630126}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pearl knows whether Ed's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ralph can now know that Ralph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pearl","Ed","Ralph"],"index":18580,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980154037,"difficulty":0.0019845963}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"John can now know whether Roy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Roy","John"],"index":56348,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997498393,"difficulty":0.0002501607}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alma knows whether William's forehead is muddy. It is publicly announced that Alma knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"William can now know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Betty","David","William","Alma"],"index":48883,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994443059,"difficulty":0.0005556941}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Karen is thirsty. It is publicly announced that Tyson is thirsty. It is publicly announced that Karen is thirsty. It is publicly announced that Tyson is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 1 ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 1 ] 0","hypothesis":"Karen can now know that Tyson can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tyson","Karen","William"],"index":30292,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997168183,"difficulty":0.0002831817}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rick's card is shown to Tyrone. Lydia's card is shown to Tyrone. Tyrone's card is shown to Leon. Lydia's card is shown to Leon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tyrone can now know that Rick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tyrone","Rick","Lydia","Leon"],"index":30724,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982333183,"difficulty":0.0017666817}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Tom can now know whether Mary can know whether Tom's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Serena","Janet","Mary","Tom"],"index":59954,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9961355925,"difficulty":0.0038644075}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Dennis can now know that James can know that Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Dennis","Terry"],"index":38872,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9704900384,"difficulty":0.0295099616}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Dorinda can now know whether Clara can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorinda","Clara","John"],"index":18822,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernardo does not know whether Timothy is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Timothy can now know whether Clarice can know that Bernardo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bernardo","Timothy","Clarice"],"index":26893,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9963035583,"difficulty":0.0036964417}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diana does not know whether Alyssa is thirsty. It is publicly announced that Alyssa does not know whether Alice is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Geoffrey can now know that Diana can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alyssa","Geoffrey","Diana","Alice"],"index":21112,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997816682,"difficulty":0.0002183318}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jasmine does not know whether or not everyone is thirsty. It is publicly announced that Jeremy does not know whether Virginia is thirsty. It is publicly announced that Jeremy does not know whether Virginia is thirsty. It is publicly announced that Jeremy does not know whether Peter is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Virginia can now know that Jasmine can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Jeremy","Jasmine","Virginia"],"index":25662,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999779284,"difficulty":0.000220716}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Regina. Janice's card is shown to Janice. Harvey's card is shown to Janice. Elizabeth's card is shown to Harvey. Janice's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Regina","Janice","Harvey","Elizabeth"],"index":19051,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997714162,"difficulty":0.0002285838}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna does not know whether Jeannine is thirsty. It is publicly announced that Donna does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] Agentd knows that (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Robert can now know that Michael can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Jeannine","Donna","Robert"],"index":54341,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9934678674,"difficulty":0.0065321326}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandy's card is shown to Sandy. Curtis's card is shown to Lauren. It is publicly announced that someone picked a red card. It is publicly announced that Sandy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Curtis can now know that Sandy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Curtis","Sandy","Lauren"],"index":14704,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6633756757,"difficulty":0.3366243243}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Michael's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Paul does not know whether Paul picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Paul"],"index":9464,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Vicki can now know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jack","Richard","Larry","Vicki"],"index":8117,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994646907,"difficulty":0.0005353093}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy. It is publicly announced that Joey's forehead is muddy. It is publicly announced that Leonard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Billy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joey","Leonard","Billy","Sharon"],"index":31458,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981694221,"difficulty":0.0018305779}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erika's card is shown to Erika. Bessie's card is shown to Erika. Erika's card is shown to Michael. Michael's card is shown to Michael. Thomas's card is shown to Thomas. Bessie's card is shown to Thomas. Erika's card is shown to Bessie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Erika can now know that Michael can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Erika","Michael","Thomas","Bessie"],"index":3255,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997158647,"difficulty":0.0002841353}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Gertrude can now know that Timothy can know whether Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gertrude","Timothy"],"index":30488,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996927977,"difficulty":0.0003072023}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Judy can now know that Dewayne can know that Mildred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Dewayne","Arthur","Judy"],"index":36874,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998534441,"difficulty":0.001465559}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Regina knows whether Kim's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Regina can now know that Kim can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Regina","Kim"],"index":15819,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Stella can now know that Donna can know that Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stella","Todd","Donna"],"index":57816,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962946773,"difficulty":0.0037053227}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Glenn can now know that Lessie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diane","Glenn","Derek","Lessie"],"index":33368,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983423948,"difficulty":0.0016576052}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmie's card is shown to Jimmie. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Larry can now know whether Jimmie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jimmie","Larry"],"index":9169,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Joan picked a red card. It is publicly announced that Joan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] 0","hypothesis":"Joan can now know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joan","Barbara"],"index":49794,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6317077875,"difficulty":1.6317077875}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Audrey's card is shown to Audrey. Charlotte's card is shown to Howard. Earl's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Charlotte does not know whether or not everyone picked a red card. It is publicly announced that Earl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Audrey can now know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Audrey","Charlotte","Howard","Earl"],"index":9930,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6028549075,"difficulty":1.6028549075}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Charles can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Stephanie","Margaret","Mattie"],"index":29108,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Ronald. Anthony's card is shown to Ronald. Ronald's card is shown to Judith. Anthony's card is shown to Judith. Ronald's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Judith can now know that Anthony can know whether Judith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Judith","Anthony"],"index":51751,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8505958915,"difficulty":1.8505958915}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Courtney is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Mary can now know that Courtney can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Mary","Daniel","Courtney"],"index":39718,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9852542281,"difficulty":0.0147457719}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Robert's card is shown to Elaine. It is publicly announced that someone picked a red card. It is publicly announced that Elaine does not know whether Elaine picked a red card. It is publicly announced that Elaine knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Elaine can now know that Robert can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Elaine"],"index":15844,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8872141242,"difficulty":0.1127858758}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Jessie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Linda can now know that Charles can know whether Linda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Charles","Jessie"],"index":31811,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9485546947,"difficulty":0.0514453053}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Steven can now know whether Daniel can know whether Glenn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Glenn","Steven","Daniel"],"index":59989,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997174144,"difficulty":0.0002825856}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen does not know whether Jerry is thirsty. It is publicly announced that Helen does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Thomas can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Thomas","Jerry"],"index":47759,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961076379,"difficulty":0.0038923621}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. Cecil's card is shown to Therese. Daniel's card is shown to Cecil. It is publicly announced that someone picked a red card. It is publicly announced that Daniel does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Therese can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daniel","Therese","Cecil","Elizabeth"],"index":24613,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7979804873,"difficulty":0.2020195127}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenny's card is shown to Anna. Kenny's card is shown to Kenny. It is publicly announced that someone picked a red card. It is publicly announced that Anna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Kenny can now know whether Anna can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anna","Kenny"],"index":9344,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9750316739,"difficulty":0.0249683261}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Steven's card is shown to Steven. Joan's card is shown to Neal. Steven's card is shown to Neal. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know that Joan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joan","Steven","Neal"],"index":36445,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980011582,"difficulty":0.0019988418}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan does not know whether Anna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Claudia can now know whether Paul can know whether Anna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anna","Claudia","Susan","Paul"],"index":8235,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991568327,"difficulty":0.0008431673}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda knows whether someone is thirsty. It is publicly announced that Nicole is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Marc can now know that Linda can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marc","Linda","Nicole"],"index":58068,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984366298,"difficulty":0.0015633702}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Tina can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathleen","Michael","Tina","Alice"],"index":29964,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995235205,"difficulty":0.0004764795}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Larry can now know whether Larry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Larry","Jason"],"index":51248,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989174604,"difficulty":0.0010825396}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"William can now know that Betty can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Betty"],"index":30260,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997300506,"difficulty":0.0002699494}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Hipolito can now know that Estelle can know whether Claire is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hipolito","Estelle","Claire","Janice"],"index":67612,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975245595,"difficulty":0.0024754405}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Abigail's card is shown to Abigail. Julie's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Julie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Abigail can now know whether Julie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Abigail","Julie"],"index":29766,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leonard is not thirsty. It is publicly announced that Leonard does not know whether Haywood is thirsty. It is publicly announced that Dennis does not know whether Cody is thirsty. It is publicly announced that Dennis does not know whether Cody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Haywood can now know whether Cody can know whether Leonard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dennis","Haywood","Leonard","Cody"],"index":55535,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982494712,"difficulty":0.0017505288}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"James can now know whether Helen can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Betty","Robt","James"],"index":12382,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999722898,"difficulty":0.000277102}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Blanca can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Blanca","Michael"],"index":33393,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997602105,"difficulty":0.0002397895}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Winnifred's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Marion can now know whether Winnifred can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marion","Winnifred"],"index":66435,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adam knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Adam can now know that Shawn can know whether Adam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adam","Shawn","Alma"],"index":20844,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997060895,"difficulty":0.0002939105}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Laura. Patricia's card is shown to Stanley. Jamie's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Patricia can now know that Laura picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Stanley","Patricia","Jamie"],"index":9806,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958945513,"difficulty":0.0041054487}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jill's card is shown to Mark. Mark's card is shown to Jill. Virginia's card is shown to Virginia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Virginia can now know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Jill","Virginia"],"index":251,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977655411,"difficulty":0.0022344589}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie does not know whether Julie's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether Steven's forehead is muddy. It is publicly announced that Julie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Steven can now know whether Damon can know that Damon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julie","Damon","Steven"],"index":2704,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8739795685,"difficulty":0.1260204315}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Kevin can now know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Kevin","Patricia"],"index":44323,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997329116,"difficulty":0.0002670884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl's forehead is not muddy. It is publicly announced that Elizabeth's forehead is muddy. It is publicly announced that Carl knows whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carl can now know whether Elizabeth can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carl","Elizabeth","David"],"index":23029,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ryan does not know whether Roxanna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Nicholas can now know that Roxanna can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ryan","Isabel","Roxanna","Nicholas"],"index":65044,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997028708,"difficulty":0.0002971292}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alfred does not know whether Mary is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"Alfred can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Crystal","Alfred","John"],"index":54194,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982320666,"difficulty":0.0017679334}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herbert knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kristy can now know that Kristy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Herbert","Gary","Kristy","Anthony"],"index":17049,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9972786307,"difficulty":0.0027213693}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ashley can now know that Christina can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christina","Ashley","Kenneth"],"index":44195,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997562766,"difficulty":0.0002437234}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. Shelby's card is shown to Carol. Robert's card is shown to Carol. Gregory's card is shown to Shelby. Shelby's card is shown to Shelby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Carol can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Carol","Shelby","Robert"],"index":64437,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997753501,"difficulty":0.0002246499}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Wesley can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Karen","Wesley","Homer"],"index":59849,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983116388,"difficulty":0.0016883612}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marie does not know whether Margaret is thirsty. It is publicly announced that Roger does not know whether Marie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Roger can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Marie","Roger"],"index":67169,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985974431,"difficulty":0.0014025569}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonell's card is shown to Jonell. Jennifer's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Jonell picked a red card. It is publicly announced that Jonell knows whether or not nobody picked a red card. It is publicly announced that Jonell does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jennifer can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonell","Jennifer","Lawrence"],"index":53240,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason does not know whether Teresa is thirsty. It is publicly announced that Jason does not know whether Rachael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Jason can now know whether Teresa can know that Rachael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Teresa","Michael","Rachael"],"index":22320,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9842979312,"difficulty":0.0157020688}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to David. Jane's card is shown to Robert. David's card is shown to Jane. Jane's card is shown to Jane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jane can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Robert","Jane"],"index":64378,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997702241,"difficulty":0.0002297759}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sophie can now know that Victor can know that Sophie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victor","Michelle","Kimberly","Sophie"],"index":3327,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982745647,"difficulty":0.0017254353}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mona knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Erin can now know that Erin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erin","Mona"],"index":58189,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970695376,"difficulty":0.0029304624}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Katherine. Katherine's card is shown to Judy. Edna's card is shown to Judy. Katherine's card is shown to Edna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Edna can now know that Katherine can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katherine","Judy","Edna"],"index":66836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997153878,"difficulty":0.0002846122}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tyler does not know whether or not everyone is thirsty. It is publicly announced that Fritz does not know whether or not everyone is thirsty. It is publicly announced that Carl knows whether Carl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Carl can now know that Alvin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alvin","Carl","Fritz","Tyler"],"index":6026,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.818841517,"difficulty":0.181158483}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Mae is thirsty. It is publicly announced that Mae does not know whether Janel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Janel can now know whether Mae can know that Janel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mae","George","Sharon","Janel"],"index":27883,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9748402834,"difficulty":0.0251597166}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yvonne does not know whether Darin is thirsty. It is publicly announced that Li does not know whether Yvonne is thirsty. It is publicly announced that Yvonne does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Li","Yvonne","Darin","Gregory"],"index":35302,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997317195,"difficulty":0.0002682805}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether someone's forehead is muddy. It is publicly announced that Jason knows whether Lillian's forehead is muddy. It is publicly announced that Lillian's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] Agentc knows whether (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"Jason can now know whether Lillian can know whether Jason's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lillian","Daniel","Jason"],"index":26124,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9973570108,"difficulty":0.0026429892}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Sachiko is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Sachiko can now know that Sachiko is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sachiko","Debora"],"index":41705,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5563985109,"difficulty":1.5563985109}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"James can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daniel","Jack","James"],"index":7125,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9983025789,"difficulty":0.0016974211}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Donna can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Brian","David","Mary"],"index":42420,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9819245338,"difficulty":0.0180754662}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Keisha knows whether Keisha is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Keisha can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kenneth","Keisha","John"],"index":55377,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997083545,"difficulty":0.0002916455}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that John knows whether or not everyone is thirsty. It is publicly announced that Angela knows whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] Agentb knows that (Agentd knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Christopher can now know that Angela can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Christopher","Maurice","Angela"],"index":39731,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9278057218,"difficulty":0.0721942782}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helga knows whether Helga is thirsty. It is publicly announced that Helga does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Helga can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ingrid","Helga"],"index":32609,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957784414,"difficulty":0.0042215586}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucas's card is shown to William. William's card is shown to Lucas. Lucas's card is shown to Lucas. Donna's card is shown to Lucas. Lucas's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Lucas can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Lucas","Donna"],"index":29670,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7835858464,"difficulty":1.7835858464}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Iris does not know whether Madonna is thirsty. It is publicly announced that Iris knows whether Iris is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"David can now know whether Madonna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Madonna","David","Iris"],"index":54097,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9786655307,"difficulty":0.0213344693}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Larry can now know that Roy can know that Roy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roy","Edward","Larry","Denise"],"index":47077,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982548356,"difficulty":0.0017451644}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Bonnie can now know that George can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Scott","Bonnie"],"index":35647,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999781549,"difficulty":0.000218451}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maya can now know that Dwayne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dwayne","Larry","Maya"],"index":45561,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986346364,"difficulty":0.0013653636}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harvey can now know that Judy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steve","Harvey","Violet","Judy"],"index":55322,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931934476,"difficulty":0.0068065524}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Barbara. Nathan's card is shown to Nathan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barbara","David","Margie","Nathan"],"index":7710,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997614026,"difficulty":0.0002385974}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wade knows whether someone's forehead is muddy. It is publicly announced that Wade knows whether someone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Michael can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Wade"],"index":23168,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979699254,"difficulty":0.0020300746}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Nicole is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Nicole can now know that George can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Marion","George","Nicole"],"index":55660,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984128475,"difficulty":0.0015871525}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aaron knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Tyrone can now know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Douglas","Aaron","Tyrone"],"index":13272,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9970434308,"difficulty":0.0029565692}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Blanche's card is shown to Laura. Laura's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Blanche can now know that Laura picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Blanche","Laura"],"index":38321,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983248115,"difficulty":0.0016751885}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose's forehead is not muddy. It is publicly announced that Carlos knows whether Latasha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Latasha can now know that Jose can know whether Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Latasha","Carlos","Jose"],"index":12629,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996426105,"difficulty":0.0003573895}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerardo knows whether Gerardo's forehead is muddy. It is publicly announced that Gerardo knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Gerardo can now know that Gerardo's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerardo","Carlton","Andres","Delfina"],"index":66961,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8312659264,"difficulty":0.1687340736}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether Mary's forehead is muddy. It is publicly announced that Dennis does not know whether or not everyone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy. It is publicly announced that Mary knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mary can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dennis","Mary"],"index":10602,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9932070374,"difficulty":0.0067929626}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Mary. Brian's card is shown to Mary. Peter's card is shown to Mignon. Mary's card is shown to Peter. Brian's card is shown to Peter. Mary's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Mignon does not know whether Brian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Brian can now know that Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Mignon","Peter","Brian"],"index":27634,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9466736913,"difficulty":0.0533263087}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vivian knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ethel can now know whether Vivian is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ethel","Rochelle","Vivian","Barbara"],"index":16804,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5186406374,"difficulty":0.4813593626}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Myrtle can now know whether Erwin can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roland","Miguel","Erwin","Myrtle"],"index":19919,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997497201,"difficulty":0.0002502799}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Billy. Michael's card is shown to Billy. Billy's card is shown to Michael. Billy's card is shown to Kirk. It is publicly announced that someone picked a red card. It is publicly announced that Kirk knows whether Billy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Billy can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","Michael","Kirk","Faith"],"index":67026,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8974481821,"difficulty":1.8974481821}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ivana knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Betty can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ivana","David","Betty"],"index":59795,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997484088,"difficulty":0.0002515912}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alva does not know whether Helen is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Eva can now know whether Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Eva","Alva","Michael"],"index":29968,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9946246743,"difficulty":0.0053753257}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Celeste does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Deborah can now know whether Celeste can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Celeste","Sylvia","Marcia"],"index":31406,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roberto knows whether Domingo's forehead is muddy. It is publicly announced that Roberto's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Roberto can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","Roberto","Domingo","Terry"],"index":36685,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997748733,"difficulty":0.0002251267}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether James is thirsty. It is publicly announced that Kimberly does not know whether or not everyone is thirsty. It is publicly announced that Kimberly is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] [ ! (1|2) ] (Agentb knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] [ ! (1|2) ] 0","hypothesis":"Kimberly can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Kimberly"],"index":38485,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christa knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Christa can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Christa"],"index":49798,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9754531384,"difficulty":0.0245468616}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack knows whether Ashley's forehead is muddy. It is publicly announced that Debra does not know whether Debra's forehead is muddy. It is publicly announced that Donald knows whether Ashley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jack can now know that Debra can know that Jack's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ashley","Donald","Jack","Debra"],"index":42932,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9932391644,"difficulty":0.0067608356}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James knows whether Luis's forehead is muddy. It is publicly announced that Wayne knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Luis can now know that Wayne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Kevin","Luis","Wayne"],"index":62315,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966048002,"difficulty":0.0033951998}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anita knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know that Ronald can know that Anita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Johnnie","Ronald","Anita","John"],"index":41126,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9177470207,"difficulty":0.0822529793}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Melissa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"William can now know that Melissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roberta","Melissa","William"],"index":6832,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9968824387,"difficulty":0.0031175613}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cliff's card is shown to Brian. Brian's card is shown to Cliff. It is publicly announced that someone picked a red card. It is publicly announced that Brian knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Brian can now know whether Cliff picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brian","Cliff"],"index":61027,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9101877809,"difficulty":1.9101877809}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josephine does not know whether Audrey is thirsty. It is publicly announced that John does not know whether Audrey is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"John can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Audrey","John","Moises","Josephine"],"index":8458,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983727932,"difficulty":0.0016272068}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Rose can now know whether Irma can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Rose","Irma"],"index":57987,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997498393,"difficulty":0.0002501607}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lester can now know that Tammie can know that Tammie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Beryl","Lester","Tammie","Amanda"],"index":13518,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981870055,"difficulty":0.0018129945}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robin does not know whether Kelvin is thirsty. It is publicly announced that Bryon does not know whether Robin is thirsty. It is publicly announced that Kelvin does not know whether or not everyone is thirsty. It is publicly announced that Jared does not know whether Robin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Jared can now know whether Robin can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Bryon","Jared","Kelvin"],"index":8550,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997720122,"difficulty":0.0002279878}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicholas is thirsty. It is publicly announced that Nicholas knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Nicholas can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Nicholas","Ricky"],"index":20462,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985392094,"difficulty":0.0014607906}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] 0","hypothesis":"Barbara can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Keith","Michael"],"index":33220,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Curtis can now know that Teresa can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Teresa","Lani","Curtis"],"index":20003,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999725759,"difficulty":0.000274241}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Dudley can now know that Patricia can know that Peter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Patricia","Guy","Dudley"],"index":37184,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6465643048,"difficulty":0.3534356952}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Roger. John's card is shown to Donald. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know whether Roger picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roger","Donald","John"],"index":13555,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9250535965,"difficulty":0.0749464035}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Michael can now know that William can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Michael"],"index":32737,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996154308,"difficulty":0.0003845692}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin does not know whether or not everyone's forehead is muddy. It is publicly announced that Karen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Cora can now know that Robin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robin","Mary","Karen","Cora"],"index":2218,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6156631708,"difficulty":1.6156631708}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ray's forehead is muddy. It is publicly announced that Patricia knows whether Annette's forehead is muddy. It is publicly announced that Annette does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Harold can now know whether Harold's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ray","Annette","Harold","Patricia"],"index":39757,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7337745428,"difficulty":1.7337745428}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Grace is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Paul can now know whether Grace can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Grace","Paul"],"index":10017,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993502498,"difficulty":0.0006497502}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorthy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Juan can now know that Dorthy can know that June is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorthy","Juan","June"],"index":64889,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9028378725,"difficulty":0.0971621275}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Peter. Catherine's card is shown to Lois. Nadine's card is shown to Nadine. Catherine's card is shown to Nadine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nadine can now know whether Lois can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Lois","Nadine","Catherine"],"index":19878,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9164472222,"difficulty":1.9164472222}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Norma can now know that Jutta can know that Kelly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","James","Norma","Jutta"],"index":60601,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9944592714,"difficulty":0.0055407286}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeff's card is shown to Joy. Patrick's card is shown to Patrick. Patrick's card is shown to Jeff. It is publicly announced that someone picked a red card. It is publicly announced that Patrick picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Joy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joy","Patrick","Jeff"],"index":12063,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984995127,"difficulty":0.0015004873}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holly's card is shown to Kristal. Carlota's card is shown to Carlota. Carlota's card is shown to Holly. It is publicly announced that someone picked a red card. It is publicly announced that Kristal does not know whether Kristal picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kristal can now know that Holly can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kristal","Carlota","Holly"],"index":54457,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981003404,"difficulty":0.0018996596}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara is thirsty. It is publicly announced that Steven does not know whether Sasha is thirsty. It is publicly announced that Steven does not know whether Janie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Janie can now know that Sasha can know whether Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Janie","Sasha","Barbara"],"index":3671,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9822111726,"difficulty":0.0177888274}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Crystal's card is shown to Michael. Marlene's card is shown to Marlene. It is publicly announced that someone picked a red card. It is publicly announced that Marlene picked a red card. It is publicly announced that Michael does not know whether Michael picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3) ] [ ! (1&2&3) ] 0","hypothesis":"Michael can now know that Crystal can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Crystal","Michael","Marlene"],"index":1995,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9907994866,"difficulty":0.0092005134}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jose can now know that Barbara can know that Harold's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Jose","Harold"],"index":49509,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982680082,"difficulty":0.0017319918}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Larry. Mark's card is shown to Barbara. Barbara's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that Mark can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Larry","Barbara","Mark"],"index":54034,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983063936,"difficulty":0.0016936064}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Judith can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Judith","Robert"],"index":58403,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984874725,"difficulty":0.0015125275}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Martha can now know whether Jennifer can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Martha","Helen","Jennifer","Laura"],"index":62210,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993989468,"difficulty":0.0006010532}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Paul's card is shown to Michael. Denise's card is shown to Michael. Denise's card is shown to Denise. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Paul","Denise"],"index":5267,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5950528383,"difficulty":0.4049471617}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlotte's card is shown to Charlotte. Dennis's card is shown to Dennis. Yajaira's card is shown to Dennis. Dennis's card is shown to Yajaira. Dennis's card is shown to Debora. It is publicly announced that someone picked a red card. It is publicly announced that Charlotte does not know whether Dennis picked a red card. It is publicly announced that Dennis picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Charlotte can now know that Debora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlotte","Dennis","Yajaira","Debora"],"index":11041,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9494527578,"difficulty":0.0505472422}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henry's card is shown to Pamela. Geraldine's card is shown to Geraldine. Geraldine's card is shown to Henry. It is publicly announced that someone picked a red card. It is publicly announced that Geraldine does not know whether Henry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Geraldine can now know whether Henry can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pamela","Geraldine","Henry"],"index":9105,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Kevin knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kevin can now know whether Rafael can know whether Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Rafael"],"index":52226,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997217059,"difficulty":0.0002782941}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martin's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Roger can now know that David can know whether Roger's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Martin","Roger","John","David"],"index":21156,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995217323,"difficulty":0.0004782677}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gertrude's card is shown to Robert. David's card is shown to Robert. Gertrude's card is shown to Gertrude. David's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Gertrude","David"],"index":49864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998136282,"difficulty":0.001863718}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valeria does not know whether Valeria's forehead is muddy. It is publicly announced that Valeria does not know whether Valeria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Dorothy can now know that Valeria can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","Valeria","Joseph"],"index":37634,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983500242,"difficulty":0.0016499758}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Erik can now know that Jennifer can know that Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Erik","Jennifer","Marcia"],"index":42493,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984318614,"difficulty":0.0015681386}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobby's card is shown to Dorathy. Dorathy's card is shown to Wade. Bobby's card is shown to Wade. Wade's card is shown to Bobby. It is publicly announced that someone picked a red card. It is publicly announced that Dorathy does not know whether Dorathy picked a red card. It is publicly announced that Dorathy knows whether Bobby picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Dorathy can now know whether Bobby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dorathy","Wade","Bobby"],"index":19962,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5091670752,"difficulty":1.5091670752}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Frances can now know that Thomas can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frances","Thomas"],"index":42,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9956539869,"difficulty":0.0043460131}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mike is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Henry can now know whether Mike is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Henry","Francisco","Beatrice","Mike"],"index":66420,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8477658033,"difficulty":0.1522341967}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Zoila can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Douglas","Zoila","David"],"index":24677,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997701049,"difficulty":0.0002298951}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether Cyndy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Robert can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cyndy","Helen","Robert"],"index":52472,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997519851,"difficulty":0.0002480149}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfonso knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Alfonso can now know whether Theresa can know that Alfonso's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alfonso","Jeanette","Theresa"],"index":55692,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993677735,"difficulty":0.0006322265}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samuel does not know whether Nicholas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Nicholas can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chrystal","Nicholas","John","Samuel"],"index":12549,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983665347,"difficulty":0.0016334653}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Mary can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alfredo","Mary","Andrew","Stephen"],"index":62726,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998415947,"difficulty":0.001584053}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myra knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Tammy can now know that Michael can know that Tammy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Myra","Tammy","Mark","Michael"],"index":46283,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980623126,"difficulty":0.0019376874}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether Manuel is thirsty. It is publicly announced that Manuel does not know whether Lila is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Kathryn can now know whether Frances can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Frances","Lila","Manuel"],"index":5323,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994472861,"difficulty":0.0005527139}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Judy. Judy's card is shown to Louis. Judy's card is shown to James. Louis's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Judy","Louis","James"],"index":21935,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6024140716,"difficulty":1.6024140716}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelo's card is shown to Joe. Joe's card is shown to Timothy. Angelo's card is shown to Timothy. Joe's card is shown to Carlos. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Timothy can now know that Carlos picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joe","Timothy","Angelo","Carlos"],"index":17663,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984619617,"difficulty":0.0015380383}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ethel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Lucille can now know that Anne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ethel","Anne","Alan","Lucille"],"index":55495,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965586066,"difficulty":0.0034413934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Gertrude","Ruth","Sally"],"index":50815,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9938859344,"difficulty":0.0061140656}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Kennith's card is shown to Kennith. Louis's card is shown to Kennith. Edward's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Kennith does not know whether Angela picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kennith can now know that Louis can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Kennith","Louis","Edward"],"index":42775,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985415936,"difficulty":0.0014584064}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Bertha is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Bertha can now know that Michael can know that Bertha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alayna","Michael","Bertha"],"index":64281,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973537922,"difficulty":0.0026462078}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Sadie does not know whether Sharon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Sharon can now know that Sharon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Timothy","Sadie","Sharon"],"index":4033,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9925028086,"difficulty":0.0074971914}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Viola's forehead is muddy. It is publicly announced that Rhonda's forehead is not muddy. It is publicly announced that Viola knows whether Rhonda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Rhonda can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rhonda","Viola","Angela"],"index":61161,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michele does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Thomas can now know that Michele can know whether Michele's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Emily","Michele","Thomas"],"index":9748,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.594959259,"difficulty":0.405040741}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether or not everyone's forehead is muddy. It is publicly announced that Joe does not know whether Joe's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Johnna can now know that Joe can know that Johnna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joe","Estela","Johnna"],"index":20803,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7978790402,"difficulty":0.2021209598}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sammie can now know that Daniel can know that Ernest's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sammie","Daniel","Ernest","Michael"],"index":38477,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986322522,"difficulty":0.0013677478}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret does not know whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Nora can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nora","Margaret","Thomas","Sarah"],"index":44845,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986208677,"difficulty":0.0013791323}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether Toi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Belinda can now know that Toi can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dan","Travis","Belinda","Toi"],"index":42244,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982985854,"difficulty":0.0017014146}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Johnny","Louis"],"index":21011,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986251593,"difficulty":0.0013748407}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know whether Mike can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mike","Daniel","Gary","Anne"],"index":53205,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996856451,"difficulty":0.0003143549}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Frank can now know that Thomas can know whether Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Frank","Zachary"],"index":6035,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994700551,"difficulty":0.0005299449}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"John can now know whether Frank picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Arlene","Frank","Bryan"],"index":2858,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8878768682,"difficulty":0.1121231318}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Candice can now know whether Marvin can know whether Candice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cody","Candice","Roy","Marvin"],"index":20358,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996955395,"difficulty":0.0003044605}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy. It is publicly announced that Mary knows whether Wendy's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Wendy can now know whether Todd can know that Todd's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wendy","Mary","Todd"],"index":53023,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99957937,"difficulty":0.00042063}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Charles can now know that John can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","John","Bill"],"index":66201,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9802395701,"difficulty":0.0197604299}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna does not know whether Karen is thirsty. It is publicly announced that Karen does not know whether Carrie is thirsty. It is publicly announced that Donna does not know whether Karen is thirsty. It is publicly announced that Donna does not know whether Katrina is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentc knows that (Agenta knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Carrie can now know that Katrina can know whether Donna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katrina","Karen","Carrie","Donna"],"index":42692,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9820404053,"difficulty":0.0179595947}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alex knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Alex can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brenda","Alex","Maynard","Barbara"],"index":53524,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980839491,"difficulty":0.0019160509}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose knows whether Rose's forehead is muddy. It is publicly announced that John knows whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Melanie can now know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joyce","Rose","Melanie","John"],"index":47259,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997363687,"difficulty":0.0002636313}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Diane can now know whether Chris can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Chris","Sheena"],"index":26676,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6066185832,"difficulty":0.3933814168}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pablo knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Tracy can now know that Pablo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pablo","Reva","Tracy","Elvis"],"index":22816,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984379411,"difficulty":0.0015620589}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Derrick knows whether Larry's forehead is muddy. It is publicly announced that Larry knows whether Larry's forehead is muddy. It is publicly announced that Derrick knows whether Derrick's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Derrick can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Derrick","Larry"],"index":9019,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983578324,"difficulty":0.0016421676}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tabitha knows whether Tabitha is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jamie can now know whether Tabitha can know whether Francisco is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jamie","Francisco","Tabitha"],"index":54436,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988542795,"difficulty":0.0011457205}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher does not know whether or not everyone is thirsty. It is publicly announced that Christopher does not know whether Norma is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Christopher can now know that Kenneth can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norma","Kenneth","Christopher"],"index":61609,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5503645539,"difficulty":1.5503645539}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan knows whether Chong's forehead is muddy. It is publicly announced that Chong does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Juan can now know that Chong can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Juan","Chong"],"index":20513,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelia knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Ethel can now know that Scott can know whether Ethel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carrie","Scott","Ethel","Shelia"],"index":66115,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9964005947,"difficulty":0.0035994053}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kurt knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jeffrey can now know that Eric can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edith","Eric","Jeffrey","Kurt"],"index":61326,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982958436,"difficulty":0.0017041564}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Don's card is shown to Leann. Michael's card is shown to Daryl. Leann's card is shown to Don. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Don can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Leann","Daryl","Don"],"index":46818,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997662902,"difficulty":0.0002337098}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Margaret's card is shown to Margaret. Margaret's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Margaret","Janice"],"index":59018,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979029894,"difficulty":0.0020970106}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Cynthia can now know whether Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlotte","Richard","Joshua","Cynthia"],"index":60830,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.995172441,"difficulty":0.004827559}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jose can now know that Vanessa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vanessa","Jose","Timothy"],"index":11861,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6411478519,"difficulty":0.3588521481}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Sara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Sara can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anita","William","Frances","Sara"],"index":62040,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984942675,"difficulty":0.0015057325}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theresa knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Theresa can now know whether Caroline can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Caroline","Theresa"],"index":49973,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Margaret. Manuel's card is shown to Manuel. Herman's card is shown to Herman. It is publicly announced that someone picked a red card. It is publicly announced that Manuel picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Manuel does not know whether Margaret picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Manuel can now know whether Herman can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Manuel","Herman"],"index":52885,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Michael's card is shown to Thomas. Clarence's card is shown to Thomas. Thomas's card is shown to Michael. Michael's card is shown to Michael. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Carl can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Thomas","Michael","Clarence"],"index":7362,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997131228,"difficulty":0.0002868772}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie does not know whether Julie's forehead is muddy. It is publicly announced that Debra does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Debra can now know whether Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debra","Julie","Maria","Lenora"],"index":58550,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7387311459,"difficulty":0.2612688541}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vicki knows whether or not everyone's forehead is muddy. It is publicly announced that Edwin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Vicki can now know whether Edwin can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edwin","Vicki"],"index":48299,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997039437,"difficulty":0.0002960563}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Sheila. Conrad's card is shown to Sheila. Sheila's card is shown to Conrad. It is publicly announced that someone picked a red card. It is publicly announced that Conrad does not know whether Conrad picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Sheila can now know that Conrad can know whether Conrad picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sheila","Conrad"],"index":15463,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8250254393,"difficulty":1.8250254393}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether or not everyone is thirsty. It is publicly announced that Brian does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Brian can now know that Scott can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Edith","Scott","Damon"],"index":40792,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977226853,"difficulty":0.0022773147}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mattie is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Kevin can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kevin","Mattie","Mark","James"],"index":38922,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997397065,"difficulty":0.0002602935}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Amanda's forehead is muddy. It is publicly announced that Amanda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Kimberly can now know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kimberly","Amanda"],"index":22350,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8473086357,"difficulty":0.1526913643}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Faye's card is shown to Claire. Karen's card is shown to Claire. Laurence's card is shown to Karen. Karen's card is shown to Laurence. It is publicly announced that someone picked a red card. It is publicly announced that Claire does not know whether Claire picked a red card. It is publicly announced that Claire picked a black card. It is publicly announced that Faye does not know whether Faye picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Karen can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Claire","Faye","Karen","Laurence"],"index":11382,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997823834,"difficulty":0.0002176166}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Tina can now know whether Harold can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tina","Charlie","James","Harold"],"index":7404,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9907631278,"difficulty":0.0092368722}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Helen can now know that Georgia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Helen","Georgia","Patricia"],"index":11522,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5690427423,"difficulty":0.4309572577}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Sandra can now know whether Mary can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Troy","Sandra","Mary"],"index":26781,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9252489805,"difficulty":0.0747510195}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether or not everyone's forehead is muddy. It is publicly announced that Donald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Richard can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Donald","Richard"],"index":25171,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997296929,"difficulty":0.0002703071}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Diane knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Diane can now know that Diane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Jose","Diane","Carlos"],"index":61900,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8765126467,"difficulty":0.1234873533}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Morgan. Kenneth's card is shown to Kenneth. Morgan's card is shown to Leroy. Kenneth's card is shown to Leroy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Minda can now know whether Morgan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Morgan","Kenneth","Minda","Leroy"],"index":44827,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Anna. Anna's card is shown to Miguel. Chris's card is shown to Miguel. Dorothy's card is shown to Dorothy. Chris's card is shown to Dorothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know that Miguel can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anna","Miguel","Dorothy","Chris"],"index":3735,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984381795,"difficulty":0.0015618205}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Vivian can now know that David can know whether Vivian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vivian","David","John","Robert"],"index":126,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995846152,"difficulty":0.0004153848}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bobby knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Dollie can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bobby","Dollie","Delmar"],"index":36532,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997623563,"difficulty":0.0002376437}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos does not know whether Carlos's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Richard can now know that Wilbert can know whether Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carlos","Wilbert","Richard"],"index":6966,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995494485,"difficulty":0.0004505515}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Mary. Elizabeth's card is shown to Genaro. Rodney's card is shown to Elizabeth. Genaro's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Genaro can now know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Rodney","Genaro","Elizabeth"],"index":14470,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9320977926,"difficulty":1.9320977926}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia knows whether Guadalupe's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Alicia can now know whether Alicia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alicia","Guadalupe"],"index":33591,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9923244715,"difficulty":0.0076755285}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tricia's card is shown to Charmaine. Charmaine's card is shown to Charmaine. Charmaine's card is shown to Zachary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tricia can now know whether Charmaine can know whether Zachary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tricia","Charmaine","Zachary","Mary"],"index":39884,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985339642,"difficulty":0.0014660358}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julian does not know whether or not everyone is thirsty. It is publicly announced that Glen does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Julian can now know that Charles can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julian","Charles","Glen"],"index":7136,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980047345,"difficulty":0.0019952655}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Melissa can now know that Troy can know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Troy","Edward","Melissa"],"index":20008,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995330572,"difficulty":0.0004669428}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beau's card is shown to Donna. Laura's card is shown to Donna. Beau's card is shown to Beau. Natalie's card is shown to Beau. Laura's card is shown to Beau. Beau's card is shown to Natalie. Beau's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Natalie knows whether Beau picked a red card. It is publicly announced that Laura does not know whether Donna picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Laura can now know whether Natalie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Beau","Natalie","Laura"],"index":39787,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997723699,"difficulty":0.0002276301}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to George. George's card is shown to George. Joseph's card is shown to Andrew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","George","Andrew"],"index":14509,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982349873,"difficulty":0.0017650127}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anton's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Anton can now know whether Gail can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anton","David","Gail"],"index":37000,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997184873,"difficulty":0.0002815127}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Tamika can now know whether Tamika is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Tamika","Betty"],"index":64096,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9965627789,"difficulty":0.0034372211}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Fernando does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Fernando can now know whether Jerry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Fernando","Jerry"],"index":26360,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5004512668,"difficulty":0.4995487332}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bobbi","Robert","Michael"],"index":51359,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983751774,"difficulty":0.0016248226}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Renee's card is shown to Renee. Renee's card is shown to Nicholas. Nicholas's card is shown to Nicholas. It is publicly announced that someone picked a red card. It is publicly announced that Nicholas knows whether Nicholas picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Nicholas can now know that Renee can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Renee","Nicholas"],"index":5302,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Earl can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arthur","Nancy","Alan","Earl"],"index":26876,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937930107,"difficulty":0.0062069893}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon's forehead is muddy. It is publicly announced that Shannon knows whether James's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Douglas can now know whether James can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Douglas","Shannon"],"index":40544,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996851683,"difficulty":0.0003148317}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernest's card is shown to William. William's card is shown to Ernest. It is publicly announced that someone picked a red card. It is publicly announced that Ernest does not know whether or not everyone picked a red card. It is publicly announced that Ernest does not know whether Ernest picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ernest can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Ernest"],"index":55069,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981765747,"difficulty":0.0018234253}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that Charles knows whether or not nobody is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Carolyn can now know whether Charles can know whether Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Carolyn"],"index":48806,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986324906,"difficulty":0.0013675094}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy. It is publicly announced that Amy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Amy can now know that Letha can know that Deloris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amy","Letha","Linda","Deloris"],"index":60143,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.906612277,"difficulty":0.093387723}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Berniece does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Todd can now know that Patricia can know whether Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Berniece","Todd","Willie","Patricia"],"index":43114,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995083809,"difficulty":0.0004916191}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Latonya knows whether someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Latonya can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Latonya","Charles","Michael","Louis"],"index":31460,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997807145,"difficulty":0.0002192855}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Kenneth can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kenneth","Catherine"],"index":29346,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9934872389,"difficulty":0.0065127611}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Amanda's card is shown to Amanda. Robyn's card is shown to Robyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amanda can now know whether Anthony can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Amanda","Robyn"],"index":27752,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995519519,"difficulty":0.0004480481}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dulce knows whether Ruby's forehead is muddy. It is publicly announced that Dulce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Ruby can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Dulce","Ruby","Michael"],"index":49515,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996161461,"difficulty":0.0003838539}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert knows whether Yvonne's forehead is muddy. It is publicly announced that Albert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kelly can now know whether Yvonne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Kelly","Yvonne","Albert"],"index":33684,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997490048,"difficulty":0.0002509952}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether Raymond's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"Raymond can now know that Jose can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","John","Jose","Winifred"],"index":26271,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997170568,"difficulty":0.0002829432}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aida is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Belinda can now know that Belinda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Aida","Belinda","Carolyn"],"index":36771,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941250086,"difficulty":0.0058749914}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Grace does not know whether Scott is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Erica can now know that Grace can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Grace","Scott","Erica"],"index":22898,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984488487,"difficulty":0.0015511513}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Daniel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Randy","Daniel","Vernon"],"index":36657,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997783303,"difficulty":0.0002216697}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher knows whether or not nobody is thirsty. It is publicly announced that Christopher does not know whether Mark is thirsty. It is publicly announced that Tina does not know whether or not everyone is thirsty. It is publicly announced that Christopher does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know that Tina can know that Tina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Christopher","Tina"],"index":51240,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9674303532,"difficulty":0.0325696468}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine knows whether Adrian's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Catherine can now know whether Shelley can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Catherine","Adrian","Shelley"],"index":47456,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999525547,"difficulty":0.000474453}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Augustine knows whether Augustine's forehead is muddy. It is publicly announced that Steve knows whether Eva's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Eva can now know whether Steve's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eva","Augustine","Steve","Casandra"],"index":42828,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997355342,"difficulty":0.0002644658}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Virginia. Mary's card is shown to Virginia. Virginia's card is shown to Elizabeth. Virginia's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Elizabeth can now know that Virginia can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Soon","Virginia","Elizabeth","Mary"],"index":37660,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7308598757,"difficulty":1.7308598757}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Eugene's card is shown to Daniel. Warren's card is shown to Daniel. Warren's card is shown to Warren. Daniel's card is shown to Dorothy. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether Warren picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Dorothy can now know that Eugene can know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eugene","Daniel","Warren","Dorothy"],"index":61107,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993386209,"difficulty":0.006613791}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Susan. Susan's card is shown to Alice. Alice's card is shown to Tara. Tara's card is shown to Tara. Susan's card is shown to Cynthia. Cynthia's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether or not everyone picked a red card. It is publicly announced that Susan picked a red card. It is publicly announced that Susan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Susan can now know whether Cynthia can know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Alice","Tara","Cynthia"],"index":3069,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980758429,"difficulty":0.0019241571}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Corrine knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Gary can now know that Stacey can know whether Gary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gary","Corrine","Stacey"],"index":20132,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9919359684,"difficulty":0.0080640316}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew does not know whether Randy is thirsty. It is publicly announced that Matthew knows whether Matthew is thirsty. It is publicly announced that Randy does not know whether Matthew is thirsty. It is publicly announced that Bridgett does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Randy can now know whether Bridgett can know that Matthew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Randy","Matthew","Bridgett"],"index":45953,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9884948134,"difficulty":0.0115051866}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sonya does not know whether Sonya's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Diana can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diana","Joan","Sonya","Scott"],"index":2672,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985672235,"difficulty":0.0014327765}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Johnny can now know that Bradley can know that Johnny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Fred","Bradley","Johnny","Alfonso"],"index":2202,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981034994,"difficulty":0.0018965006}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie does not know whether or not everyone's forehead is muddy. It is publicly announced that Julie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Tamara can now know that Margaret can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Tamara","Julie","James"],"index":36689,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bertha knows whether Jamie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Earline can now know that Jeffrey can know whether Earline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Bertha","Earline","Jamie"],"index":6794,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997358918,"difficulty":0.0002641082}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Samuel can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Samuel","Michelle","Kenneth","Isabel"],"index":2954,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985812902,"difficulty":0.0014187098}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lasonya's card is shown to Lasonya. Lasonya's card is shown to Stuart. Stuart's card is shown to Stuart. Lasonya's card is shown to Darlene. Stuart's card is shown to Darlene. Darlene's card is shown to Darlene. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Lasonya can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lasonya","Stuart","Darlene"],"index":33688,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982878566,"difficulty":0.0017121434}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Liliana can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Liliana","Louis","Ella"],"index":52392,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936850667,"difficulty":0.0063149333}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kim does not know whether Madison is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Angela can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kim","Gerard","Angela","Madison"],"index":37573,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997166991,"difficulty":0.0002833009}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cameron does not know whether Cameron's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Cameron can now know whether John can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Cameron","John"],"index":34301,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993725419,"difficulty":0.0006274581}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Verna does not know whether Emily is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Thelma can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thelma","Emily","John","Verna"],"index":22887,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973646998,"difficulty":0.0026353002}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Mark is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Myra can now know whether William can know that Mark is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elsa","Myra","Mark","William"],"index":3900,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9893264771,"difficulty":0.0106735229}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Duane can now know that Parker can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Parker","Duane","Rosie","Manual"],"index":29459,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996830225,"difficulty":0.0003169775}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daisy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Daisy can now know whether Brian is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Mark","Daisy"],"index":1620,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9903443456,"difficulty":0.0096556544}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Amanda can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amanda","Maria","Curtis","Anita"],"index":21933,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984930754,"difficulty":0.0015069246}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Launa can now know whether Launa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Launa","Noel","Patricia","Randy"],"index":42902,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996805191,"difficulty":0.0003194809}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jack does not know whether Patricia is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Jack is thirsty. It is publicly announced that Jack does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Patricia can now know that Gary can know that Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Patricia","Jack","Maria"],"index":17393,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7396814823,"difficulty":0.2603185177}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Tiffany can know that Gertrude's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tiffany","Mary","Gertrude"],"index":58856,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998622179,"difficulty":0.001377821}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfred knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kathleen can now know that Alfred's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathleen","James","Alfred","Christy"],"index":51178,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983617663,"difficulty":0.0016382337}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Gary knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Sharon can now know that Gary can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gary","Sharon"],"index":26541,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985336065,"difficulty":0.0014663935}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Ralph can now know whether Gregory can know whether Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gregory","Ralph","Barbara"],"index":8419,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988008738,"difficulty":0.0011991262}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roderick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Carolyn can now know whether Gary can know whether Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marilyn","Roderick","Carolyn","Gary"],"index":29192,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979966283,"difficulty":0.0020033717}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Emily's card is shown to Helen. Emily's card is shown to Judith. Annie's card is shown to Judith. Judith's card is shown to Emily. Emily's card is shown to Emily. Emily's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that Helen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentc knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Emily can now know whether Helen can know that Annie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Judith","Emily","Annie"],"index":6365,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9199985862,"difficulty":0.0800014138}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jaqueline's card is shown to Kerri. Cathy's card is shown to Cathy. Cathy's card is shown to Jaqueline. Jaqueline's card is shown to Jaqueline. Jaqueline's card is shown to Martha. It is publicly announced that someone picked a red card. It is publicly announced that Kerri knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jaqueline can now know whether Cathy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kerri","Cathy","Jaqueline","Martha"],"index":20202,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7301183939,"difficulty":1.7301183939}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Janet. Eugene's card is shown to Eugene. It is publicly announced that someone picked a red card. It is publicly announced that Eugene does not know whether Janet picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Janet can now know that Eugene can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janet","Eugene"],"index":47225,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997028708,"difficulty":0.0002971292}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cassi knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Brian can now know that Cassi can know that Cassi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brian","Cassi"],"index":46777,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7639052868,"difficulty":0.2360947132}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Joseph can now know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debra","Joseph","Nina","Barbara"],"index":11050,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957175851,"difficulty":0.0042824149}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amber knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kenneth can now know that John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Kenneth","Amber"],"index":2388,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983416796,"difficulty":0.0016583204}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose does not know whether Jose's forehead is muddy. It is publicly announced that Bonnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] 0","hypothesis":"Margaret can now know whether Neil's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margaret","Neil","Bonnie","Jose"],"index":39885,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995933175,"difficulty":0.0004066825}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holley's card is shown to Holley. Judy's card is shown to Holley. Judy's card is shown to Annis. Holley's card is shown to Judy. It is publicly announced that someone picked a red card. It is publicly announced that Judy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Holley can now know that Annis can know that Holley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Holley","Annis","Judy"],"index":62767,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.578053534,"difficulty":0.421946466}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rex knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Rex can now know that Ezequiel can know whether Ezequiel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Arlene","Ezequiel","Rex"],"index":26234,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995937943,"difficulty":0.0004062057}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alyce knows whether or not everyone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentc knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Alyce can now know that Joseph can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hazel","Connie","Alyce","Joseph"],"index":7402,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.5788250566,"difficulty":0.4211749434}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether Mary is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mike can now know that Mike is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mike","Mary"],"index":13019,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8103585243,"difficulty":0.1896414757}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Darci can now know that Wayne can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Wayne","Darci"],"index":20935,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Justin can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dale","Rose","Mamie","Justin"],"index":66119,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9925173521,"difficulty":0.0074826479}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy. It is publicly announced that Cynthia does not know whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Cynthia can now know that Steve can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cynthia","Steve","Jennifer"],"index":18543,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8385128975,"difficulty":0.1614871025}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(2) ] 0","hypothesis":"Patrick can now know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patrick","James","Margaret","Angelica"],"index":24349,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995266199,"difficulty":0.0004733801}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ethel's card is shown to Tracey. Tracey's card is shown to Donna. Ethel's card is shown to Donna. Donna's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tracey can now know whether Ethel can know that Tracey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tracey","Ethel","Donna"],"index":58432,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6649048924,"difficulty":1.6649048924}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Teresa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] 0","hypothesis":"Adam can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Glen","Teresa","Adam","Melvin"],"index":7321,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9958047271,"difficulty":0.0041952729}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Audrey's card is shown to Audrey. Jody's card is shown to Audrey. Aaron's card is shown to Jody. Jody's card is shown to Aaron. It is publicly announced that someone picked a red card. It is publicly announced that Audrey does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jody can now know that Audrey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Audrey","Jody","Aaron"],"index":23487,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7931936979,"difficulty":1.7931936979}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Joel can now know that Connie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Connie","Thomas","Angela","Joel"],"index":3085,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984207153,"difficulty":0.0015792847}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norbert knows whether Jeannie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Laura can now know that Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norbert","Jeannie","Laura","Denise"],"index":363,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979242086,"difficulty":0.0020757914}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Don's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Don can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dana","Tonya","Don","Richard"],"index":56904,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997414947,"difficulty":0.0002585053}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brent does not know whether Paula is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Paula can now know whether Brent can know whether Brent is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paula","Brent"],"index":3277,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980900884,"difficulty":0.0019099116}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether someone's forehead is muddy. It is publicly announced that Laura knows whether Allan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Renae can now know that Allan can know that Allan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Annie","Allan","Renae","Laura"],"index":5167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974709749,"difficulty":0.0025290251}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lien's card is shown to Lien. Charles's card is shown to Charles. Lien's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lien can now know whether Joseph can know whether Lien picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lien","Charles","Joseph"],"index":35787,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986948371,"difficulty":0.0013051629}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lottie knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lori can now know that Rodolfo can know that Rodolfo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rodolfo","Lori","Mario","Lottie"],"index":54641,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980371594,"difficulty":0.0019628406}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Kathleen can now know whether Diane can know whether Claudia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Claudia","Kathleen","Diane"],"index":66736,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999725759,"difficulty":0.000274241}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melvin knows whether or not nobody's forehead is muddy. It is publicly announced that Walter knows whether Melvin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Walter can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Melvin","Walter"],"index":54226,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982103109,"difficulty":0.0017896891}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Miguel does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Miguel can now know that Kimberly can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","Miguel","Bonnie","Richard"],"index":2502,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983264804,"difficulty":0.0016735196}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bill does not know whether Patricia is thirsty. It is publicly announced that Allison does not know whether Justin is thirsty. It is publicly announced that Bill knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Allison can now know whether Bill can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Bill","Justin","Allison"],"index":14718,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995429516,"difficulty":0.0004570484}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether Judith's forehead is muddy. It is publicly announced that Judith knows whether Jeff's forehead is muddy. It is publicly announced that Judith does not know whether Judith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Judith can now know that Jeff's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeff","Ralph","Judith"],"index":67154,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9880332947,"difficulty":0.0119667053}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harrison knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Emmanuel can now know that Patty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harrison","Patty","Emmanuel","Bradley"],"index":57903,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975742698,"difficulty":0.0024257302}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank's forehead is muddy. It is publicly announced that Gregory's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Juanita can now know whether Juanita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Jimmie","Juanita","Frank"],"index":45884,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9226866961,"difficulty":0.0773133039}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Adriene. Ruth's card is shown to Adriene. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Adriene can now know that Paula can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paula","Adriene","Ruth"],"index":35005,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983550906,"difficulty":0.0016449094}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryn's card is shown to Cheryl. Cheryl's card is shown to Kathryn. It is publicly announced that someone picked a red card. It is publicly announced that Cheryl knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Kathryn can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cheryl","Kathryn"],"index":24423,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997732043,"difficulty":0.0002267957}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Raymond can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Maria","Raymond"],"index":49920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997345805,"difficulty":0.0002654195}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marta knows whether or not everyone's forehead is muddy. It is publicly announced that Marta knows whether Edna's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Mark can now know that Marta can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edna","Marta","Mark"],"index":36238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984157085,"difficulty":0.0015842915}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jannie's card is shown to Jannie. Cynthia's card is shown to Jannie. Denise's card is shown to Florence. Jannie's card is shown to Denise. Denise's card is shown to Denise. Jannie's card is shown to Cynthia. Denise's card is shown to Cynthia. Cynthia's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether Florence picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,3 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,3 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Florence can now know that Jannie can know that Jannie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jannie","Florence","Denise","Cynthia"],"index":29289,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.982838273,"difficulty":0.017161727}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ilona's card is shown to Ilona. Brian's card is shown to Ilona. Karen's card is shown to Jennifer. Brian's card is shown to Jennifer. Jennifer's card is shown to Karen. Karen's card is shown to Karen. Brian's card is shown to Karen. Ilona's card is shown to Brian. Jennifer's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 Agentc:2,3,4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 Agentc:2,3,4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ilona","Jennifer","Karen","Brian"],"index":65602,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984785914,"difficulty":0.0015214086}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hector knows whether Hector's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Isabel can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dawn","Isabel","Hector","Patricia"],"index":2782,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997500777,"difficulty":0.0002499223}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that April does not know whether April's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Barbara can now know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alma","Barbara","Eric","April"],"index":51590,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997068584,"difficulty":0.002931416}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dottie knows whether James's forehead is muddy. It is publicly announced that James knows whether Dottie's forehead is muddy. It is publicly announced that Ayana does not know whether Ayana's forehead is muddy. It is publicly announced that Dottie knows whether Dottie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dottie can now know that Ayana can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ayana","Dottie","James"],"index":60350,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979881048,"difficulty":0.0020118952}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie does not know whether or not everyone is thirsty. It is publicly announced that Willie does not know whether or not everyone is thirsty. It is publicly announced that Willie does not know whether or not everyone is thirsty. It is publicly announced that Willie does not know whether Anthony is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Willie can now know that Anthony can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Willie","Anthony"],"index":58163,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9589157104,"difficulty":0.0410842896}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth does not know whether or not everyone's forehead is muddy. It is publicly announced that Ruth does not know whether Ruth's forehead is muddy. It is publicly announced that Ruth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ruth can now know whether David can know that Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ruth","David"],"index":39103,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9373879433,"difficulty":1.9373879433}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irma knows whether Laura's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura does not know whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Laura can now know that Irma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Irma","Janis","Laura"],"index":18819,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9941028953,"difficulty":0.0058971047}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Percy's card is shown to Percy. Steve's card is shown to Percy. Percy's card is shown to Steve. Yon's card is shown to Steve. Steve's card is shown to Yon. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Yon can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Percy","Steve","Yon"],"index":48381,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997832179,"difficulty":0.0002167821}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Philip's card is shown to Philip. Charles's card is shown to Philip. Philip's card is shown to Charles. Cynthia's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Philip can now know that Cynthia can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Philip","Cynthia","Charles"],"index":19613,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997156262,"difficulty":0.0002843738}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louise does not know whether Donald is thirsty. It is publicly announced that James does not know whether Donald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] Agentd knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Donald can now know that James can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Louise","Roxie","James","Donald"],"index":50057,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9825713038,"difficulty":0.0174286962}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Nicholas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Nicholas can now know whether George can know whether Julian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Corey","Nicholas","Julian","George"],"index":19169,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990152121,"difficulty":0.0009847879}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emma","Justin","William"],"index":30731,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99971205,"difficulty":0.00028795}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Amanda. Frank's card is shown to Amanda. Frank's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank knows whether or not nobody picked a red card. It is publicly announced that Amanda picked a red card. It is publicly announced that Amanda knows whether Frank picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Frank can now know whether Amanda can know whether Amanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Amanda","Frank"],"index":42684,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9948988557,"difficulty":0.0051011443}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Marvin is thirsty. It is publicly announced that Michael does not know whether Marvin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Michael can now know that Salvador can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","Salvador","Michael","Scott"],"index":63045,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5256379843,"difficulty":0.4743620157}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virgil knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Michael can now know whether Caridad can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Virgil","Sherill","Caridad"],"index":31681,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997497201,"difficulty":0.0002502799}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Edward. Catherine's card is shown to Edward. Catherine's card is shown to Mark. Mark's card is shown to Catherine. Carolyn's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Carolyn can now know whether Edward can know whether Carolyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Mark","Carolyn","Catherine"],"index":15889,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983573556,"difficulty":0.0016426444}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Reginald. Reginald's card is shown to Laura. Mary's card is shown to Laura. Opal's card is shown to Mary. Reginald's card is shown to Opal. Laura's card is shown to Opal. It is publicly announced that someone picked a red card. It is publicly announced that Reginald does not know whether Opal picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Laura can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Reginald","Laura","Mary","Opal"],"index":3414,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985937476,"difficulty":0.0014062524}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Glen's card is shown to John. John's card is shown to Glen. Glen's card is shown to Glen. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"John can now know that Glen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Glen"],"index":38028,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984258413,"difficulty":0.0015741587}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pearl is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Randy can now know that Dorothy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Pearl","Randy","Micheal"],"index":41471,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9236302972,"difficulty":1.9236302972}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rachel does not know whether Philip is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Rachel can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Philip","Rachel"],"index":11601,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954032898,"difficulty":0.0045967102}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Marc's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jose can now know that Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shirley","Marc","Jose"],"index":32464,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974929094,"difficulty":0.0025070906}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether Sandra can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Sanjuanita","Robert","David"],"index":51894,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996905327,"difficulty":0.0003094673}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Juan. Juan's card is shown to Vanessa. It is publicly announced that someone picked a red card. It is publicly announced that Juan knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Juan can now know whether Vanessa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Juan","Vanessa"],"index":22042,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renee's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Lorraine can now know whether Renee can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Renee","Lorraine"],"index":50741,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5390037894,"difficulty":1.5390037894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chelsea knows whether someone's forehead is muddy. It is publicly announced that Donna knows whether Chelsea's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Donna can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Antonia","Donna","Sharon","Chelsea"],"index":303,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996913671,"difficulty":0.0003086329}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jeff knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jeff can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Barbara","Jeff"],"index":47931,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986960292,"difficulty":0.0013039708}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Randy can now know that Irene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Irene","Randy","Rosie"],"index":38894,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9497991204,"difficulty":0.0502008796}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Derrick does not know whether David is thirsty. It is publicly announced that Ashley does not know whether Derrick is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"David can now know whether Ashley can know whether Ashley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","David","Derrick","Ashley"],"index":37592,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985992312,"difficulty":0.0014007688}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gloria does not know whether Ralph is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Frank can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Frank","Gloria"],"index":41910,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982703924,"difficulty":0.0017296076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marlene does not know whether or not everyone's forehead is muddy. It is publicly announced that Pamela knows whether someone's forehead is muddy. It is publicly announced that Marlene does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Pamela can now know whether Brian can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Marlene","Pamela","Brian"],"index":412,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997113347,"difficulty":0.0002886653}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to David. Brenda's card is shown to David. David's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Gregory","Jason","Brenda"],"index":13119,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Nancy can now know that Gary can know that Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Gary","Jose"],"index":50753,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931638837,"difficulty":0.0068361163}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Lindsy can now know whether Ann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ann","Michael","Cesar","Lindsy"],"index":57290,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999750793,"difficulty":0.000249207}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Gerald can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Isabel","Gerald","Christie"],"index":36819,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997680783,"difficulty":0.0002319217}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Katherine can now know whether Jerilyn can know whether Katherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfonso","Jacques","Katherine","Jerilyn"],"index":23573,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992819428,"difficulty":0.0007180572}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Della. Della's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Della knows whether Mary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Della can now know whether Mary can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Della","Mary"],"index":43279,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9048362374,"difficulty":0.0951637626}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Kathleen can now know whether Patsy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandon","Kathleen","Jeanne","Patsy"],"index":32398,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999785006,"difficulty":0.000214994}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katherine does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Susan can now know whether Rhonda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Rhonda","Katherine","Elizabeth"],"index":19543,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957834482,"difficulty":0.0042165518}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erika's card is shown to Erika. Erika's card is shown to Mary. Mary's card is shown to Mary. Sidney's card is shown to Mary. Mary's card is shown to Sidney. Sidney's card is shown to Sidney. Albert's card is shown to Sidney. Albert's card is shown to Albert. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether Sidney picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mary can now know that Erika picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erika","Mary","Sidney","Albert"],"index":2922,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964601398,"difficulty":0.0035398602}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"John can now know that Jean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","John","Jean","Sandra"],"index":63716,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983318448,"difficulty":0.0016681552}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Theresa can now know whether Celia can know that Theresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Theresa","Celia","Alicia"],"index":66597,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995337725,"difficulty":0.0004662275}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Brad. Brad's card is shown to Brad. Anna's card is shown to Brad. Chris's card is shown to Anna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Chris can now know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Chris","Casey","Brad","Anna"],"index":58041,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7429926395,"difficulty":1.7429926395}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Robert can now know that Jacob can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jacob","Robert"],"index":553,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9797021747,"difficulty":0.0202978253}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Terry does not know whether Kari is thirsty. It is publicly announced that David does not know whether Terry is thirsty. It is publicly announced that Terry does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Terry can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Terry","Kari","Emily"],"index":18387,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9063241482,"difficulty":0.0936758518}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kelly can now know that Elizabeth can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Kelly","Elizabeth"],"index":57472,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997329116,"difficulty":0.0002670884}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheryl does not know whether Sheryl's forehead is muddy. It is publicly announced that Kyle does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Hubert can now know that Hubert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sheryl","Kyle","Manual","Hubert"],"index":29327,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5592226386,"difficulty":1.5592226386}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susana does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Susana can now know whether Donna can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susana","Donna","Rhonda","Lisa"],"index":37281,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997738004,"difficulty":0.0002261996}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Robert's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Brenda picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Brenda can now know whether Robert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Brenda"],"index":47402,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996763468,"difficulty":0.0003236532}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Steve can now know that Marcia can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Victoria","Colleen","Marcia","Steve"],"index":47834,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997207522,"difficulty":0.0002792478}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kay does not know whether Hortensia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kay can now know whether Leon can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hortensia","Kay","Leon"],"index":62783,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977554679,"difficulty":0.0022445321}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Dolly's forehead is muddy. It is publicly announced that Dolly knows whether Charles's forehead is muddy. It is publicly announced that Charles's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Dolly can now know that Cynthia can know that Dolly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dolly","Charles","Cynthia"],"index":43957,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9699665308,"difficulty":0.0300334692}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara is not thirsty. It is publicly announced that Gerald does not know whether Lindsay is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] Agentc knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Barbara can now know that Gerald can know that Gerald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lindsay","Stephanie","Barbara","Gerald"],"index":5315,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8363093138,"difficulty":1.8363093138}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Alexandra can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Theresa","George","Alexandra"],"index":56613,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997410178,"difficulty":0.0002589822}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Robert can now know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jacob","Robert","Mary"],"index":18681,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997243285,"difficulty":0.0002756715}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Louise can now know whether Daniel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Jennifer","Louise","Daniel"],"index":48454,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9930417538,"difficulty":0.0069582462}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Blanche's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Kimberly can now know that Grace's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kimberly","Blanche","Grace"],"index":22203,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998316288,"difficulty":0.001683712}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Tori. John's card is shown to John. John's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Tori can now know whether Teresa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Tori","John","Teresa"],"index":1218,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8799639344,"difficulty":1.8799639344}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jose can now know that Dennis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Max","Dennis","Jose"],"index":4484,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937081337,"difficulty":0.0062918663}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Iris does not know whether or not everyone is thirsty. It is publicly announced that Patrick knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Lyla can now know whether Patrick is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patrick","Iris","Lyla"],"index":29829,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6422618628,"difficulty":1.6422618628}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Emily is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Emily can now know that David can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Darrell","Emily"],"index":22401,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997783303,"difficulty":0.0002216697}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara knows whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Maria can now know that Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Maria","Carlos","Barbara"],"index":52790,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982149601,"difficulty":0.0017850399}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice does not know whether Alice's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Wilfred can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wilfred","Alice","Andrew"],"index":24288,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997029901,"difficulty":0.0002970099}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Laura. Laura's card is shown to Laura. Laura's card is shown to Margareta. It is publicly announced that someone picked a red card. It is publicly announced that Margareta knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Laura can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Laura","Margareta"],"index":43341,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997199178,"difficulty":0.0002800822}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Brian can now know that Charles is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Charles","Erica","Kay"],"index":13053,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971314669,"difficulty":0.0028685331}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Don can now know whether Linda can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Don","Virginia"],"index":47739,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997754693,"difficulty":0.0002245307}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eva can now know whether Jerry can know whether Anthony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Eva","Anthony","Jerry"],"index":14883,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997296929,"difficulty":0.0002703071}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Muriel can now know whether Krystal can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Krystal","Heidi","Muriel"],"index":25620,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996926785,"difficulty":0.0003073215}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Freddie can now know that Christopher can know whether Van's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Van","Freddie","Ricky"],"index":65104,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997319579,"difficulty":0.0002680421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"David can now know whether Joe can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joe","David","Mary"],"index":15202,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996404648,"difficulty":0.0003595352}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Eleanor. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Eleanor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Mary","Valerie","Eleanor"],"index":31905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998414278,"difficulty":0.001585722}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathy's card is shown to Laura. Laura's card is shown to Cathy. Laura's card is shown to Wanda. Cathy's card is shown to Wanda. Wanda's card is shown to Wanda. It is publicly announced that someone picked a red card. It is publicly announced that Wanda knows whether Cathy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Wanda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Laura","Cathy","Wanda"],"index":4226,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9557747245,"difficulty":1.9557747245}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Martha","Lezlie","Donald"],"index":40419,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997361302,"difficulty":0.0002638698}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Mary. Shawn's card is shown to Shawn. Andrew's card is shown to Shawn. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Shawn can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Shawn","Andrew"],"index":47353,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8272404075,"difficulty":0.1727595925}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marlo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"James can now know whether Ed can know that Marlo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Marlo","James","Ed"],"index":59309,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997012019,"difficulty":0.0002987981}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elsie knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"William can now know that Jeffrey can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elsie","Jeffrey","William"],"index":60546,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9228033423,"difficulty":0.0771966577}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Ocie. Scott's card is shown to Ocie. Chris's card is shown to Chris. Chris's card is shown to Gary. Scott's card is shown to Scott. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ocie can now know whether Scott can know that Gary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ocie","Chris","Gary","Scott"],"index":39865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9710044265,"difficulty":0.0289955735}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Jerry. Mark's card is shown to Jerry. Mark's card is shown to Lakisha. Jerry's card is shown to Jean. Jean's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Jean does not know whether Mark picked a red card. It is publicly announced that Lakisha does not know whether Jean picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lakisha can now know that Lakisha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Lakisha","Jean","Mark"],"index":49104,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9775231481,"difficulty":0.0224768519}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernice knows whether someone is thirsty. It is publicly announced that Charles does not know whether Bernice is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Anthony can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bernice","Charles","Anthony"],"index":36138,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941238761,"difficulty":0.0058761239}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that Brian can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sina","James","Brian"],"index":53025,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983444214,"difficulty":0.0016555786}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Robert can now know that Wendy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fredrick","Robert","Wendy","Vickie"],"index":39073,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981334805,"difficulty":0.0018665195}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Elizabeth. Ronnie's card is shown to Elizabeth. Elizabeth's card is shown to Louis. Pamela's card is shown to Ronnie. Elizabeth's card is shown to Pamela. Louis's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Louis does not know whether Louis picked a red card. It is publicly announced that Louis does not know whether Ronnie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Ronnie can now know whether Louis can know whether Ronnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Louis","Ronnie","Pamela"],"index":54695,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970288873,"difficulty":0.0029711127}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virgina's card is shown to Don. Don's card is shown to Virgina. Virgina's card is shown to Virgina. It is publicly announced that someone picked a red card. It is publicly announced that Virgina knows whether someone picked a red card. It is publicly announced that Virgina knows whether Don picked a red card. It is publicly announced that Don does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Virgina can now know that Don can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Don","Virgina"],"index":47929,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997005463,"difficulty":0.0002994537}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Erik's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Regina can now know that Erik can know that Erik's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Erik","Regina","Susan"],"index":8919,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975979924,"difficulty":0.0024020076}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Sean's card is shown to Sean. Sean's card is shown to Gerald. Linda's card is shown to Nellie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether Nellie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Sean","Gerald","Nellie"],"index":45415,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9357181787,"difficulty":0.0642818213}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arthur does not know whether Diana is thirsty. It is publicly announced that Angie does not know whether Arthur is thirsty. It is publicly announced that Diana is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Violet can now know whether Angie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Violet","Arthur","Diana","Angie"],"index":58638,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.970164299,"difficulty":0.029835701}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Kenneth's card is shown to John. Kenneth's card is shown to Kenneth. John's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"John can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Kenneth","Paul"],"index":62285,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997722507,"difficulty":0.0002277493}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Patricia can now know that Kristina can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Benjamin","Kristina"],"index":42544,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983832836,"difficulty":0.0016167164}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine does not know whether Catherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Anne can now know whether Dawn can know whether Anne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lloyd","Catherine","Anne","Dawn"],"index":17258,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989871383,"difficulty":0.0010128617}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Martha can now know that James can know whether Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Martha"],"index":6871,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99937433,"difficulty":0.00062567}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hannah's card is shown to Hannah. Geraldine's card is shown to Hannah. Hannah's card is shown to Shawn. It is publicly announced that someone picked a red card. It is publicly announced that Hannah knows whether someone picked a red card. It is publicly announced that Hannah does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Geraldine can now know whether Hannah can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hannah","Geraldine","Shawn"],"index":59619,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9819907546,"difficulty":0.0180092454}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Doris can now know whether Walter can know whether Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lindsey","Walter","Doris"],"index":55107,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995939136,"difficulty":0.0004060864}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Frances does not know whether Jennifer is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sara can now know that Frances is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sara","Clay","Jennifer","Frances"],"index":27589,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951511621,"difficulty":0.0048488379}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Marsha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Chase can now know that Patricia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marsha","Douglas","Chase","Patricia"],"index":18112,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983365536,"difficulty":0.0016634464}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Kathy can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathy","Evelyn","Lillian","Maria"],"index":20552,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997609258,"difficulty":0.0002390742}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Travis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Grant can now know whether Travis can know whether Travis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Henry","Grant","Travis"],"index":45047,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996414185,"difficulty":0.0003585815}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah knows whether Sarah is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Kathleen can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sarah","Kathleen"],"index":47387,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997807145,"difficulty":0.0002192855}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jayne's card is shown to Susan. Susan's card is shown to John. Beatrice's card is shown to Jayne. Susan's card is shown to Beatrice. John's card is shown to Beatrice. Beatrice's card is shown to Beatrice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jayne can now know whether Jayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","John","Jayne","Beatrice"],"index":52830,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8590472937,"difficulty":1.8590472937}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tom can now know that Adam can know whether Brenda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tom","Adam","Brenda"],"index":34292,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9968294501,"difficulty":0.0031705499}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryce's card is shown to Bryce. Sylvia's card is shown to Bryce. Bryce's card is shown to Justin. Justin's card is shown to Justin. Sylvia's card is shown to Justin. Bryce's card is shown to Sylvia. Sylvia's card is shown to Sylvia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bryce can now know whether Justin can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bryce","Justin","Sylvia"],"index":42676,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hope does not know whether or not everyone is thirsty. It is publicly announced that Hope does not know whether Paul is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Willie can now know that Hope can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Willie","Paul","Zoila","Hope"],"index":48212,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978394508,"difficulty":0.0021605492}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Valentine's forehead is muddy. It is publicly announced that Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] Agenta knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] 0","hypothesis":"Melissa can now know whether Jerry can know that Jerry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melissa","James","Jerry","Valentine"],"index":40445,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9782717824,"difficulty":0.0217282176}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Ruby can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ruby","Robert","Russell"],"index":25532,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985122085,"difficulty":0.0014877915}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Brandy. William's card is shown to William. Brandy's card is shown to Terry. William's card is shown to Terry. It is publicly announced that someone picked a red card. It is publicly announced that Terry does not know whether Terry picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Terry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Brandy can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brandy","William","Terry"],"index":16391,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.720779717,"difficulty":0.279220283}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Melanie is thirsty. It is publicly announced that Melanie is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] Agentd knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"David can now know that Norman can know that Norman is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Norman","Christin","Melanie","David"],"index":66495,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9850487113,"difficulty":0.0149512887}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emily's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Marisa can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shelly","Emily","Marisa"],"index":24018,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983496666,"difficulty":0.0016503334}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jon knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Rex can now know whether Carolyn can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Rex","Jessica","Jon"],"index":67168,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997108579,"difficulty":0.0002891421}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Rebecca can now know that John can know whether Sara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Sara","Donald","Rebecca"],"index":37468,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99973315,"difficulty":0.00026685}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Alice can now know that Ernest can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alice","Ernest"],"index":14024,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984617233,"difficulty":0.0015382767}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal's forehead is muddy. It is publicly announced that Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] Agentc knows that (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Crystal can now know that Roger can know that Rachel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Mireya","Crystal","Rachel"],"index":43647,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7307265401,"difficulty":1.7307265401}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Randy can now know whether John can know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathy","John","Edward","Randy"],"index":51443,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980727434,"difficulty":0.0019272566}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Andrew's card is shown to Andrew. Guadalupe's card is shown to Guadalupe. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Guadalupe can now know whether Andrew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Andrew","Guadalupe"],"index":17621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cindy does not know whether or not everyone is thirsty. It is publicly announced that Cindy knows whether Cindy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Alfred can now know that Cindy can know that Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alfred","Cindy","Paul"],"index":1821,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6760157347,"difficulty":0.3239842653}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellen does not know whether or not everyone is thirsty. It is publicly announced that Dennis knows whether Ellen is thirsty. It is publicly announced that Kimberly does not know whether Dennis is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Kimberly can now know that Ellen can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Ellen","Kimberly"],"index":64711,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982675314,"difficulty":0.0017324686}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Beatrice does not know whether or not everyone is thirsty. It is publicly announced that Harry knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Curtis can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beatrice","Curtis","Harry","Alfredo"],"index":38049,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5276905894,"difficulty":0.4723094106}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Margaret knows whether Anna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Danielle can now know whether Margaret can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Danielle","Anna"],"index":54898,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999628067,"difficulty":0.000371933}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason does not know whether Teresa is thirsty. It is publicly announced that Fatima is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Fatima can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Teresa","Fatima","Jason"],"index":1296,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985431433,"difficulty":0.0014568567}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randall does not know whether David is thirsty. It is publicly announced that David does not know whether Rhonda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Rhonda can now know whether Randall can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Randall","Rhonda","David"],"index":20477,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Robert can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Linda","Robert"],"index":276,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976027608,"difficulty":0.0023972392}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Saul's card is shown to Saul. Carol's card is shown to Saul. Aaron's card is shown to Saul. Andrew's card is shown to Saul. Saul's card is shown to Carol. Aaron's card is shown to Aaron. Saul's card is shown to Andrew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know whether Aaron can know that Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Saul","Carol","Aaron","Andrew"],"index":15223,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7080956697,"difficulty":0.2919043303}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katie knows whether someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Katie can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Albert","Katie"],"index":13231,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997729659,"difficulty":0.0002270341}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Doris is thirsty. It is publicly announced that Doris is not thirsty. It is publicly announced that Doris does not know whether Michael is thirsty. It is publicly announced that Michael knows whether Doris is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Michael can now know whether Doris can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Doris","Charles"],"index":50436,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978715181,"difficulty":0.0021284819}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly is not thirsty. It is publicly announced that Kimberly does not know whether Douglas is thirsty. It is publicly announced that William knows whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Douglas can now know whether William can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Douglas","William","Alyssa"],"index":56954,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999778688,"difficulty":0.000221312}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Palmer knows whether Danny's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Gina can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gina","Palmer","Adrian","Danny"],"index":56040,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9865923524,"difficulty":0.0134076476}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Shirley can now know that Steve can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shirley","Steve"],"index":51571,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997596145,"difficulty":0.0002403855}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Mary can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bonnie","Mary","Kevin","Ira"],"index":19636,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983408451,"difficulty":0.0016591549}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Christopher can now know whether Ida's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christopher","Raquel","Ida"],"index":32365,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995298386,"difficulty":0.0004701614}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Belinda is thirsty. It is publicly announced that Belinda knows whether Belinda is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Belinda can now know that Priscilla is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Belinda","Priscilla"],"index":35340,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6537300944,"difficulty":0.3462699056}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy. It is publicly announced that Frank does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Doris can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Doris","Frank"],"index":32855,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997250438,"difficulty":0.0002749562}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Troy can now know whether Amanda can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tammy","Troy","Amanda","Edward"],"index":52285,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996991158,"difficulty":0.0003008842}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hollie knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Dorothy can now know that Hollie can know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brenda","Dorothy","Hollie"],"index":67240,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977346659,"difficulty":0.0022653341}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Rebeca. Rebeca's card is shown to Jonathan. George's card is shown to Jonathan. Rebeca's card is shown to George. George's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jonathan can now know whether Rebeca can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebeca","Jonathan","George"],"index":33528,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8324301839,"difficulty":0.1675698161}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billie's card is shown to Billie. Billie's card is shown to Grover. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Grover can now know that Billie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Billie","Grover"],"index":20730,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982340336,"difficulty":0.0017659664}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sally","Robert","Joe","Linda"],"index":66506,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985488057,"difficulty":0.0014511943}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Michael can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Joyce","Helen","Michael"],"index":53142,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997348189,"difficulty":0.0002651811}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Libby does not know whether Libby's forehead is muddy. It is publicly announced that Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Libby can now know whether Sarah can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sarah","Libby"],"index":49545,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997820258,"difficulty":0.0002179742}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ariel is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Gladys can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ariel","Gladys"],"index":12349,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8794571757,"difficulty":1.8794571757}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Waldo can now know whether Hugo can know whether Waldo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hugo","Waldo"],"index":61350,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9981678724,"difficulty":0.0018321276}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know that Terry can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Terry","Charles","James"],"index":54924,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Earl knows whether Cristy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Russel can now know whether Cristy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Russel","Cristy","Earl","Thomas"],"index":27534,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997345805,"difficulty":0.0002654195}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renee knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Harry can now know that Renee can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harry","Renee","Barbara","Roberto"],"index":6634,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977707863,"difficulty":0.0022292137}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ofelia knows whether Nedra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Robert can now know that Nedra can know that Nedra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Ofelia","Nedra"],"index":35156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975090027,"difficulty":0.0024909973}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elisabeth knows whether Elisabeth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jay can now know whether Albert can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elisabeth","Albert","Jay"],"index":10088,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Leo can now know that Kayla can know whether Leo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beverly","Kayla","Leo"],"index":40032,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997418523,"difficulty":0.0002581477}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loraine knows whether Loraine's forehead is muddy. It is publicly announced that Patrica knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Patrica can now know whether Loraine can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Loraine","Marisa","Patrica"],"index":60553,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997768998,"difficulty":0.0002231002}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"George can now know that Elaine can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Elaine","Karen","Davida"],"index":54239,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9602401257,"difficulty":0.0397598743}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresita's card is shown to Carol. Angela's card is shown to Dorothy. Teresita's card is shown to Dorothy. Carol's card is shown to Teresita. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether Angela picked a red card. It is publicly announced that Carol picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 1 ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 1 ] 0","hypothesis":"Carol can now know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Dorothy","Angela","Teresita"],"index":52150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6824221611,"difficulty":0.3175778389}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Byron does not know whether Byron's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Crystal can now know whether Byron can know that Crystal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Byron","Crystal","Myrtle"],"index":49905,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9327763915,"difficulty":0.0672236085}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristen knows whether Peter is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kristen can now know whether Peter is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Peter","Kristen"],"index":33814,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9939777851,"difficulty":1.9939777851}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlotte knows whether Mary's forehead is muddy. It is publicly announced that Charlotte knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Charlotte can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Gala","Mary","Charlotte"],"index":20697,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998555243,"difficulty":0.001444757}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patrick does not know whether or not everyone is thirsty. It is publicly announced that Patrick does not know whether Sandra is thirsty. It is publicly announced that Patrick does not know whether Sallie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Sallie can now know whether Patrick can know whether Sandra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patrick","Sandra","Beverly","Sallie"],"index":61068,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984028935,"difficulty":0.0015971065}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fallon's card is shown to Fallon. Stella's card is shown to Fallon. Tristan's card is shown to Fallon. Tristan's card is shown to Stella. Tristan's card is shown to Tristan. It is publicly announced that someone picked a red card. It is publicly announced that Tristan does not know whether or not everyone picked a red card. It is publicly announced that Tristan does not know whether or not everyone picked a red card. It is publicly announced that Stella does not know whether Stella picked a red card. It is publicly announced that Fallon knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Tristan can now know that Stella picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Fallon","Stella","Tristan"],"index":49395,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5449723005,"difficulty":0.4550276995}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffery's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Ervin can now know that Jeffery can know that Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruth","Ervin","Jeffery","Lillie"],"index":40194,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928141236,"difficulty":0.0071858764}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jewell knows whether Jewell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Loren can now know that Loren's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Jewell","Loren","Amparo"],"index":54054,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998167634,"difficulty":0.001832366}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Dennis does not know whether Larry is thirsty. It is publicly announced that Rose does not know whether Murray is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Dennis can now know whether Rose can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Dennis","Larry","Murray"],"index":5720,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976561069,"difficulty":0.0023438931}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie's forehead is muddy. It is publicly announced that Willie knows whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Catherine can now know that Willie can know that Catherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Delores","Catherine","Willie"],"index":56185,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9369630814,"difficulty":0.0630369186}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jose knows whether Jose's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jose can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Robert","Sylvester","Marc"],"index":52942,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9924887419,"difficulty":0.0075112581}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Warren can now know whether Betty can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Todd","Betty","Warren"],"index":43940,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999722302,"difficulty":0.000277698}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fidel can now know that Alina can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Caleb","Fidel","Elise","Alina"],"index":16106,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983927608,"difficulty":0.0016072392}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kevin can now know whether Rodney's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kevin","Ana","Conrad","Rodney"],"index":16876,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997264743,"difficulty":0.0002735257}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anna knows whether someone is thirsty. It is publicly announced that Tamika does not know whether Anna is thirsty. It is publicly announced that Tamika is thirsty. It is publicly announced that Stephen does not know whether Anna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Judith can now know whether Judith is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Judith","Tamika","Anna","Stephen"],"index":37139,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9919114709,"difficulty":0.0080885291}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernard's card is shown to Patrick. Velma's card is shown to Velma. Velma's card is shown to Bernard. Bernard's card is shown to Bernard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Velma can now know whether Velma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Velma","Bernard"],"index":3910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9362908602,"difficulty":0.0637091398}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jane knows whether Jane is thirsty. It is publicly announced that Jane is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 3 ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 3 ] 0","hypothesis":"Jennifer can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Carl","Jane"],"index":52725,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997907281,"difficulty":0.0002092719}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to Hailey. Hailey's card is shown to Connie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Hailey can now know that Connie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Hailey","Connie","Tanya"],"index":42985,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984419942,"difficulty":0.0015580058}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mike's card is shown to Yvonne. Yvonne's card is shown to Jerri. Mike's card is shown to Jerri. Jerri's card is shown to Mike. Mike's card is shown to Mike. It is publicly announced that someone picked a red card. It is publicly announced that Jerri does not know whether Jerri picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Mike can now know that Jerri picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yvonne","Jerri","Mike"],"index":60403,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9934030175,"difficulty":0.0065969825}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jon's card is shown to Jon. Wilburn's card is shown to Jon. Patrick's card is shown to Jon. Jon's card is shown to Patricia. Wilburn's card is shown to Patricia. Patrick's card is shown to Wilburn. Jon's card is shown to Patrick. Wilburn's card is shown to Patrick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jon can now know that Patrick can know that Patrick picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jon","Patricia","Wilburn","Patrick"],"index":64191,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996237278,"difficulty":0.003762722}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esther's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"John can now know whether Esther can know that Jacqueline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Esther","John","Jacqueline"],"index":39617,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996620417,"difficulty":0.0003379583}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lisa can now know that Marvin can know whether Helen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Marvin","Lisa","Helen"],"index":31448,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963374138,"difficulty":0.0036625862}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Derek does not know whether James is thirsty. It is publicly announced that Maudie does not know whether Alicia is thirsty. It is publicly announced that Derek does not know whether Maudie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Derek can now know that Maudie can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maudie","Alicia","James","Derek"],"index":11284,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985240102,"difficulty":0.0014759898}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Phyllis can now know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alfred","Christopher","Phyllis","Charles"],"index":1733,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982376099,"difficulty":0.0017623901}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Nancy's forehead is not muddy. It is publicly announced that Randy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Randy can now know that Nancy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randy","Nancy"],"index":35522,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997543693,"difficulty":0.0002456307}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billie's card is shown to Thomas. Ora's card is shown to Thomas. Thomas's card is shown to Billie. Billie's card is shown to Billie. Thomas's card is shown to Ora. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Billie","Ora"],"index":24090,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983820915,"difficulty":0.0016179085}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Charles can now know that Jonathan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonathan","Joseph","Charles"],"index":16461,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9972502589,"difficulty":0.0027497411}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christina is not thirsty. It is publicly announced that Billy knows whether or not everyone is thirsty. It is publicly announced that Matthew is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Billy can now know whether Matthew can know whether Christina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Billy","Christina","Matthew"],"index":6432,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987725616,"difficulty":0.0012274384}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy. It is publicly announced that Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Daniel can now know whether Francis can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Francis","Karen"],"index":46059,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995767474,"difficulty":0.0004232526}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Anna. Donald's card is shown to Donald. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anna can now know that Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anna","Donald","James"],"index":50781,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981926084,"difficulty":0.0018073916}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judy knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Judy can now know whether Mark can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Judy","Sharon","Mark"],"index":8477,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996936321,"difficulty":0.0003063679}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether Ta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Martha can now know that Kiyoko can know that Martha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Ta","Kiyoko","Judith"],"index":23072,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983825684,"difficulty":0.0016174316}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew does not know whether Julia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Donovan can now know whether Julia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julia","Andrew","Myrtle","Donovan"],"index":59247,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.988819778,"difficulty":0.011180222}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Letitia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Morgan can now know that Morgan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Morgan","Letitia"],"index":33968,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978455305,"difficulty":0.0021544695}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan does not know whether Jonathan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Cody can now know whether Jonathan can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jonathan","John","Cody"],"index":55664,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980013967,"difficulty":0.0019986033}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ben does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Giovanni can now know that Florence can know whether Giovanni's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Giovanni","Ben","Florence","William"],"index":21566,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9969730377,"difficulty":0.0030269623}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Grace knows whether Melanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Roy can now know whether Grace can know that Jeanette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeanette","Grace","Roy","Melanie"],"index":30572,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996618032,"difficulty":0.0003381968}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Shante can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christina","Shante","Dana"],"index":2121,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983072281,"difficulty":0.0016927719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonita's forehead is not muddy. It is publicly announced that Debra knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Bonita can now know that Edward can know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Debra","Edward","Bonita","Andrew"],"index":67083,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955883026,"difficulty":0.0044116974}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deanna does not know whether Janetta is thirsty. It is publicly announced that Janetta does not know whether or not everyone is thirsty. It is publicly announced that Janetta does not know whether Allison is thirsty. It is publicly announced that Janetta does not know whether Allison is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Janetta can now know that Allison can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deanna","Janetta","Allison"],"index":8929,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997150302,"difficulty":0.0002849698}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terese's card is shown to Terese. Terese's card is shown to Jennifer. Anthony's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terese","Anthony","Jennifer"],"index":30146,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983377457,"difficulty":0.0016622543}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alfonso does not know whether Cindy is thirsty. It is publicly announced that Alfonso does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Mary can now know that Alfonso can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cindy","Alfonso","Mary"],"index":47824,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983302951,"difficulty":0.0016697049}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Millicent can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thomas","Millicent"],"index":48655,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985412359,"difficulty":0.0014587641}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neil knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Jerri can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jerri","Neil"],"index":2781,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997432828,"difficulty":0.0002567172}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Sylvia can now know that Edwin can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edwin","Jon","Sylvia","Robert"],"index":49357,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983951449,"difficulty":0.0016048551}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Stanley can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stanley","Robert","Janet"],"index":38299,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982597232,"difficulty":0.0017402768}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Curtis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Joe can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Curtis","Anthony","Joe"],"index":32442,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997834563,"difficulty":0.0002165437}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Erika can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Erika"],"index":8413,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985515475,"difficulty":0.0014484525}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donna can now know whether Ashley can know whether Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ashley","Donna","Robert"],"index":30379,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9894574285,"difficulty":0.0105425715}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph does not know whether Ralph's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ralph can now know whether Irene can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Irene","Ralph"],"index":55351,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9954317808,"difficulty":1.9954317808}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentb knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Amanda can now know that Patricia can know whether Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Amanda","Margaret","Patricia"],"index":40228,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997429252,"difficulty":0.0002570748}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helena knows whether Sally's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Kathleen can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathleen","Terri","Helena","Sally"],"index":28451,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982585311,"difficulty":0.0017414689}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Sarah is thirsty. It is publicly announced that Edith does not know whether Ronald is thirsty. It is publicly announced that Ronald does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know whether Edith is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edith","Ronald","Sarah","James"],"index":25461,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8387736678,"difficulty":0.1612263322}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael knows whether or not everyone is thirsty. It is publicly announced that Peggy is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Peggy can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sheila","Michael","Peggy"],"index":36700,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997289777,"difficulty":0.0002710223}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wesley's card is shown to Wesley. Penny's card is shown to Penny. Clara's card is shown to Penny. Clara's card is shown to Clara. Wesley's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Wesley can now know that Sarah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wesley","Penny","Clara","Sarah"],"index":64515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945300221,"difficulty":0.0054699779}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tony's card is shown to William. Mary's card is shown to Mary. Lawrence's card is shown to Tony. William's card is shown to Tony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lawrence can now know that Mary can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lawrence","William","Mary","Tony"],"index":58976,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7715022564,"difficulty":0.2284977436}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annette's card is shown to Eric. Eric's card is shown to Harold. Annette's card is shown to Annette. It is publicly announced that someone picked a red card. It is publicly announced that Eric picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Eric can now know whether Harold can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Harold","Annette"],"index":53066,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997119308,"difficulty":0.0002880692}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnson's card is shown to Leonard. Leonard's card is shown to Phyllis. Leonard's card is shown to Johnson. Phyllis's card is shown to Johnson. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Johnson can now know that Phyllis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leonard","Phyllis","Johnson"],"index":24731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982084036,"difficulty":0.0017915964}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tangela can now know whether Paul can know whether Albert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Albert","Tangela"],"index":16065,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999206841,"difficulty":0.000793159}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alex does not know whether Agnes is thirsty. It is publicly announced that Rory is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Alex can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Agnes","Alex","Rory"],"index":26011,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984336495,"difficulty":0.0015663505}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Peggy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Charles can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Peggy","Maria"],"index":13551,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984862208,"difficulty":0.0015137792}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"David can now know that Darrel can know that Darrel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darrel","Margaret","David"],"index":29683,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962490201,"difficulty":0.0037509799}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caleb's card is shown to Caleb. Merlin's card is shown to Caleb. Brian's card is shown to Merlin. Brian's card is shown to Brian. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know whether Merlin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Caleb","Merlin","Brian","Matthew"],"index":53724,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8760768771,"difficulty":0.1239231229}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether Tara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Felicitas can now know that Tara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Felicitas","Norma","Tara"],"index":59534,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984980822,"difficulty":0.0015019178}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Eleanor's card is shown to William. Ernest's card is shown to William. William's card is shown to Ernest. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Eleanor can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Eleanor","Ernest"],"index":5916,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982703924,"difficulty":0.0017296076}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Seth knows whether Ray's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Ray can now know whether Ray's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Terry","Seth","Ray"],"index":49784,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995517135,"difficulty":0.0004482865}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ricardo knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Ricardo can now know whether Christopher can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ricardo","Christopher"],"index":59535,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997742772,"difficulty":0.0002257228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dave does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Anna can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dave","Frank","Anna","Robert"],"index":59016,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983209968,"difficulty":0.0016790032}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corinna knows whether Corinna's forehead is muddy. It is publicly announced that Corinna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Corinna","David","Joseph","Jane"],"index":49586,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9757130146,"difficulty":0.0242869854}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald's forehead is muddy. It is publicly announced that Ronald knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Linda can now know whether Ronald can know whether Jerome's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronald","Linda","Jerome"],"index":34750,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999268949,"difficulty":0.000731051}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Gracie. Gracie's card is shown to Irene. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card. It is publicly announced that Carmen knows whether Carmen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Irene can now know that Carmen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gracie","Irene","Carmen"],"index":18215,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965211153,"difficulty":0.0034788847}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Mitchell does not know whether Jessica is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mitchell can now know that Jessica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Mitchell","Dorothy","Mike"],"index":59475,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978001714,"difficulty":0.0021998286}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy. It is publicly announced that David knows whether Clinton's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"David can now know whether Clinton can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Clinton"],"index":67489,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997344613,"difficulty":0.0002655387}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Shannon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Robert can now know that Shannon can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Billie","Shannon"],"index":3685,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99975878,"difficulty":0.00024122}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irving's card is shown to Irving. Irving's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Gregory knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Irving can now know that Irving picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Irving","Gregory"],"index":4747,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9928887486,"difficulty":0.0071112514}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether or not everyone's forehead is muddy. It is publicly announced that Shannon does not know whether Shannon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Laurence can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Guadalupe","Shannon","Jennifer","Laurence"],"index":61268,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9479383826,"difficulty":0.0520616174}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. John's card is shown to Mack. Robert's card is shown to Mack. It is publicly announced that someone picked a red card. It is publicly announced that Mack picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"John can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Mack","Robert"],"index":8924,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978721142,"difficulty":0.0021278858}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Teresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Terry can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Teresa","Thomas","Tristan","Terry"],"index":45506,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996850491,"difficulty":0.0003149509}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Thaddeus can now know that James can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessica","Thaddeus","James","Jose"],"index":53963,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983971715,"difficulty":0.0016028285}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Roland. Shirley's card is shown to Roland. Thomas's card is shown to Thomas. Roland's card is shown to Shirley. It is publicly announced that someone picked a red card. It is publicly announced that Roland knows whether Thomas picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Roland can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roland","Thomas","Shirley"],"index":54841,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bradley can now know that Lisa can know whether Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Bradley","Lisa","Brenda"],"index":55430,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997424483,"difficulty":0.0002575517}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan does not know whether Jonathan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Joy can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicole","Albert","Jonathan","Joy"],"index":66905,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9865483642,"difficulty":0.0134516358}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eileen's forehead is muddy. It is publicly announced that Eileen's forehead is muddy. It is publicly announced that Ada's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Eileen can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Tina","Ada","Eileen"],"index":54637,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984240532,"difficulty":0.0015759468}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Ann. Ann's card is shown to Phyllis. Phyllis's card is shown to Phyllis. It is publicly announced that someone picked a red card. It is publicly announced that Ann does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Phyllis can now know whether Ann can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ann","Phyllis"],"index":33180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Robert's card is shown to Helen. Debbie's card is shown to Robert. Robert's card is shown to Debbie. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Helen can now know whether Debbie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Robert","Debbie"],"index":5563,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996855259,"difficulty":0.0003144741}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Beverly's card is shown to Sheila. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card. It is publicly announced that Beverly does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Sheila","Beverly"],"index":21184,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998021245,"difficulty":0.001978755}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Israel knows whether Israel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Donald can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicole","Israel","Alfonso","Donald"],"index":9775,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985602498,"difficulty":0.0014397502}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy. It is publicly announced that Sharon does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Asuncion can now know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Asuncion","Bryan","Sharon"],"index":12642,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9056832194,"difficulty":1.9056832194}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Alice can now know that Anna can know that Anna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anna","Alice","Leslie"],"index":29697,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981701374,"difficulty":0.0018298626}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernestine's card is shown to Ernestine. Ernestine's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Janet can now know whether Ernestine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ernestine","Janet"],"index":25679,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994966984,"difficulty":0.0005033016}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is muddy. It is publicly announced that George knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"George can now know that Edward can know that Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mellie","Edward","George"],"index":33004,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9666774273,"difficulty":0.0333225727}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Austin's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Helen can now know whether Austin can know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Helen","Austin"],"index":6745,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5859262943,"difficulty":1.5859262943}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is not thirsty. It is publicly announced that Annette is not thirsty. It is publicly announced that John does not know whether Sherrie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Sherrie can now know whether Annette can know that Sherrie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sherrie","John","Mary","Annette"],"index":24383,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9788178802,"difficulty":0.0211821198}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yolanda's card is shown to Yolanda. Lissette's card is shown to Yolanda. Derek's card is shown to Yolanda. Yolanda's card is shown to Lissette. Lissette's card is shown to Lissette. Yolanda's card is shown to Derek. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alexis can now know whether Yolanda can know whether Yolanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alexis","Yolanda","Lissette","Derek"],"index":48680,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9974345565,"difficulty":0.0025654435}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tonie knows whether Tonie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Tonie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tonie","Rolland","Janyce"],"index":36075,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984213114,"difficulty":0.0015786886}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon does not know whether Edward is thirsty. It is publicly announced that Alecia does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Edward can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sharon","Edward","Phillip","Alecia"],"index":37666,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997101426,"difficulty":0.0002898574}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Sylvester knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Charles can now know that David can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Denise","David","Charles","Sylvester"],"index":63251,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997531772,"difficulty":0.0002468228}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Hermelinda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Hermelinda can now know that Andrew can know whether Hermelinda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrew","Hermelinda"],"index":51326,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997279048,"difficulty":0.0002720952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lois does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Edward can now know that Eleanor can know that Edward is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eleanor","Lois","Edward","Gregory"],"index":27055,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8585158587,"difficulty":0.1414841413}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shane's card is shown to Debra. Debra's card is shown to Shane. It is publicly announced that someone picked a red card. It is publicly announced that Shane does not know whether Shane picked a red card. It is publicly announced that Shane does not know whether Shane picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Shane can now know whether Debra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debra","Shane"],"index":10183,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.696952045,"difficulty":1.696952045}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suk does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robin can now know whether Humberto can know that Suk's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Suk","Francis","Robin","Humberto"],"index":42074,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9961056113,"difficulty":0.0038943887}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adele knows whether Adele's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Norma can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Isabel","Norma","Adele"],"index":21158,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982965589,"difficulty":0.0017034411}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mike is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Mike can now know whether Amy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Zachary","Mike","Jeremy","Amy"],"index":65238,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9912123084,"difficulty":0.0087876916}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rita's card is shown to Rita. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Rita can now know that Jill can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jill","Rita","Mary"],"index":10040,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7653334141,"difficulty":0.2346665859}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Earl knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Earl can now know that James can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Earl","James"],"index":36335,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999778688,"difficulty":0.000221312}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"April can now know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["April","Elizabeth","Marissa","Joseph"],"index":19553,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979392886,"difficulty":0.0020607114}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Micah is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Scott can now know whether Curtis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Micah","Marilyn","Curtis","Scott"],"index":35255,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942455888,"difficulty":0.0057544112}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Jason can now know that Richard can know that Tiffany is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jason","Tiffany","Richard","Evelyn"],"index":46092,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9736576676,"difficulty":0.0263423324}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Oliver can now know that John can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Linda","Oliver"],"index":11851,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984596968,"difficulty":0.0015403032}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Etta knows whether Etta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Cora can now know whether Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Cora","Etta"],"index":2805,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999730289,"difficulty":0.000269711}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doreen's card is shown to Doreen. Doreen's card is shown to Carolyn. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn knows whether someone picked a red card. It is publicly announced that Carolyn does not know whether Carolyn picked a red card. It is publicly announced that Carolyn does not know whether Carolyn picked a red card. It is publicly announced that Carolyn does not know whether Carolyn picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Carolyn can now know that Doreen can know that Carolyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Doreen","Carolyn"],"index":43141,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8951873183,"difficulty":0.1048126817}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lillian does not know whether Christopher is thirsty. It is publicly announced that Christopher does not know whether Marcia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Lillian can now know that Marcia can know whether Lillian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Aaron","Lillian","Marcia","Christopher"],"index":60690,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9808658361,"difficulty":0.0191341639}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tim is thirsty. It is publicly announced that Margaret does not know whether Anne is thirsty. It is publicly announced that John knows whether or not nobody is thirsty. It is publicly announced that John is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentd knows whether (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Tim can now know whether John can know that Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anne","Margaret","John","Tim"],"index":65089,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9891373515,"difficulty":0.0108626485}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd does not know whether Lloyd's forehead is muddy. It is publicly announced that Lloyd's forehead is muddy. It is publicly announced that Robert's forehead is muddy. It is publicly announced that Justin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Justin can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lloyd","Justin","Robert","Brian"],"index":1710,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980384707,"difficulty":0.0019615293}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Justin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Justin can now know whether James can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","James","Mary","Amanda"],"index":50469,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995182753,"difficulty":0.0004817247}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelli knows whether Kelli is thirsty. It is publicly announced that Lillian does not know whether Kelli is thirsty. It is publicly announced that Michelle does not know whether Alma is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kelli can now know that Lillian can know whether Kelli is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelli","Alma","Lillian","Michelle"],"index":51765,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9660450816,"difficulty":0.0339549184}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephanie's card is shown to Stephanie. Sherry's card is shown to Stephanie. Stephanie's card is shown to Kevin. Kevin's card is shown to Kevin. Stephanie's card is shown to Sherry. Ruth's card is shown to Sherry. It is publicly announced that someone picked a red card. It is publicly announced that Stephanie does not know whether Ruth picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kevin can now know that Stephanie can know whether Sherry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Kevin","Ruth","Sherry"],"index":64783,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9098221064,"difficulty":1.9098221064}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandy can now know that Cindy can know whether Cindy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cindy","Joyce","John","Sandy"],"index":49897,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962452054,"difficulty":0.0037547946}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Melanie can now know that Brandon can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melanie","Dorothy","Gregory","Brandon"],"index":3068,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996289015,"difficulty":0.0003710985}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Thomas can now know whether Leanora can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Thomas","Leanora"],"index":55524,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9882033467,"difficulty":0.0117966533}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nikia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Angela can now know whether Virginia can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nikia","Angela","Virginia"],"index":19115,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997666478,"difficulty":0.0002333522}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Olivia does not know whether James is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Olivia can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mireya","James","Olivia","Gregory"],"index":63684,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5417013168,"difficulty":0.4582986832}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Tina's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Mary can now know that Tina can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tina","Mary"],"index":51786,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972249269,"difficulty":0.0027750731}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Santos's forehead is muddy. It is publicly announced that Santos's forehead is muddy. It is publicly announced that Nathan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Nathan can now know that Derrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Derrick","Chance","Nathan","Santos"],"index":10475,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7350150943,"difficulty":0.2649849057}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tamra can now know that Robert can know that Juana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tamra","Juana","Linda","Robert"],"index":12400,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986258745,"difficulty":0.0013741255}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Earl's forehead is muddy. It is publicly announced that Arthur's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Arthur can now know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Earl","Anne","Arthur","James"],"index":23051,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997238517,"difficulty":0.0002761483}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Mary can now know whether Phillip can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phillip","Stephen","Mary"],"index":45687,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9944726825,"difficulty":0.0055273175}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Sol. Manuel's card is shown to Keith. Manuel's card is shown to Manuel. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Keith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sol","Keith","Manuel","William"],"index":26820,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9273033738,"difficulty":0.0726966262}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mae knows whether Kathy's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Kathy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathy","Richard","John","Mae"],"index":1937,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986573458,"difficulty":0.0013426542}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward does not know whether Edward's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Edward can now know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harry","Frederick","Edward","Melanie"],"index":25508,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9723310471,"difficulty":0.0276689529}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol does not know whether or not everyone is thirsty. It is publicly announced that Timothy knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Eleanor can now know that Timothy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Gregory","Timothy","Eleanor"],"index":55326,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9417921901,"difficulty":0.0582078099}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jasmin does not know whether or not everyone is thirsty. It is publicly announced that Cindy knows whether Cindy is thirsty. It is publicly announced that Andre is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Cindy can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jasmin","Andre","Cindy","Daniel"],"index":41622,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Vernell's forehead is muddy. It is publicly announced that Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Vernell can now know that Vernell's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Vernell","Melissa"],"index":906,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5111213923,"difficulty":1.5111213923}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether James is thirsty. It is publicly announced that Paula knows whether someone is thirsty. It is publicly announced that Paula does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Paula can now know that James can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Paula","James","Jeffrey"],"index":15771,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9599658847,"difficulty":0.0400341153}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Martha can now know whether Danielle can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Danielle","Martha"],"index":46616,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996042848,"difficulty":0.0003957152}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Robert can now know that Marie can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Marie","Robert","Joyce"],"index":9065,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997535348,"difficulty":0.0002464652}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan knows whether or not nobody's forehead is muddy. It is publicly announced that Juan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Bobby can now know that Juan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bobby","Juan"],"index":23770,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8146147728,"difficulty":1.8146147728}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan does not know whether or not everyone's forehead is muddy. It is publicly announced that Bryan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Bryan can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bryan","Leroy"],"index":47219,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9770844579,"difficulty":1.9770844579}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patrick does not know whether Irene is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Patrick can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patrick","Irene"],"index":47299,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Latesha. Latesha's card is shown to Curtis. Curtis's card is shown to Curtis. Curtis's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Latesha can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Latesha","Curtis","Donald"],"index":64701,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997233748,"difficulty":0.0002766252}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen does not know whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Anthony can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sarah","Anthony","Rita","Kathleen"],"index":50505,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.98606354,"difficulty":0.01393646}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Mary's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Gerald can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbera","Mary","Gerald","David"],"index":52760,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9862784743,"difficulty":0.0137215257}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Marvin. Jennie's card is shown to Marvin. Jason's card is shown to Marvin. Jennie's card is shown to Luis. Marvin's card is shown to Jason. Jennie's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marvin can now know that Jennie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","Luis","Jennie","Jason"],"index":52104,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982690811,"difficulty":0.0017309189}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria does not know whether Maria's forehead is muddy. It is publicly announced that Bruce knows whether someone's forehead is muddy. It is publicly announced that Bruce knows whether Randy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Maria can now know that Randy can know whether Randy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Bruce","Randy"],"index":47529,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9536517859,"difficulty":0.0463482141}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly's forehead is muddy. It is publicly announced that Ann does not know whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Betty can now know that Kelly can know that Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Kelly","Ann"],"index":54099,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5264855027,"difficulty":1.5264855027}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brigid","James"],"index":44313,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981826544,"difficulty":0.0018173456}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Racheal's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Racheal can now know whether Donald can know whether Racheal's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cheryll","Donald","Racheal"],"index":65380,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997153878,"difficulty":0.0002846122}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Martha can now know whether Anna can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Virginia","Vanessa","Martha","Anna"],"index":29894,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997406602,"difficulty":0.0002593398}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Gloria. Judith's card is shown to Gloria. Judith's card is shown to Judith. Brian's card is shown to Judith. Gloria's card is shown to Eric. Judith's card is shown to Eric. Gloria's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Gloria knows whether Gloria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Judith can now know that Brian can know that Brian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Judith","Eric","Brian"],"index":42080,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9780765772,"difficulty":0.0219234228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Ray is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Victoria can now know whether Richard can know whether Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Richard","Victoria","Ray"],"index":50375,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988986254,"difficulty":0.0011013746}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katia does not know whether Robbie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Pamelia can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pamelia","Robbie","Katia"],"index":34059,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963179827,"difficulty":0.0036820173}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy knows whether Amy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Robert can now know that Wendy can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Debra","Wendy","Amy"],"index":46182,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997583032,"difficulty":0.0002416968}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Harry can now know whether Louise can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Harry","Louise"],"index":3831,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999535203,"difficulty":0.000464797}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Woodrow's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Woodrow can now know that Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edward","James","Helen","Woodrow"],"index":14144,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9953932762,"difficulty":0.0046067238}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Troy's card is shown to Mark. Jame's card is shown to Mark. Jame's card is shown to Troy. Troy's card is shown to Jame. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether Mark picked a red card. It is publicly announced that Rebecca does not know whether or not everyone picked a red card. It is publicly announced that Mark knows whether Jame picked a red card. It is publicly announced that Troy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Troy can now know that Rebecca picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Rebecca","Troy","Jame"],"index":51549,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6476830244,"difficulty":0.3523169756}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis does not know whether Louis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mamie can now know whether Ernest can know whether Mamie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louis","Mamie","Ernest"],"index":52617,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984202385,"difficulty":0.0015797615}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Edwin. Brian's card is shown to Edwin. Vanessa's card is shown to Eve. Edwin's card is shown to Brian. Vanessa's card is shown to Brian. Eve's card is shown to Vanessa. It is publicly announced that someone picked a red card. It is publicly announced that Vanessa does not know whether Edwin picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Vanessa does not know whether Brian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Brian can now know whether Vanessa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edwin","Eve","Brian","Vanessa"],"index":10772,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994968176,"difficulty":0.0005031824}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry knows whether Leland's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Sherry can now know that Patricia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sherry","Ashley","Patricia","Leland"],"index":54204,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9895572066,"difficulty":0.0104427934}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theodore does not know whether Rebekah is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Horace can now know that Rebekah can know whether Horace is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebekah","Theodore","Horace"],"index":37700,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961685538,"difficulty":0.0038314462}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vicki knows whether Ben's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mary can now know that Vicki can know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ben","Mary","Vicki"],"index":14721,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997131228,"difficulty":0.0002868772}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adrian knows whether Bennie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Letitia can now know whether Adrian can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Letitia","Bennie","Adrian"],"index":17630,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997624755,"difficulty":0.0002375245}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Ramon can now know that William can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carey","William","Ramon"],"index":65961,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975316525,"difficulty":0.0024683475}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kathleen can now know whether Bobbye can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Susan","Bobbye","Mary"],"index":9449,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9831296802,"difficulty":0.0168703198}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ethel knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Harold can now know whether Ethel can know that Ethel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ethel","Katheryn","Harold"],"index":48187,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9260972142,"difficulty":0.0739027858}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ruth can now know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Gerardo","Donald","Sarah"],"index":8061,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8464677334,"difficulty":0.1535322666}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Sharon can now know that Victoria can know whether Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Victoria","Carla","Sharon"],"index":66935,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997144341,"difficulty":0.0002855659}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Edward can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","Leanna","Lynn","Marie"],"index":17553,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7166221738,"difficulty":0.2833778262}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Micah can now know that Joseph can know that Cassandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Micah","Cassandra","Carolyn"],"index":27449,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998494029,"difficulty":0.001505971}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Margo. Cecil's card is shown to Donald. Margo's card is shown to Cecil. Cecil's card is shown to Clarence. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Cecil does not know whether or not everyone picked a red card. It is publicly announced that Cecil picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 3 ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Donald can now know that Margo can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margo","Donald","Cecil","Clarence"],"index":38061,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5697113872,"difficulty":1.5697113872}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne does not know whether Yvonne's forehead is muddy. It is publicly announced that Victor knows whether or not nobody's forehead is muddy. It is publicly announced that Victor does not know whether Victor's forehead is muddy. It is publicly announced that Robert knows whether Yvonne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Yvonne can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yvonne","Victor","Robert"],"index":16363,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984167814,"difficulty":0.0015832186}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Jack. Jim's card is shown to Jack. Thelma's card is shown to Jack. Thelma's card is shown to Betty. Jack's card is shown to Jim. Betty's card is shown to Jim. Jim's card is shown to Jim. Jack's card is shown to Thelma. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1,2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1,2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thelma can now know whether Jack can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jack","Betty","Jim","Thelma"],"index":46735,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996882677,"difficulty":0.0003117323}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angelo does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Craig can now know whether Angelo is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Angelo","Cleo","Diane","Craig"],"index":44474,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9534801841,"difficulty":0.0465198159}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that Stephen can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Stephen","Joshua"],"index":24317,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997577071,"difficulty":0.0002422929}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mildred knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Teresa can now know that Teresa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Teresa","Carl","Lisa","Mildred"],"index":32923,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982878566,"difficulty":0.0017121434}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Etsuko. Kyle's card is shown to Etsuko. Charles's card is shown to David. David's card is shown to David. David's card is shown to Kyle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Charles can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Etsuko","Charles","David","Kyle"],"index":36204,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Matthew can now know whether James can know whether Matthew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","James","Matthew"],"index":60291,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983412027,"difficulty":0.0016587973}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Evelyn. Evelyn's card is shown to Brett. Evelyn's card is shown to Nolan. It is publicly announced that someone picked a red card. It is publicly announced that Nolan does not know whether or not everyone picked a red card. It is publicly announced that Evelyn picked a red card. It is publicly announced that Brett does not know whether Brett picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Nolan can now know that Brett can know that Brett picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Evelyn","Brett","Nolan"],"index":48885,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5165461898,"difficulty":0.4834538102}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is not thirsty. It is publicly announced that John knows whether or not everyone is thirsty. It is publicly announced that Michael does not know whether Kip is thirsty. It is publicly announced that Kip knows whether Kip is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kip can now know whether John can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Michael","Kip"],"index":37536,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975858927,"difficulty":0.0024141073}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Helen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Matthew can now know that Helen can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Mary","Matthew","Lenora"],"index":45119,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996995926,"difficulty":0.0003004074}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leon knows whether Leon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Bessie can now know whether Scott can know that Benjamin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leon","Benjamin","Bessie","Scott"],"index":10409,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985409975,"difficulty":0.0014590025}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bessie's forehead is muddy. It is publicly announced that Bessie knows whether someone's forehead is muddy. It is publicly announced that James knows whether William's forehead is muddy. It is publicly announced that Phillip does not know whether Phillip's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Bessie can now know whether James can know whether Phillip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","James","Phillip","Bessie"],"index":22863,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992824197,"difficulty":0.0007175803}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josephine's card is shown to Clarence. Clarence's card is shown to Josephine. Josephine's card is shown to Josephine. Josephine's card is shown to Marie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clarence can now know whether Clarence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clarence","Josephine","Marie"],"index":46503,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7029163837,"difficulty":1.7029163837}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Viola is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"John can now know whether Mark can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Viola","John"],"index":30197,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9956633449,"difficulty":0.0043366551}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emma does not know whether Sandra is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Sandra can now know whether Leo can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Emma","Leo"],"index":32102,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilfred knows whether Wilfred's forehead is muddy. It is publicly announced that Craig knows whether Samuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Alice can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Samuel","Alice","Wilfred","Craig"],"index":3722,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997476935,"difficulty":0.0002523065}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerome knows whether Linda's forehead is muddy. It is publicly announced that Jerome knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Jerome can now know whether Linda can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Jerome"],"index":5071,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.994643569,"difficulty":0.005356431}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hazel knows whether or not everyone's forehead is muddy. It is publicly announced that Hazel knows whether Hazel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Christopher can now know whether Hazel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christopher","Hazel"],"index":20877,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995268583,"difficulty":0.0004731417}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances knows whether or not nobody's forehead is muddy. It is publicly announced that Glenn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentd knows that (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know that Florence can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florence","Glenn","Frances","Michael"],"index":59790,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952203631,"difficulty":0.0047796369}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Charles is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","James","Charles","Paul"],"index":36133,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9779681563,"difficulty":0.0220318437}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy. It is publicly announced that Dan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Dan can now know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Doris","Michelle","Richard","Dan"],"index":25090,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5694473982,"difficulty":0.4305526018}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to David. David's card is shown to David. Bobby's card is shown to David. Bobby's card is shown to Bobby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","David","Bobby"],"index":26724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999725163,"difficulty":0.000274837}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Joanne. Michelle's card is shown to Joanne. Joanne's card is shown to Michelle. Michelle's card is shown to Vanessa. Ryan's card is shown to Vanessa. Vanessa's card is shown to Ryan. It is publicly announced that someone picked a red card. It is publicly announced that Michelle picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Vanessa can now know whether Ryan can know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joanne","Michelle","Vanessa","Ryan"],"index":56972,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988176227,"difficulty":0.0011823773}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Susie can now know whether William can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susie","James","Gina","William"],"index":46172,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7774161696,"difficulty":0.2225838304}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Anthony can now know whether Walter can know that Walter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Lala","Katheryn","Anthony"],"index":15880,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8226311207,"difficulty":1.8226311207}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Agnes's card is shown to Agnes. Agnes's card is shown to Arthur. Jessica's card is shown to Arthur. Agnes's card is shown to Jessica. Edward's card is shown to Jessica. Arthur's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Agnes can now know whether Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Agnes","Edward","Arthur","Jessica"],"index":61692,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8204336762,"difficulty":0.1795663238}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elinor knows whether or not nobody's forehead is muddy. It is publicly announced that Elinor knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Floyd can now know whether Elinor can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elinor","Floyd"],"index":30596,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.986908555,"difficulty":0.013091445}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Raymond. Stephen's card is shown to Raymond. Raymond's card is shown to Stephen. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Stephen picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Raymond can now know whether Mary can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raymond","Stephen","Mary"],"index":5968,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.734384656,"difficulty":0.265615344}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maureen knows whether or not everyone's forehead is muddy. It is publicly announced that Maureen knows whether someone's forehead is muddy. It is publicly announced that Maureen knows whether Maureen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Philip can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maureen","Philip"],"index":61712,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981923699,"difficulty":0.0018076301}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Will can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Will","Christopher"],"index":63416,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982665181,"difficulty":0.0017334819}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfred knows whether Alfred's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Alfred can now know that Meghann can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Meghann","Alfred"],"index":52017,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982714653,"difficulty":0.0017285347}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen knows whether someone is thirsty. It is publicly announced that Maurice knows whether Helen is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Helen can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Helen","Maurice"],"index":10281,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998606503,"difficulty":0.001393497}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roger knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Diana can now know whether Roger can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roger","Diana","Kim"],"index":62026,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995791316,"difficulty":0.0004208684}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sue knows whether Sue's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"George can now know that Julie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angie","Julie","Sue","George"],"index":26377,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999742806,"difficulty":0.000257194}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathryn knows whether Nelson's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Alfred can now know that Kathryn can know that Nelson's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Flora","Kathryn","Nelson","Alfred"],"index":27391,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978389144,"difficulty":0.0021610856}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Homer's card is shown to Homer. Marquetta's card is shown to Marquetta. Nancy's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marquetta can now know that Homer can know whether Marquetta picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Homer","Marquetta","Elizabeth","Nancy"],"index":17653,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8415921926,"difficulty":0.1584078074}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvette's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Quincy can now know that Yvette can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Yvette","Quincy"],"index":5470,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999785006,"difficulty":0.000214994}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry knows whether or not nobody is thirsty. It is publicly announced that Kimberly does not know whether Larry is thirsty. It is publicly announced that Larry is thirsty. It is publicly announced that Elaine does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kimberly can now know that Billy can know that Larry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Billy","Elaine","Larry"],"index":51221,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7936903834,"difficulty":0.2063096166}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Brian is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Brian can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Brian"],"index":21766,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997728467,"difficulty":0.0002271533}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether Edward's forehead is muddy. It is publicly announced that Edward knows whether Kathleen's forehead is muddy. It is publicly announced that Kathleen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] Agenta knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Edward can now know that Kenneth can know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edward","Kathleen","Kenneth"],"index":52408,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8917436004,"difficulty":0.1082563996}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerald knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Thomas can now know that Gerald can know that Diana is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Diana","Gerald","Thomas"],"index":38308,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998490572,"difficulty":0.001509428}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Frances can now know that Joseph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frances","Joseph","Audrey"],"index":36969,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997547269,"difficulty":0.0002452731}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Lisa can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Jordan","Arlene","David"],"index":31249,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983760118,"difficulty":0.0016239882}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Jerry knows whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that Jerry can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Paul","Jerry"],"index":20236,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999776423,"difficulty":0.000223577}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Angela can now know that Tricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","John","Tricia"],"index":30069,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9303663373,"difficulty":0.0696336627}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick knows whether or not nobody's forehead is muddy. It is publicly announced that Kristin's forehead is not muddy. It is publicly announced that Frederick's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"Bobby can now know that Frederick can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kristin","Lisa","Bobby","Frederick"],"index":2453,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984902143,"difficulty":0.0015097857}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Patti. Aaron's card is shown to Aaron. Grace's card is shown to Aaron. Patti's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Aaron picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Grace can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patti","Aaron","Grace"],"index":60008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984967709,"difficulty":0.0015032291}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Allan can now know whether Christopher can know whether Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Emmett","Allan","Christopher"],"index":11798,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995231628,"difficulty":0.0004768372}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kai's card is shown to Carrie. Paula's card is shown to Carrie. Kai's card is shown to Kai. Pat's card is shown to Kai. Kai's card is shown to Pat. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kai can now know that Carrie can know that Kai picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carrie","Kai","Pat","Paula"],"index":27965,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962911606,"difficulty":0.0037088394}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Catherine can now know that Paul can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sydney","Paul","Catherine"],"index":50235,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997480512,"difficulty":0.0002519488}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Ivan. Ivan's card is shown to Matthew. Matthew's card is shown to Matthew. Matthew's card is shown to Amy. Matthew's card is shown to Charles. Amy's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ivan can now know whether Matthew can know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ivan","Matthew","Amy","Charles"],"index":56491,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9964380264,"difficulty":0.0035619736}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice knows whether Curtis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Alice can now know that David can know whether Alice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Alice","Curtis"],"index":22416,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997193217,"difficulty":0.0002806783}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wanda does not know whether Alan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Alma can now know that Wanda can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wanda","Alma","Alan"],"index":7326,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Elizabeth is thirsty. It is publicly announced that Elizabeth knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Willie can now know that Elizabeth can know whether Elizabeth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Joseph","Juan","Elizabeth"],"index":37038,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991650581,"difficulty":0.0008349419}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tyler's forehead is not muddy. It is publicly announced that Cora does not know whether Cora's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Tyler can now know that Cora can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cora","Tyler","Richard"],"index":29455,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997810721,"difficulty":0.0002189279}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerry does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Kathryn can now know whether Jerry can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathryn","Jerry"],"index":42818,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994618297,"difficulty":0.0005381703}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annalee does not know whether Brenda is thirsty. It is publicly announced that Brenda does not know whether Harry is thirsty. It is publicly announced that Harry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Harry can now know that Harry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alice","Brenda","Harry","Annalee"],"index":7381,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9827693701,"difficulty":0.0172306299}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Philip. Samuel's card is shown to Judith. Judith's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Samuel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Judith can now know whether Philip picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Philip","Judith","Samuel"],"index":52510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7628574371,"difficulty":0.2371425629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Grace does not know whether Grace's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Marion can now know whether Christopher can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Grace","Christopher","Marion","Stacie"],"index":42506,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999761045,"difficulty":0.000238955}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodney's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Donald can now know whether Rodney can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Rodney","Elisha","Faye"],"index":21397,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virgil's card is shown to Rodney. Steven's card is shown to Rodney. Steven's card is shown to Stephen. Rodney's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Virgil can now know that Steven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rodney","Stephen","Virgil","Steven"],"index":28545,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982182384,"difficulty":0.0017817616}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Leon can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gregory","Leon","Steven","Richard"],"index":52746,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997635484,"difficulty":0.0002364516}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederic knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Darcey knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Thomas can now know that Frederic can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darcey","Thomas","Frederic","John"],"index":18401,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984998703,"difficulty":0.0015001297}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy. It is publicly announced that Olive's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"William can now know whether Olive can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tiffany","William","Hattie","Olive"],"index":52972,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997110963,"difficulty":0.0002889037}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Lora does not know whether Dennis is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Dennis does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Lora can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Dennis","Lora"],"index":6718,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997287393,"difficulty":0.0002712607}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorraine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Renee can now know that Renee's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Renee","William","Lorraine"],"index":47621,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9924686551,"difficulty":0.0075313449}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Dawn can now know whether Carmella can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Dawn","Carmella"],"index":15627,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996391535,"difficulty":0.0003608465}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that James knows whether Nadine's forehead is muddy. It is publicly announced that Nadine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"Nadine can now know that Jay can know whether Nadine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nadine","Jay","James"],"index":51726,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995897412,"difficulty":0.0004102588}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Margaret can now know that Wesley can know whether Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Kevin","Wesley","Rosanne"],"index":14515,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997486472,"difficulty":0.0002513528}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Michael can now know whether Cyndy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Cyndy","Connie","Walter"],"index":33935,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Maria can now know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kevin","Tiffaney","Maria"],"index":1063,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9645083547,"difficulty":0.0354916453}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tonya does not know whether or not everyone is thirsty. It is publicly announced that Patricia does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Patricia can now know that Tonya is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wendy","Patricia","Michael","Tonya"],"index":30076,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.935439527,"difficulty":1.935439527}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sean's card is shown to Sean. Gary's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sean can now know whether Robert can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Sean","Gary"],"index":11650,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9952183366,"difficulty":0.0047816634}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to Monica. Christina's card is shown to Monica. Christina's card is shown to Christina. It is publicly announced that someone picked a red card. It is publicly announced that Christina does not know whether or not everyone picked a red card. It is publicly announced that Christina does not know whether Monica picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Christina can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Monica","Christina"],"index":26742,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997825563,"difficulty":0.002174437}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas knows whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Brenton can now know whether Robin can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Brenton","Robin"],"index":22611,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977706671,"difficulty":0.0022293329}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Shayla can now know whether Jaime can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shayla","Jaime"],"index":6771,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9895695448,"difficulty":0.0104304552}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Dennis's forehead is not muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Dennis can now know whether Barbara can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barbara","Dennis"],"index":9657,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"William can now know that Harold can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Harold"],"index":37740,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981393814,"difficulty":0.0018606186}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas knows whether Thomas is thirsty. It is publicly announced that Christopher does not know whether Juan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Christopher can now know that Thomas can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Juan","Christopher"],"index":24348,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998517096,"difficulty":0.001482904}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Billy can now know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Billy","Alan","Maria","Winifred"],"index":27888,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984422326,"difficulty":0.0015577674}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Patricia can now know whether Dorothy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Patricia","Dorothy","Beth"],"index":57420,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.996154964,"difficulty":0.003845036}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dewey's card is shown to Beatrice. Dewey's card is shown to Dewey. Frances's card is shown to Dewey. Beatrice's card is shown to Frances. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dewey can now know that Beatrice can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Beatrice","Dewey","Frances"],"index":39709,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984422326,"difficulty":0.0015577674}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Paul can now know that Florence can know that Amber's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florence","Paul","Leta","Amber"],"index":16310,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9685589671,"difficulty":0.0314410329}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Keiko can now know whether Daniel can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Keiko","Daniel"],"index":62853,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9718570113,"difficulty":1.9718570113}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harlan's card is shown to Harlan. Thomas's card is shown to Thomas. Nicole's card is shown to Nicole. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nicole can now know whether Thomas can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harlan","Thomas","Nicole"],"index":24936,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9958406091,"difficulty":0.0041593909}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Winona does not know whether Matthew is thirsty. It is publicly announced that Winona knows whether or not nobody is thirsty. It is publicly announced that Matthew knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Matthew can now know whether Winona can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Matthew","Winona"],"index":26488,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9653937221,"difficulty":0.0346062779}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eric can now know that David can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Eric","Gale","Valerie"],"index":53594,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983611703,"difficulty":0.0016388297}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwayne knows whether someone's forehead is muddy. It is publicly announced that Janet knows whether Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Melody can now know that Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janet","Melody","Dwayne","Zachary"],"index":19517,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974561334,"difficulty":0.0025438666}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Milton can now know whether Reginald can know whether Reginald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Milton","Daniel","Reginald"],"index":63529,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996680021,"difficulty":0.0003319979}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Thomas can now know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dennis","Arthur","Thomas","Dorothy"],"index":47947,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9779309034,"difficulty":0.0220690966}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy. It is publicly announced that Angelo's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Michael can now know that Angelo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Traci","Diana","Angelo","Michael"],"index":27571,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.912219882,"difficulty":0.087780118}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Howard's card is shown to Nancy. Maria's card is shown to Howard. Howard's card is shown to Howard. Ralph's card is shown to Howard. Nancy's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Ralph does not know whether or not everyone picked a red card. It is publicly announced that Ralph does not know whether Ralph picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Ralph can now know that Nancy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Nancy","Howard","Ralph"],"index":2886,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947597384,"difficulty":0.0052402616}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juanita does not know whether or not everyone is thirsty. It is publicly announced that Jonathan does not know whether Edwin is thirsty. It is publicly announced that Juanita does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jonathan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edwin","Juanita","Jonathan"],"index":37146,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982282519,"difficulty":0.0017717481}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Helen can now know whether Christine can know that Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michele","Helen","Christine"],"index":32223,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994679093,"difficulty":0.0005320907}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neal knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Nicholas can now know that Neal can know that Nicholas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicholas","Neal","Holly"],"index":51033,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979444146,"difficulty":0.0020555854}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Frances. Frances's card is shown to Cori. Cori's card is shown to Cori. It is publicly announced that someone picked a red card. It is publicly announced that Cori knows whether Cori picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Frances can now know whether Cori can know that Frances picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frances","Cori"],"index":39831,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8199663162,"difficulty":0.1800336838}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Mary is thirsty. It is publicly announced that Kate does not know whether Mary is thirsty. It is publicly announced that Kate does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Kate can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Mary","Kate"],"index":11039,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9936980605,"difficulty":0.0063019395}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erlinda is thirsty. It is publicly announced that Erlinda does not know whether Anita is thirsty. It is publicly announced that Eugene does not know whether Anita is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Anita can now know whether Erlinda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eugene","Mark","Anita","Erlinda"],"index":21693,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8841704726,"difficulty":1.8841704726}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Steven can now know whether Connie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Connie","Michael","Tracey","Steven"],"index":18128,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967384934,"difficulty":0.0032615066}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bryan is thirsty. It is publicly announced that Bryan does not know whether James is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Bryan can now know whether James can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bryan","James"],"index":7340,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9968767166,"difficulty":0.0031232834}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Raymond. Eddie's card is shown to Mozelle. Raymond's card is shown to Eddie. Eddie's card is shown to Eddie. Bruce's card is shown to Eddie. Mozelle's card is shown to Bruce. It is publicly announced that someone picked a red card. It is publicly announced that Bruce does not know whether or not everyone picked a red card. It is publicly announced that Bruce does not know whether Bruce picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentb knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Mozelle can now know whether Bruce can know that Bruce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Mozelle","Eddie","Bruce"],"index":16513,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9416290522,"difficulty":0.0583709478}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Opal's card is shown to Opal. Mary's card is shown to Opal. Nina's card is shown to Nina. Mary's card is shown to Katherine. Opal's card is shown to Mary. Nina's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Opal can now know whether Katherine can know that Opal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Opal","Nina","Katherine","Mary"],"index":54487,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.795209527,"difficulty":0.204790473}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobbie's card is shown to Shari. Shari's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Frank's card is shown to Elizabeth. Shari's card is shown to Bobbie. Frank's card is shown to Bobbie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shari can now know whether Frank can know whether Bobbie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shari","Elizabeth","Frank","Bobbie"],"index":8881,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998013854,"difficulty":0.001986146}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeff knows whether Jeff's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeff","Robert","Mary"],"index":52295,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984727502,"difficulty":0.0015272498}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Arlene can now know whether Sally can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sally","Arlene"],"index":48947,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Mary. Judith's card is shown to Judith. Mary's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that Gerald knows whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mary can now know whether Gerald can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Judith","Gerald"],"index":40957,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5120469332,"difficulty":1.5120469332}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know that Trina can know that Johnnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Johnnie","Bruce","Trina","Michelle"],"index":53347,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984731078,"difficulty":0.0015268922}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Karen can now know that Hermine can know that Hermine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Bertha","Hermine","Karen"],"index":28179,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983763695,"difficulty":0.0016236305}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monica knows whether or not nobody is thirsty. It is publicly announced that Kyla does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Phyllis can now know that Monica can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Phyllis","Kyla","Monica"],"index":48105,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9929456115,"difficulty":0.0070543885}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Robert can now know whether Mamie can know whether Hazel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hazel","Mamie","Robert"],"index":32451,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997078776,"difficulty":0.0002921224}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marjorie does not know whether Kurtis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Lloyd can now know whether Lloyd is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lloyd","Kurtis","Edward","Marjorie"],"index":2419,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9925677776,"difficulty":0.0074322224}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danny knows whether Bernard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Bernard can now know whether Richard can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Richard","Danny","Bernard"],"index":13165,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9740748405,"difficulty":0.0259251595}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean does not know whether Jean's forehead is muddy. It is publicly announced that Jean does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Tara can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jean","Tara"],"index":44245,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9719544053,"difficulty":0.0280455947}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel does not know whether Joel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Verna can now know whether Charles can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Constance","Charles","Verna","Joel"],"index":62898,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9953795671,"difficulty":0.0046204329}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricardo's card is shown to Maryann. Anita's card is shown to Ricardo. Maryann's card is shown to Anita. Ricardo's card is shown to Anita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ricardo can now know that Maryann can know that Maryann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maryann","Ricardo","Anita"],"index":3021,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993830502,"difficulty":0.006169498}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tina's card is shown to Helen. Lisa's card is shown to Helen. Casey's card is shown to Casey. Lisa's card is shown to Casey. Helen's card is shown to Tina. Casey's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know that Tina can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Casey","Tina","Lisa"],"index":5586,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997143149,"difficulty":0.0002856851}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guillermo knows whether Leslie's forehead is muddy. It is publicly announced that Leslie knows whether Guillermo's forehead is muddy. It is publicly announced that Elwood does not know whether Elwood's forehead is muddy. It is publicly announced that Guillermo knows whether Guillermo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Leslie can now know whether Guillermo can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elwood","Guillermo","Leslie"],"index":62251,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patrick is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Patrick can now know that Patrick is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Eugene","Whitney"],"index":5397,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9800249934,"difficulty":0.0199750066}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Orville knows whether Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Darrell can now know that Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darrell","Orville","Matthew","Terri"],"index":35566,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975492358,"difficulty":0.0024507642}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Rodney is thirsty. It is publicly announced that Linda does not know whether Grace is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Grace can now know that Rodney can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rodney","Linda","Grace"],"index":39640,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997826219,"difficulty":0.0002173781}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Sandra. Cheryl's card is shown to Helen. Helen's card is shown to Helen. Rex's card is shown to Helen. Sandra's card is shown to Rex. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Cheryl picked a black card. It is publicly announced that Cheryl picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Helen can now know whether Cheryl can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Cheryl","Helen","Rex"],"index":50009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9943528175,"difficulty":0.0056471825}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows that (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Lamont can now know that Lauri can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tony","Kenneth","Lamont","Lauri"],"index":12551,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997858405,"difficulty":0.0002141595}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Arthur","Edwin"],"index":57018,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983509779,"difficulty":0.0016490221}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Nancy can now know that Brenda can know that Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nancy","Brenda"],"index":26556,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979402423,"difficulty":0.0020597577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brittany does not know whether Lela is thirsty. It is publicly announced that Richard knows whether someone is thirsty. It is publicly announced that Richard does not know whether Brittany is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Brittany can now know that Linda can know that Brittany is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brittany","Richard","Lela","Linda"],"index":10594,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9523077011,"difficulty":0.0476922989}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether or not everyone's forehead is muddy. It is publicly announced that Susan knows whether or not nobody's forehead is muddy. It is publicly announced that Cleo knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Cleo can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Susan","Cleo"],"index":67403,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971113205,"difficulty":0.0028886795}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon's forehead is muddy. It is publicly announced that Violeta does not know whether Violeta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Johnnie can now know that Violeta can know that Violeta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Violeta","Johnnie","Shannon"],"index":39302,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8854057789,"difficulty":0.1145942211}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda does not know whether Amanda's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Timothy can now know whether Amanda can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Amanda","Dennis","Timothy"],"index":61011,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997727275,"difficulty":0.0002272725}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Ashley can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ashley","David","Robert"],"index":64546,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998517096,"difficulty":0.001482904}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leola knows whether or not nobody is thirsty. It is publicly announced that Leola does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Randall can now know whether Leola is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leola","Jesse","Randall"],"index":18362,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9716892838,"difficulty":0.0283107162}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether someone's forehead is muddy. It is publicly announced that Irma does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Amy can now know that Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amy","Carol","Jeffrey","Irma"],"index":18231,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5258511901,"difficulty":0.4741488099}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"David can now know that Lara can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["David","Lara"],"index":42393,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976180196,"difficulty":0.0023819804}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jared does not know whether Stephanie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Robert can now know that Stephanie can know that Jared is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jared","Stephanie","Robert"],"index":65307,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977933168,"difficulty":0.0022066832}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anita's card is shown to Mike. Anita's card is shown to Anita. It is publicly announced that someone picked a red card. It is publicly announced that Mike picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Anita can now know that Mike can know that Mike picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mike","Anita"],"index":30747,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5794347525,"difficulty":1.5794347525}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shaun does not know whether or not everyone is thirsty. It is publicly announced that Teresa knows whether Teresa is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Teresa can now know that Shaun is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Teresa","Shaun"],"index":55614,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9409718513,"difficulty":1.9409718513}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jackie does not know whether John is thirsty. It is publicly announced that Dewayne does not know whether Tracey is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 2) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"John can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jackie","Tracey","Dewayne","John"],"index":62857,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985001087,"difficulty":0.0014998913}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Beth is not thirsty. It is publicly announced that Shelia knows whether Beth is thirsty. It is publicly announced that Beth does not know whether Sheri is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Shelia can now know whether Shelia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shelia","Theresa","Sheri","Beth"],"index":36937,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9929668903,"difficulty":0.0070331097}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Gloria can now know that Wendy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wendy","Gloria","Sheila","Cecil"],"index":30252,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7955985665,"difficulty":1.7955985665}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Howard. Anthony's card is shown to Howard. Howard's card is shown to Irene. Irene's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Irene can now know that Anthony can know whether Howard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Howard","Irene","Anthony"],"index":63438,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7196663022,"difficulty":0.2803336978}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathleen does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kathleen can now know whether Marlene can know whether Kathleen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Tony","Marlene"],"index":14009,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9981087446,"difficulty":0.0018912554}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Roy can now know whether Victor can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Victor","Roy","Max"],"index":37968,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996211529,"difficulty":0.0003788471}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Francis. Francis's card is shown to Janie. Janie's card is shown to Janie. Charles's card is shown to Janie. Francis's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Francis can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francis","Janie","Charles"],"index":4982,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8144107461,"difficulty":0.1855892539}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco does not know whether Francisco's forehead is muddy. It is publicly announced that Katie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Katie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Katie","Adam","Francisco"],"index":5305,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9512249231,"difficulty":0.0487750769}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marguerite knows whether Denise's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Marguerite can now know whether Sonja can know whether Sonja's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Denise","Marguerite","Kim","Sonja"],"index":25672,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995711446,"difficulty":0.0004288554}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Johnnie can now know whether Stephen can know whether Stephen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnnie","Anthony","Stephen"],"index":56862,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7732316852,"difficulty":0.2267683148}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maggie's forehead is muddy. It is publicly announced that Maggie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Maggie can now know whether Lawrence can know whether Dina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maggie","Dina","Arthur","Lawrence"],"index":4175,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996987581,"difficulty":0.0003012419}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Roseann can now know that Greg can know that Douglas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Greg","Dorothy","Roseann","Douglas"],"index":19789,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985247254,"difficulty":0.0014752746}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah does not know whether Archie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Archie can now know that Helen can know that Archie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Archie","Deborah","Helen"],"index":25365,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973546267,"difficulty":0.0026453733}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether Gloria's forehead is muddy. It is publicly announced that June knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Gloria can now know that Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gloria","Gregory","June","Steven"],"index":14969,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9421504736,"difficulty":0.0578495264}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Carlos's forehead is muddy. It is publicly announced that Clay knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Clay can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clay","Ben","Robert","Carlos"],"index":15869,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Lynn's card is shown to Michael. Roy's card is shown to Michael. Michael's card is shown to Lynn. Lynn's card is shown to Lynn. Roy's card is shown to Lynn. Lynn's card is shown to Roy. Roy's card is shown to Roy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Lynn","Roy"],"index":3790,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997729659,"difficulty":0.0002270341}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adam does not know whether or not everyone is thirsty. It is publicly announced that Adam does not know whether Bret is thirsty. It is publicly announced that Avery does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Avery can now know whether Gerald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Avery","Adam","Gerald","Bret"],"index":64531,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7816287875,"difficulty":0.2183712125}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lee's card is shown to John. John's card is shown to Lee. John's card is shown to Russell. Lee's card is shown to Russell. It is publicly announced that someone picked a red card. It is publicly announced that Russell does not know whether Russell picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Lee","Russell"],"index":63522,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997162223,"difficulty":0.0002837777}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fred's card is shown to Fred. Christie's card is shown to Fred. Christie's card is shown to Christie. John's card is shown to Christie. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Fred can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Fred","Christie","John"],"index":26280,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997268319,"difficulty":0.0002731681}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene knows whether or not nobody's forehead is muddy. It is publicly announced that Irene knows whether Bonnie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Irene can now know whether Bonnie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bonnie","Irene"],"index":27095,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994646907,"difficulty":0.0005353093}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christina does not know whether Juan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Juan can now know whether Riley can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christina","Riley","Michael","Juan"],"index":6276,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995298386,"difficulty":0.0004701614}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Madeline does not know whether Stefanie is thirsty. It is publicly announced that Nicole does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nicole can now know that Madeline is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Madeline","Stefanie","Connie","Nicole"],"index":33452,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9089654088,"difficulty":0.0910345912}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erica does not know whether or not everyone is thirsty. It is publicly announced that Clifford does not know whether Florence is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Clifford can now know whether Erica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Florence","Erica","Clifford"],"index":20271,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8112864494,"difficulty":1.8112864494}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether someone's forehead is muddy. It is publicly announced that Gary's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Gary can now know whether Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Daniel","Gary"],"index":36620,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995130301,"difficulty":0.0004869699}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald does not know whether Felicia is thirsty. It is publicly announced that Marc is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] 0","hypothesis":"Marc can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Felicia","Marc","Douglas","Donald"],"index":18788,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984862804,"difficulty":0.0015137196}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arthur does not know whether Loren is thirsty. It is publicly announced that Loren does not know whether Rose is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Rose can now know whether Arthur is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arthur","Roger","Rose","Loren"],"index":60834,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9936835766,"difficulty":0.0063164234}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Lucius can now know that William can know whether Lucius's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dianne","William","Lucius"],"index":51252,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99973768,"difficulty":0.00026232}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carroll's card is shown to Calvin. Bradley's card is shown to Carroll. Carroll's card is shown to Dustin. It is publicly announced that someone picked a red card. It is publicly announced that Carroll does not know whether or not everyone picked a red card. It is publicly announced that Carroll does not know whether or not everyone picked a red card. It is publicly announced that Calvin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Dustin can now know that Carroll picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Calvin","Carroll","Dustin","Bradley"],"index":52439,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9386384487,"difficulty":0.0613615513}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Sabrina can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Scot","Sabrina","Yolanda"],"index":44941,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether Jerry is thirsty. It is publicly announced that Anthony knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Anthony can now know that Jerry can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anthony","Jerry"],"index":47282,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.956305325,"difficulty":1.956305325}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty knows whether someone is thirsty. It is publicly announced that Tristan does not know whether Latonya is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Tristan can now know whether Latonya is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Tristan","Robert","Latonya"],"index":39886,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951411486,"difficulty":0.0048588514}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Mario's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Mario can now know that Thomas can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Lorraine","Mario"],"index":26960,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984257221,"difficulty":0.0015742779}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert is not thirsty. It is publicly announced that Brenda is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Brenda can now know that Angela is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brenda","Robert","Angela","Kenneth"],"index":8593,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9843668342,"difficulty":0.0156331658}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Helena is thirsty. It is publicly announced that Roy is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Helena can now know whether Michael can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roy","Michael","Lillian","Helena"],"index":41860,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983668923,"difficulty":0.0016331077}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Norbert can now know whether Leon can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norbert","Leon","Shirley","Elvira"],"index":24422,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997442365,"difficulty":0.0002557635}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard knows whether Betty's forehead is muddy. It is publicly announced that Mark knows whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Betty can now know whether Mark can know whether Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Howard","Betty","Mark"],"index":65978,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995396137,"difficulty":0.0004603863}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Susan. Susan's card is shown to Elinor. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susan can now know whether Brenda can know whether Elinor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Brenda","Elinor","James"],"index":62949,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988425374,"difficulty":0.0011574626}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Amanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Terri can now know whether Amanda can know whether Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Terri","Matthew"],"index":3462,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997084737,"difficulty":0.0002915263}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ira is thirsty. It is publicly announced that Joseph does not know whether Christina is thirsty. It is publicly announced that Ira knows whether Ira is thirsty. It is publicly announced that Joseph does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Christina can now know whether Ira is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Christina","Ira"],"index":19452,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7553185821,"difficulty":0.2446814179}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marion knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Leanne can now know that Thomasine can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomasine","Marion","Leanne"],"index":37489,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982561469,"difficulty":0.0017438531}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ian's card is shown to Matt. Matt's card is shown to Tracy. Ian's card is shown to Tracy. Tracy's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Ian knows whether Tracy picked a red card. It is publicly announced that Matt does not know whether Tracy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ian can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matt","Ian","Tracy"],"index":14525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998617053,"difficulty":0.001382947}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Tammy. Tammy's card is shown to Robert. John's card is shown to Robert. Tammy's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tammy can now know whether Robert can know whether Tammy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tammy","Robert","John"],"index":65994,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99774158,"difficulty":0.00225842}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bethany can now know that James can know that Vanessa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bethany","Frankie","Vanessa","James"],"index":15197,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986290932,"difficulty":0.0013709068}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Anna can now know that Paul can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Anna","James","Paul"],"index":39420,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978529215,"difficulty":0.0021470785}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"David can now know whether Julie can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Patricia","Julie"],"index":62038,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9875097275,"difficulty":0.0124902725}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that Edward knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edward","Yolanda","James"],"index":2353,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6014786363,"difficulty":0.3985213637}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jorge can now know that Joan can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joan","Jorge","Dennis"],"index":24993,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983338714,"difficulty":0.0016661286}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Kelly can know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","David","Kelly"],"index":15852,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979711175,"difficulty":0.0020288825}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Janet can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Franklin","Michael","Janet","Addie"],"index":33251,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Elliott. Elliott's card is shown to Brian. Brian's card is shown to Brian. Brian's card is shown to Kristin. Kristin's card is shown to Kristin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kristin can now know whether Kristin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elliott","Brian","Kristin"],"index":38469,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9316671491,"difficulty":0.0683328509}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Toni is thirsty. It is publicly announced that Mabel does not know whether Toni is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Toni can now know whether Terri is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mabel","Toni","David","Terri"],"index":30412,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7556734085,"difficulty":0.2443265915}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diann's card is shown to Joe. Joe's card is shown to Ismael. Diann's card is shown to Ismael. Joe's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ismael can now know whether Joe picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joe","Ismael","Diann","Melissa"],"index":24463,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8322622776,"difficulty":0.1677377224}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Annmarie is thirsty. It is publicly announced that Annmarie is not thirsty. It is publicly announced that John is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] Agentb knows that (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] 0","hypothesis":"John can now know that Chad can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annmarie","John","August","Chad"],"index":54392,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9956912398,"difficulty":0.0043087602}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"April can now know that Margaret can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","April","Margaret"],"index":26367,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5625842214,"difficulty":1.5625842214}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Casey knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Kellie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Casey","Kellie","Charles"],"index":14919,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981758595,"difficulty":0.0018241405}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to William. William's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Eric knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"William can now know that Eric can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Eric"],"index":31746,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9742281437,"difficulty":0.0257718563}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Mildred. Carol's card is shown to Mildred. Mildred's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Mildred knows whether Mildred picked a red card. It is publicly announced that Carol does not know whether or not everyone picked a red card. It is publicly announced that Carol does not know whether Carol picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Carol can now know whether Mildred can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mildred","Carol"],"index":34090,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997728467,"difficulty":0.0002271533}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Randy can now know whether Melissa can know whether Randy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kent","Melissa","Katherine","Randy"],"index":49300,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9981651902,"difficulty":0.0018348098}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not nobody's forehead is muddy. It is publicly announced that Ronald knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"John can now know that Ronald can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ronald","John"],"index":48109,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971455932,"difficulty":0.0028544068}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurice's card is shown to John. Darryl's card is shown to Darryl. Darryl's card is shown to Lucille. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Maurice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Darryl","Lucille","Maurice"],"index":34884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984058738,"difficulty":0.0015941262}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Elsie is thirsty. It is publicly announced that Jolene does not know whether Elsie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Elsie can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edna","David","Jolene","Elsie"],"index":65716,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9928319454,"difficulty":0.0071680546}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether Paulette is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Kimberly can now know whether Breann can know whether Breann is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","Paulette","Breann"],"index":45778,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9879081845,"difficulty":0.0120918155}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether or not everyone's forehead is muddy. It is publicly announced that Jane knows whether Jane's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joselyn can now know that Jane can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joselyn","Jane"],"index":24701,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999704659,"difficulty":0.000295341}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chantel's card is shown to Chana. Chana's card is shown to James. Chantel's card is shown to James. Chana's card is shown to Chantel. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Chana can now know whether James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chana","James","Chantel"],"index":6127,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997726083,"difficulty":0.0002273917}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Thomas. Thomas's card is shown to Ruby. Ruby's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether Ruby picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Thomas can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thomas","Ruby"],"index":23034,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9189993739,"difficulty":0.0810006261}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Scotty can now know whether Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Scotty","Robert","Derek"],"index":50341,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9858189821,"difficulty":0.0141810179}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Solomon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Solomon can now know that Larry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Larry","Marcus","Solomon"],"index":57287,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9488623142,"difficulty":0.0511376858}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deb's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Deb can now know that Janet can know that Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Deb","William","Janet"],"index":43365,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9838405252,"difficulty":0.0161594748}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Steve can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alta","Robert","Steve","Angelo"],"index":53405,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983172417,"difficulty":0.0016827583}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mike's card is shown to Florence. Mike's card is shown to Mike. Mike's card is shown to Will. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Will can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Florence","Mike","Will"],"index":55091,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983410835,"difficulty":0.0016589165}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether Jane's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jane can now know that Jose can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jolene","James","Jane","Jose"],"index":849,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984625578,"difficulty":0.0015374422}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emily does not know whether Jon is thirsty. It is publicly announced that Emily does not know whether Jon is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Emily can now know that Jon can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Emily","Jon"],"index":40147,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997829795,"difficulty":0.0002170205}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Carol. Jason's card is shown to Carmen. Carol's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carol","Fredrick","Carmen","Jason"],"index":38326,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bunny does not know whether or not everyone is thirsty. It is publicly announced that Bunny does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Gloria can now know that Bunny can know whether Gloria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gloria","Bunny"],"index":107,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.710380733,"difficulty":1.710380733}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terry's card is shown to Terry. Burton's card is shown to Terry. Mary's card is shown to Terry. Terry's card is shown to Burton. Burton's card is shown to Burton. Mary's card is shown to Burton. Burton's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terry can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terry","Burton","Mary"],"index":20220,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998380661,"difficulty":0.001619339}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that Alton's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Alton can now know whether Alton's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alton","Shirley","Juliana","David"],"index":13464,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6347115636,"difficulty":1.6347115636}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Jared. Marianne's card is shown to Jared. Jared's card is shown to Marianne. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Jared can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jared","Marianne"],"index":2173,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997215867,"difficulty":0.0002784133}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Patricia is thirsty. It is publicly announced that Daniel does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Daniel can now know that Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Daniel","Patricia"],"index":56142,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8785181642,"difficulty":0.1214818358}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy. It is publicly announced that Melissa knows whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Richard can now know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Melissa","Richard"],"index":40318,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7618764043,"difficulty":0.2381235957}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Donna can now know that Alla can know whether Wanda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donna","Alla","Wanda"],"index":14715,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996299744,"difficulty":0.0003700256}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Timothy. Bonita's card is shown to Timothy. Candace's card is shown to Candace. Bonita's card is shown to Bonita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Candace can now know whether Timothy can know whether Bonita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Candace","Bonita"],"index":54856,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987596273,"difficulty":0.0012403727}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Kimberly. Kimberly's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Kimberly does not know whether or not everyone picked a red card. It is publicly announced that John picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Kimberly can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Kimberly","Christina","John"],"index":6784,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7766483426,"difficulty":1.7766483426}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether or not nobody's forehead is muddy. It is publicly announced that Arthur's forehead is muddy. It is publicly announced that Kelly's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Kevin can now know that Jordan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jordan","Arthur","Kelly","Kevin"],"index":19834,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8559672832,"difficulty":0.1440327168}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George does not know whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ralph can now know that Kathleen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ralph","Benjamin","George","Kathleen"],"index":66221,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979478717,"difficulty":0.0020521283}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Cedric can now know that Carrie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Danny","Carrie","Janice","Cedric"],"index":11097,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984645844,"difficulty":0.0015354156}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henry's card is shown to Heriberto. Ralph's card is shown to Ralph. Henry's card is shown to Ralph. Henry's card is shown to John. John's card is shown to Henry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heriberto can now know that Henry can know whether Heriberto picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heriberto","Ralph","John","Henry"],"index":59266,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8191835284,"difficulty":0.1808164716}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Kevin knows whether Shannon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Shannon can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kevin","Kimberly","Shannon"],"index":41143,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999717772,"difficulty":0.000282228}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Kevin can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kevin","Michael"],"index":58215,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985237718,"difficulty":0.0014762282}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eileen knows whether Rebecca's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Rebecca can now know whether Eileen can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eileen","Amanda","Rebecca","Brian"],"index":54367,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9832205772,"difficulty":0.0167794228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether Carly can know that Carly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Todd","Carly","Cody","Charles"],"index":47162,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9750056267,"difficulty":0.0249943733}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Michael can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amanda","Jeremy","Michael","Maria"],"index":688,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976955056,"difficulty":0.0023044944}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Frances can now know that Marcellus can know whether Marcellus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marcellus","Jackie","Frances","Richard"],"index":32596,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9789645076,"difficulty":0.0210354924}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Doris. Doris's card is shown to Beverly. Doris's card is shown to Mary. Beverly's card is shown to Mary. William's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Doris does not know whether Doris picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"William can now know whether Doris can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doris","Beverly","William","Mary"],"index":54814,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994804263,"difficulty":0.0005195737}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Denise","Lyle","Grace","Richard"],"index":50036,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998232305,"difficulty":0.001767695}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether Kathy's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Lee can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hannah","Kathy","Lee"],"index":15432,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9960684776,"difficulty":0.0039315224}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eddie knows whether or not nobody's forehead is muddy. It is publicly announced that Eddie knows whether Katrina's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Eddie can now know that Katrina can know that Katrina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Katrina","Eddie"],"index":22774,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955513477,"difficulty":0.0044486523}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen is not thirsty. It is publicly announced that Erma does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] Agentd knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Deborah can now know that David can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Erma","David","Stephen","Deborah"],"index":35029,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9780948758,"difficulty":0.0219051242}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Stephen. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether or not everyone picked a red card. It is publicly announced that Stephen does not know whether or not everyone picked a red card. It is publicly announced that Stephen knows whether someone picked a red card. It is publicly announced that David knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Stephen can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Stephen","David"],"index":66918,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9138738513,"difficulty":1.9138738513}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know whether Donna can know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cindy","Debra","Sandra","Donna"],"index":12130,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995312691,"difficulty":0.0004687309}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"William can now know that Priscilla can know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Douglas","Priscilla"],"index":46063,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970830083,"difficulty":0.0029169917}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Heather can now know whether Heather is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Laura","Heather"],"index":63862,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984112978,"difficulty":0.0015887022}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doreen knows whether Doreen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Doreen can now know that Jennifer can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Doreen","Blake","Jennifer"],"index":62531,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983841181,"difficulty":0.0016158819}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Kimberly. Jose's card is shown to Jose. Kimberly's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that Annie does not know whether Annie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kimberly can now know that Kimberly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kimberly","Jose","Annie"],"index":40361,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.982169807,"difficulty":0.017830193}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jacqueline can now know whether Melissa can know that Jacqueline's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Jacqueline","Helen","Melissa"],"index":11186,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9895864129,"difficulty":0.0104135871}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Abraham's card is shown to Stella. Abraham's card is shown to Abraham. Bertha's card is shown to Abraham. Francine's card is shown to Abraham. Francine's card is shown to Bertha. Abraham's card is shown to Francine. Francine's card is shown to Francine. It is publicly announced that someone picked a red card. It is publicly announced that Bertha does not know whether Stella picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Francine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stella","Abraham","Bertha","Francine"],"index":15993,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984948635,"difficulty":0.0015051365}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether Donna's forehead is muddy. It is publicly announced that Frank knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Frank can now know that Randall's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Randall","Zachary","Donna","Frank"],"index":33815,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972731471,"difficulty":0.0027268529}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Cheryl. Robert's card is shown to Cheryl. Cheryl's card is shown to Shawn. Cheryl's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know whether Cheryl can know that Shawn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Cheryl","Shawn","Robert"],"index":63356,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9149885774,"difficulty":0.0850114226}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether Mattie is thirsty. It is publicly announced that Janelle does not know whether Leonard is thirsty. It is publicly announced that Nancy does not know whether Janelle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Mattie can now know whether Nancy can know whether Mattie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janelle","Leonard","Mattie","Nancy"],"index":5909,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978456497,"difficulty":0.0021543503}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know whether John can know whether Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tina","John","Gregory","Bonnie"],"index":38818,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9968217611,"difficulty":0.0031782389}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly does not know whether or not everyone's forehead is muddy. It is publicly announced that Anabel knows whether someone's forehead is muddy. It is publicly announced that Kelly does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kelly can now know whether Anabel can know that Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Kelly","Anabel","Sam"],"index":61362,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9960035682,"difficulty":0.0039964318}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leroy's card is shown to Leroy. Grace's card is shown to Leroy. Grace's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Grace knows whether or not everyone picked a red card. It is publicly announced that Grace knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Grace can now know that Leroy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leroy","Grace"],"index":21521,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997006655,"difficulty":0.0002993345}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ardelia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Rebecca can now know that David can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ardelia","Rebecca","David"],"index":8400,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997801185,"difficulty":0.0002198815}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Marvin. Margaret's card is shown to Margaret. Sara's card is shown to Matthew. Margaret's card is shown to Matthew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marvin can now know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marvin","Sara","Margaret","Matthew"],"index":30940,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8896787167,"difficulty":0.1103212833}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marquita's card is shown to Hattie. Marquita's card is shown to Eric. Jack's card is shown to Jack. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jack can now know that Eric can know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hattie","Eric","Jack","Marquita"],"index":6238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9627619982,"difficulty":0.0372380018}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Nancy can now know whether Rachel can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Clifford","Rachel"],"index":45358,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99955374,"difficulty":0.00044626}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ben knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Michael can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ben","Michael"],"index":8233,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997356534,"difficulty":0.0002643466}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Kathleen's card is shown to Calvin. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Kathleen can now know that Mary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Kathleen","Calvin"],"index":8214,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983302951,"difficulty":0.0016697049}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Gloria. Jason's card is shown to Elizabeth. Jason's card is shown to Leah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leah can now know that Elizabeth can know that Gloria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Elizabeth","Leah","Jason"],"index":54380,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983238578,"difficulty":0.0016761422}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew does not know whether Andrew's forehead is muddy. It is publicly announced that Andrew does not know whether Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Andrew can now know whether Kathy can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrew","Kathy"],"index":17958,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia knows whether or not everyone's forehead is muddy. It is publicly announced that Benjamin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Joshua can now know that Julia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Joshua","Benjamin","Julia"],"index":23393,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.965573132,"difficulty":0.034426868}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Ann. Kimberly's card is shown to Kimberly. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Kimberly can now know that Kimberly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ann","Kimberly"],"index":28433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9385529757,"difficulty":0.0614470243}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Laura. Laura's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Ruby can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Laura","Ruby"],"index":53534,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997567534,"difficulty":0.0002432466}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Vicki knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Vicki","Pamela"],"index":31865,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9940617681,"difficulty":0.0059382319}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Bruce's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"Tamara can now know that Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tamara","Bruce","Renee","Carol"],"index":34677,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9883710146,"difficulty":0.0116289854}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynn's card is shown to Christopher. Christopher's card is shown to Shelley. Shelley's card is shown to Debra. Lynn's card is shown to Debra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know whether Lynn can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Shelley","Lynn","Debra"],"index":39130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997109771,"difficulty":0.0002890229}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nellie does not know whether Ronnie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Margie can now know that Melissa can know that Nellie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margie","Nellie","Ronnie","Melissa"],"index":61170,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997871995,"difficulty":0.002128005}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Mary can now know that Barbara can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Mary","Diane"],"index":25014,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982355833,"difficulty":0.0017644167}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know that Noah can know that Michele is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Troy","Dorothy","Noah","Michele"],"index":67366,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984768033,"difficulty":0.0015231967}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Ann's card is shown to Barbara. Helen's card is shown to Barbara. Barbara's card is shown to Ann. Ann's card is shown to Ann. Barbara's card is shown to Helen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ann can now know whether Barbara can know that Nicholas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicholas","Barbara","Ann","Helen"],"index":10313,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9731701612,"difficulty":0.0268298388}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Erin knows whether Azalee's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Erin can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erin","Azalee"],"index":46219,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986283779,"difficulty":0.0013716221}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Barbara can now know whether Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edward","Barbara"],"index":41714,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9929248095,"difficulty":0.0070751905}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Donna can now know that Jose can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christine","Jose","Donna"],"index":60104,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8323594332,"difficulty":1.8323594332}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Muriel knows whether someone's forehead is muddy. It is publicly announced that Muriel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Muriel can now know whether Alex can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Muriel","Alex"],"index":8911,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997215867,"difficulty":0.0002784133}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynne knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Maria can now know that Lynne can know whether Eileen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eileen","Lynne","Maria"],"index":7636,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996147156,"difficulty":0.0003852844}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randy is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jennifer can now know whether Robin can know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robin","Jennifer","Randy"],"index":31794,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9982478619,"difficulty":1.9982478619}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Hubert","Maria","Louis"],"index":54648,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978901744,"difficulty":0.0021098256}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Gilberto knows whether Terry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Terry can now know that Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lester","Terry","Gilberto","Deborah"],"index":59878,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9967563748,"difficulty":0.0032436252}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick's forehead is muddy. It is publicly announced that Johanna does not know whether Johanna's forehead is muddy. It is publicly announced that Patricia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Johanna can now know whether Johanna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patrick","Patricia","Johanna"],"index":56624,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8444281816,"difficulty":0.1555718184}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Heather knows whether Heather's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Heather","Gloria","Irene"],"index":13447,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9957921505,"difficulty":0.0042078495}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Miriam's card is shown to Louise. Louise's card is shown to Miriam. It is publicly announced that someone picked a red card. It is publicly announced that Louise does not know whether Louise picked a red card. It is publicly announced that Louise does not know whether Louise picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Miriam can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Louise","Miriam"],"index":30212,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8714039922,"difficulty":1.8714039922}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Edith can now know that Charles can know whether Edith is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Scott","Edith","Charles"],"index":13035,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7888970971,"difficulty":0.2111029029}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Tina is not thirsty. It is publicly announced that Tina is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] [ ! ~(4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] [ ! ~(4) ] 0","hypothesis":"Walter can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ross","Kathy","Walter","Tina"],"index":59224,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997332692,"difficulty":0.0002667308}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rita does not know whether Sarah is thirsty. It is publicly announced that Jason does not know whether Sarah is thirsty. It is publicly announced that Rita knows whether Rita is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Sarah can now know whether Sarah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jason","Sarah","Rita"],"index":63330,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9981997013,"difficulty":0.0018002987}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith knows whether Sheryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Adam can now know whether Edith can know whether Adam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Adam","Edith","Sheryl","Michael"],"index":31851,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997184873,"difficulty":0.0002815127}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Yvonne's card is shown to James. James's card is shown to Cheryl. Cheryl's card is shown to Cheryl. James's card is shown to Yvonne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Yvonne can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Cheryl","Yvonne"],"index":67,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9923007488,"difficulty":0.0076992512}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emma does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jeanie can now know whether Linda can know whether Linda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeanie","Emma","Ralph","Linda"],"index":14287,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9952294827,"difficulty":0.0047705173}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robert can now know whether Julie can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Julie","Robert"],"index":52331,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997013211,"difficulty":0.0002986789}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. William's card is shown to Anna. William's card is shown to Stephen. Stephen's card is shown to Stephen. Barbara's card is shown to Stephen. Stephen's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know that Stephen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Anna","Stephen","Barbara"],"index":49553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979209304,"difficulty":0.0020790696}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Gary. Harold's card is shown to Frank. Harold's card is shown to Jean. Frank's card is shown to Jean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harold","Gary","Frank","Jean"],"index":19463,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Jan. Justina's card is shown to Justina. Justina's card is shown to Rickey. Rickey's card is shown to Rickey. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know whether Jan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jan","Justina","William","Rickey"],"index":59855,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9884747863,"difficulty":0.0115252137}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angel knows whether Susan's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Susan can now know whether Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Angel","Mark"],"index":49992,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9810381532,"difficulty":0.0189618468}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Robert can now know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Robert","Matthew"],"index":6384,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9953728318,"difficulty":0.0046271682}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentc knows that (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Mary can now know that Julian can know that Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Julian","Mary","Jose"],"index":16158,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994179368,"difficulty":0.005820632}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Drew's card is shown to Robert. Robert's card is shown to James. James's card is shown to James. Drew's card is shown to James. Robert's card is shown to Drew. James's card is shown to Drew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Drew can now know whether James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","James","Drew"],"index":9977,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9927138686,"difficulty":1.9927138686}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is muddy. It is publicly announced that Ana knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Lelia can now know that Kevin can know that Lelia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lelia","Kevin","Ana"],"index":8732,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9852308035,"difficulty":0.0147691965}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alana knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Brenda can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracy","Alana","Brenda"],"index":54920,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985357523,"difficulty":0.0014642477}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether someone's forehead is muddy. It is publicly announced that Raymond knows whether or not everyone's forehead is muddy. It is publicly announced that Roger's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Merry can now know that Justin can know that Justin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Justin","Raymond","Merry"],"index":2580,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9757427573,"difficulty":0.0242572427}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fanny knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Fanny can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Henry","Fanny"],"index":30453,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981091022,"difficulty":0.0018908978}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether Kathleen's forehead is muddy. It is publicly announced that Lexie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Lexie can now know whether Lexie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathleen","Lisa","Lexie","Sharon"],"index":49909,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7187421918,"difficulty":0.2812578082}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jay's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Elenore can now know that Jay can know that Jay's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jay","Dale","Elenore"],"index":63140,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9351617098,"difficulty":0.0648382902}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Monte. Thomas's card is shown to Thomas. Cheryl's card is shown to Cheryl. Thomas's card is shown to Danny. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know whether Cheryl can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monte","Thomas","Cheryl","Danny"],"index":9053,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9925910234,"difficulty":0.0074089766}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Courtney's card is shown to Charles. Charles's card is shown to Courtney. Courtney's card is shown to Courtney. Courtney's card is shown to Douglas. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Douglas does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Douglas can now know that Charles can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Courtney","Douglas"],"index":61069,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5265925527,"difficulty":0.4734074473}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darlene knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Stacy can now know whether Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Ronald","Stacy","Darlene"],"index":38202,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999576509,"difficulty":0.000423491}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vera is thirsty. It is publicly announced that Vera does not know whether or not everyone is thirsty. It is publicly announced that Vera does not know whether or not everyone is thirsty. It is publicly announced that Maria does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Vera can now know whether Evelyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Vera","Maria"],"index":45448,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8187332153,"difficulty":1.8187332153}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Craig can now know that John can know that Craig's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jacqueline","John","Craig"],"index":63689,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984298348,"difficulty":0.0015701652}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luanne knows whether Arthur's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Nicholas can now know that Luanne can know that Nicholas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arthur","Maurice","Luanne","Nicholas"],"index":4061,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984190464,"difficulty":0.0015809536}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbra does not know whether David is thirsty. It is publicly announced that Carmen does not know whether Barbra is thirsty. It is publicly announced that Carmen does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"David can now know that Carmen can know that Barbra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbra","Carmen","David"],"index":65763,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9881333709,"difficulty":0.0118666291}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Keith's card is shown to Robert. Robert's card is shown to Keith. Marcia's card is shown to Keith. Marcia's card is shown to Marcia. It is publicly announced that someone picked a red card. It is publicly announced that Keith knows whether someone picked a red card. It is publicly announced that Marcia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Robert can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Keith","Marcia"],"index":16019,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9853736162,"difficulty":0.0146263838}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosie knows whether Rosie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Rosie can now know that Timothy can know that Rosie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Timothy","Rosie"],"index":27727,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9944175482,"difficulty":0.0055824518}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robin does not know whether Salvador is thirsty. It is publicly announced that Robin does not know whether Beverly is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Beverly can now know that Robin can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Salvador","Robin","Beverly"],"index":30323,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9356546402,"difficulty":0.0643453598}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kathryn can now know that Derrick can know whether Derrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olivia","Derrick","Karen","Kathryn"],"index":6534,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996237755,"difficulty":0.0003762245}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Derrick. Derrick's card is shown to Steven. Norman's card is shown to Steven. Steven's card is shown to Clara. Derrick's card is shown to Norman. Clara's card is shown to Norman. It is publicly announced that someone picked a red card. It is publicly announced that Norman does not know whether Norman picked a red card. It is publicly announced that Derrick knows whether or not nobody picked a red card. It is publicly announced that Clara picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Clara can now know that Derrick can know whether Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Derrick","Steven","Clara","Norman"],"index":32002,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5091288686,"difficulty":1.5091288686}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mellisa's card is shown to Hae. Matilda's card is shown to Matilda. Hae's card is shown to Mellisa. It is publicly announced that someone picked a red card. It is publicly announced that Mellisa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Mellisa can now know whether Hae picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hae","Matilda","Mellisa"],"index":15288,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8432338834,"difficulty":0.1567661166}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen knows whether Carmen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Carmen can now know that Jackeline can know whether Carmen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephani","Jackeline","Carmen"],"index":48595,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996297359,"difficulty":0.0003702641}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Faye can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Faye","Tony","Jimmie"],"index":59179,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982246757,"difficulty":0.0017753243}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Dana can now know whether Andrew is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andrew","Juan","Dana"],"index":48489,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9960657954,"difficulty":0.0039342046}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamel knows whether Jamel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Chris can now know whether Chris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jamel","Chris","Sandra"],"index":53934,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9905211926,"difficulty":1.9905211926}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard knows whether Richard is thirsty. It is publicly announced that Maren does not know whether or not everyone is thirsty. It is publicly announced that Stephanie does not know whether or not everyone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Maren can now know that James can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Maren","Stephanie","Richard"],"index":689,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5508538485,"difficulty":1.5508538485}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Craig can now know that Ricky's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Ricky","Augustus","Craig"],"index":15416,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986435771,"difficulty":0.0013564229}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Albert does not know whether Shelley is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Albert can now know whether Peter can know whether Carol is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shelley","Carol","Albert","Peter"],"index":3655,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991210103,"difficulty":0.0008789897}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte does not know whether or not everyone is thirsty. It is publicly announced that Mattie knows whether Mattie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mattie can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mattie","Charlotte"],"index":50867,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997130036,"difficulty":0.0002869964}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rebecca does not know whether Aileen is thirsty. It is publicly announced that Rebecca knows whether or not everyone is thirsty. It is publicly announced that Rebecca does not know whether Derek is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Rebecca can now know whether Aileen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rebecca","Aileen","Derek"],"index":44283,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8640150428,"difficulty":0.1359849572}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelby's card is shown to Shelby. Walter's card is shown to Shelby. Frances's card is shown to Shelby. Walter's card is shown to Walter. Walter's card is shown to Frances. It is publicly announced that someone picked a red card. It is publicly announced that Walter knows whether or not everyone picked a red card. It is publicly announced that Frances knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Shelby can now know that Walter can know that Shelby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shelby","Walter","Frances"],"index":54504,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6714131236,"difficulty":0.3285868764}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Trina knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Trina can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carol","Trina","Kate","Ann"],"index":31031,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997470975,"difficulty":0.0002529025}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jean does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Jean knows whether someone is thirsty. It is publicly announced that Jean knows whether Jean is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Frances can now know whether Jean can know that Frances is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jean","Frances"],"index":16867,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9932946563,"difficulty":0.0067053437}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Richard can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Richard","David"],"index":50786,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997772574,"difficulty":0.0002227426}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy. It is publicly announced that Bernard knows whether or not everyone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"William can now know that Bernard can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Bernard","Wilfredo","William"],"index":36951,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997110963,"difficulty":0.0002889037}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Joseph. Joseph's card is shown to Duane. It is publicly announced that someone picked a red card. It is publicly announced that Duane does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Duane can now know that Joseph can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joseph","Duane"],"index":32350,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978475571,"difficulty":0.0021524429}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is not muddy. It is publicly announced that Buford knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Patricia can now know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Buford","Leona"],"index":11177,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9868207574,"difficulty":0.0131792426}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Gary can now know that Darrell can know whether Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrell","Charles","Gary","Evelyn"],"index":9872,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995967746,"difficulty":0.0004032254}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Larry can now know that Tameka can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Tameka","Larry","Suzanne"],"index":14335,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997819066,"difficulty":0.0002180934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George does not know whether George's forehead is muddy. It is publicly announced that Georgia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Gertrude can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Scott","Gertrude","Georgia"],"index":19296,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998575449,"difficulty":0.001424551}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maribel is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Kathy can now know that Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathy","Maribel","Thomas"],"index":31779,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970081449,"difficulty":0.0029918551}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Myrna can now know that Charles can know whether Crystal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Myrna","Charles","Crystal","David"],"index":61711,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9433391094,"difficulty":0.0566608906}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Dean is thirsty. It is publicly announced that Dean does not know whether Anne is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Roger can now know whether Roger is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Roger","Dean","Anne"],"index":51730,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9956541061,"difficulty":0.0043458939}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether April is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Stephen can now know whether Barbara can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Eric","April","Barbara"],"index":60148,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl knows whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"William can now know that Darlene can know whether Darlene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carl","Darlene","William"],"index":39525,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9894134998,"difficulty":1.9894134998}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Robert. Robert's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Michael can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Michael"],"index":8217,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985182881,"difficulty":0.0014817119}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Keith. Keith's card is shown to Keith. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Keith picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Keith can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Keith","Rhonda"],"index":8618,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997820258,"difficulty":0.0002179742}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joshua can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Casey","John","Joshua"],"index":30107,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982957244,"difficulty":0.0017042756}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Phillip can now know whether Thomas can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Phillip","Thomas"],"index":46614,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997261167,"difficulty":0.0002738833}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine's forehead is not muddy. It is publicly announced that Bonnie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Bonnie can now know whether Ginger can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Catherine","Ginger"],"index":18367,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995701909,"difficulty":0.0004298091}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jill knows whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Bonnie can now know that Jerry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jill","Bonnie","Jerry","Donna"],"index":20672,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983092546,"difficulty":0.0016907454}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Nina. Nina's card is shown to Nina. Nellie's card is shown to Nellie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Scott can now know that Nina can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Nina","Nellie"],"index":59995,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Andrew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Mary can now know whether Cheryl is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rita","Cheryl","Andrew","Mary"],"index":12656,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996483922,"difficulty":0.003516078}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether Kathleen's forehead is muddy. It is publicly announced that Amy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Amy can now know whether Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Blaine","Amanda","Kathleen","Amy"],"index":19971,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997335076,"difficulty":0.0002664924}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Calvin's card is shown to Florine. Calvin's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Calvin does not know whether or not everyone picked a red card. It is publicly announced that Calvin does not know whether Florine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Calvin can now know whether Florine can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Calvin","Florine","Anna"],"index":63501,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9756270051,"difficulty":0.0243729949}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eldon knows whether Eldon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Eldon can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Eldon","John","Melissa"],"index":61662,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998473227,"difficulty":0.001526773}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rudy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Rudy can now know whether Kathy can know whether Rudy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rudy","Lorraine","Scott","Kathy"],"index":62439,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980035424,"difficulty":0.0019964576}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Kenneth's card is shown to Christy. Tyrell's card is shown to Helen. Kenneth's card is shown to Tyrell. Helen's card is shown to Tyrell. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card. It is publicly announced that Kenneth picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Tyrell can now know whether Christy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Christy","Helen","Tyrell"],"index":67363,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5682901144,"difficulty":0.4317098856}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Megan does not know whether Scott is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Megan can now know that Scott can know whether Scott is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Megan","Scott"],"index":15984,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987177849,"difficulty":0.0012822151}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lindsey is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"James can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lindsey","Scott","Debra","James"],"index":17021,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983741045,"difficulty":0.0016258955}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandi knows whether James's forehead is muddy. It is publicly announced that Anna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Sandi can now know whether Anna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anna","Elaine","Sandi","James"],"index":55833,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996832609,"difficulty":0.0003167391}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis does not know whether Maria is thirsty. It is publicly announced that Maria does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Maria can now know whether Christopher can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Dennis","James","Maria"],"index":6615,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6607525945,"difficulty":0.3392474055}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] Agentb knows that (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know that Jack can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","William","Heather","Jack"],"index":53855,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997093081,"difficulty":0.0002906919}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Rita's card is shown to Maria. Valerie's card is shown to Maria. Shirley's card is shown to Rita. Valerie's card is shown to Rita. Rita's card is shown to Valerie. Valerie's card is shown to Valerie. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Maria picked a red card. It is publicly announced that Maria does not know whether Maria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Rita can now know whether Maria can know that Shirley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirley","Maria","Rita","Valerie"],"index":66211,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9396256804,"difficulty":1.9396256804}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Roland is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jesus can now know whether Richard can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesus","Richard","Roland"],"index":42977,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994863272,"difficulty":0.0005136728}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Brent can now know that Brent's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Barbara","Brent"],"index":26649,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975289702,"difficulty":0.0024710298}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Heidi can now know whether Joy can know that Joy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Heidi","Joy","Patricia"],"index":41007,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999633193,"difficulty":0.000366807}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elton knows whether or not everyone is thirsty. It is publicly announced that Brandon is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Elton can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brandon","Elton"],"index":2530,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973369241,"difficulty":0.0026630759}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know whether Nichole can know whether Robin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Nichole","Peter","Robin"],"index":44148,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990324974,"difficulty":0.0009675026}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lauren's card is shown to Sandra. Sandra's card is shown to Lauren. Sandra's card is shown to Alicia. It is publicly announced that someone picked a red card. It is publicly announced that Sandra does not know whether or not everyone picked a red card. It is publicly announced that Sandra does not know whether Sandra picked a red card. It is publicly announced that Alicia knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Lauren can now know whether Alicia can know whether Alicia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Lauren","Alicia"],"index":50397,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9892495871,"difficulty":0.0107504129}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Jacob. Jacob's card is shown to Ruth. Ruth's card is shown to Karen. Jacob's card is shown to Thurman. Ruth's card is shown to Thurman. Karen's card is shown to Thurman. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacob","Ruth","Karen","Thurman"],"index":7056,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984949827,"difficulty":0.0015050173}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julius's forehead is not muddy. It is publicly announced that Susanne does not know whether Susanne's forehead is muddy. It is publicly announced that Susanne knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Kyle can now know whether Julius can know whether Julius's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kyle","Julius","Susanne"],"index":64844,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.943643868,"difficulty":0.056356132}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Amanda. German's card is shown to Amanda. Austin's card is shown to Austin. German's card is shown to German. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Austin can now know whether German can know whether Austin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Austin","German"],"index":31845,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979135394,"difficulty":0.0020864606}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juan does not know whether Theresa is thirsty. It is publicly announced that Theresa is not thirsty. It is publicly announced that Theresa is not thirsty. It is publicly announced that Juan knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Juan can now know that Theresa can know that Theresa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Theresa","Juan","Rebekah"],"index":26887,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9342225194,"difficulty":1.9342225194}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward does not know whether Kathy is thirsty. It is publicly announced that Todd does not know whether Robert is thirsty. It is publicly announced that Todd does not know whether Kathy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Edward can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Todd","Kathy","Robert","Edward"],"index":63661,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998426795,"difficulty":0.001573205}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Levi. David's card is shown to Levi. Levi's card is shown to Harold. David's card is shown to Harold. Levi's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether Levi can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Levi","Harold","David"],"index":10977,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9947708249,"difficulty":0.0052291751}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joanne does not know whether Joseph is thirsty. It is publicly announced that Joanne does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Joseph can now know that Joanne can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joseph","Joanne"],"index":44912,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8868370056,"difficulty":0.1131629944}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myrtie knows whether Myrtie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Marian can now know that Marian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Myrtie","Frank","Eloisa","Marian"],"index":30327,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952955842,"difficulty":0.0047044158}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that James does not know whether Virginia is thirsty. It is publicly announced that Kenneth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Virginia can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kenneth","James","Thomasena","Virginia"],"index":51092,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter knows whether Jennifer's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Walter can now know that Jennifer can know that Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Walter","Jennifer"],"index":59766,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.5443196893,"difficulty":0.4556803107}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Keith can now know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Richard","Keith","Jeremiah"],"index":27792,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9780212045,"difficulty":0.0219787955}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Ashley's card is shown to Patricia. Patricia's card is shown to Ashley. Ashley's card is shown to Ashley. Patricia's card is shown to Ray. Robert's card is shown to Ray. Ray's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know whether Ashley can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Ashley","Ray","Robert"],"index":41970,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marquerite does not know whether or not everyone is thirsty. It is publicly announced that Diane knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Diane can now know whether Diane is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marquerite","Diane"],"index":65084,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991588593,"difficulty":0.0008411407}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Martha is thirsty. It is publicly announced that Ana does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Martha can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martha","Ana","Michael","George"],"index":44226,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997730851,"difficulty":0.0002269149}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Katherine. Angel's card is shown to Alice. Katherine's card is shown to Angel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know that Katherine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katherine","Ronald","Alice","Angel"],"index":56195,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998449564,"difficulty":0.001550436}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Kelly. James's card is shown to Kelly. James's card is shown to Jose. Kelly's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that Jose can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelly","Jose","James"],"index":1874,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alexander's card is shown to Alexander. Paul's card is shown to Alexander. Paul's card is shown to Paul. Raymond's card is shown to Paul. Paul's card is shown to Raymond. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alexander can now know that Raymond can know that Alexander picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alexander","Paul","Raymond"],"index":57129,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977305532,"difficulty":0.0022694468}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Guadalupe. Jay's card is shown to Jay. Guadalupe's card is shown to Mary. Guadalupe's card is shown to Marie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Jay can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Guadalupe","Jay","Mary","Marie"],"index":56401,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997748733,"difficulty":0.0002251267}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Linda is thirsty. It is publicly announced that Pam is thirsty. It is publicly announced that Linda is thirsty. It is publicly announced that Pam is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 1 ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 1 ] 0","hypothesis":"Linda can now know whether Pam can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pam","Linda","David"],"index":23975,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997801185,"difficulty":0.0002198815}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louise knows whether Louise is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Derek can now know that Derek is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Derek","Louise"],"index":46461,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980913997,"difficulty":0.0019086003}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jill is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Sally can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sally","Paula","Jill"],"index":30690,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997835755,"difficulty":0.0002164245}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Clyde. Carla's card is shown to Clyde. Clyde's card is shown to Kim. Kim's card is shown to Kim. Carla's card is shown to Carla. Carla's card is shown to Cora. It is publicly announced that someone picked a red card. It is publicly announced that Cora does not know whether Clyde picked a red card. It is publicly announced that Clyde knows whether or not nobody picked a red card. It is publicly announced that Carla does not know whether Cora picked a red card. It is publicly announced that Kim knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Clyde can now know whether Kim can know whether Clyde picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clyde","Kim","Carla","Cora"],"index":49901,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973456264,"difficulty":0.0026543736}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adele's card is shown to Gladys. Adele's card is shown to Micheal. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Gladys can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adele","Gladys","Micheal"],"index":32730,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985530972,"difficulty":0.0014469028}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Jeffrey can now know that Frank is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Frank","Jeffrey","Annie"],"index":9227,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964722395,"difficulty":0.0035277605}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Karen's forehead is muddy. It is publicly announced that Tiffany knows whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Henry can now know that Tiffany can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Henry","Karen","Tiffany"],"index":38158,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997591376,"difficulty":0.0002408624}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hope's card is shown to Jonathan. Jonathan's card is shown to Virginia. Ashley's card is shown to Ashley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jonathan can now know whether Virginia can know that Hope picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonathan","Virginia","Hope","Ashley"],"index":6777,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9300118089,"difficulty":0.0699881911}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Troy. Maria's card is shown to Daniel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Daniel can now know that Troy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Troy","Daniel","Maria"],"index":65862,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985247254,"difficulty":0.0014752746}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to Brenda. Erin's card is shown to Erin. It is publicly announced that someone picked a red card. It is publicly announced that Brenda does not know whether Brenda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Brenda can now know that Brenda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brenda","Erin"],"index":3436,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9853656292,"difficulty":0.0146343708}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine knows whether Wendy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Wendy can now know whether Minerva can know whether Stephen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Minerva","Katherine","Wendy","Stephen"],"index":65342,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999717176,"difficulty":0.000282824}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Barbara can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Barbara","Jeffrey"],"index":53228,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997397065,"difficulty":0.0002602935}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Hazel can now know that David can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Hazel","Patrick"],"index":7582,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983577132,"difficulty":0.0016422868}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Donna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"William can now know whether Barbara can know whether Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Michael","Donna","Barbara"],"index":58822,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99597013,"difficulty":0.00402987}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bruce can now know whether Douglas can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Bruce","Richard"],"index":59459,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9867982268,"difficulty":0.0132017732}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joseph can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Warren","Michelle","Joseph"],"index":45583,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether Teresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Bill can now know whether Valerie can know that Bill's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Teresa","Bill","Dana","Valerie"],"index":65854,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9706468582,"difficulty":0.0293531418}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Berniece knows whether Craig's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Berniece can now know that Craig can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dawna","John","Berniece","Craig"],"index":30298,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995982051,"difficulty":0.0004017949}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry does not know whether Jerry's forehead is muddy. It is publicly announced that Gloria knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jerry can now know that Gloria can know whether Gloria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jerry","Gloria"],"index":61759,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7629153132,"difficulty":1.7629153132}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Naomi does not know whether or not everyone is thirsty. It is publicly announced that Naomi does not know whether or not everyone is thirsty. It is publicly announced that Naomi does not know whether Tracey is thirsty. It is publicly announced that Naomi knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Tracey can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tracey","Naomi"],"index":51712,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99971205,"difficulty":0.00028795}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Pamela can now know whether Ronald can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Adella","Ronald","Thomas","Pamela"],"index":62600,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9912098646,"difficulty":0.0087901354}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether or not everyone's forehead is muddy. It is publicly announced that Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] 0","hypothesis":"Gregory can now know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Paul","Anthony","Gregory"],"index":61402,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992491603,"difficulty":0.0007508397}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"William can now know that Stephanie can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","William","Rose","Joshua"],"index":38446,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997394681,"difficulty":0.0002605319}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Raul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Raul can now know that Daniel can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raul","Daniel","James","Carlos"],"index":65821,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996995926,"difficulty":0.0003004074}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Lisa. Traci's card is shown to John. John's card is shown to Catherine. Lisa's card is shown to Traci. It is publicly announced that someone picked a red card. It is publicly announced that Traci does not know whether or not everyone picked a red card. It is publicly announced that John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] Agentb knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"John can now know whether Traci can know that Traci picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","John","Catherine","Traci"],"index":46267,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8955866098,"difficulty":0.1044133902}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kim does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Katherine can now know that Kim can know whether Kim's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Katherine","Kim","Tyrone"],"index":43332,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5179857612,"difficulty":1.5179857612}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Donna knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Donna can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Donna","Cindy"],"index":4436,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983778,"difficulty":0.0016222}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Jason","Phillip","Michele"],"index":17684,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9089732766,"difficulty":0.0910267234}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcus does not know whether or not everyone is thirsty. It is publicly announced that Robert does not know whether Maria is thirsty. It is publicly announced that Maria does not know whether or not everyone is thirsty. It is publicly announced that Maria does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know whether Marcus is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Maria","Marcus"],"index":62674,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6996375918,"difficulty":0.3003624082}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Inez's card is shown to Garland. Inez's card is shown to Inez. It is publicly announced that someone picked a red card. It is publicly announced that Inez does not know whether or not everyone picked a red card. It is publicly announced that Garland does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Inez can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Garland","Inez"],"index":9819,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Susan can now know that Elbert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elbert","Deborah","Susan","Armando"],"index":42864,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9903167486,"difficulty":1.9903167486}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jim does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Eugene can now know that Jim can know whether Noemi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eugene","Jim","Noemi","Charles"],"index":62660,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977086782,"difficulty":0.0022913218}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lindsey does not know whether Lindsey's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lindsey knows whether Candice's forehead is muddy. It is publicly announced that Lindsey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Elnora can now know whether Candice can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lindsey","Elnora","Candice"],"index":54317,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996987581,"difficulty":0.0003012419}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Paul can now know that Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Rose","Linda"],"index":53000,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997707963,"difficulty":0.002292037}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Pauline. Pauline's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Pauline does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Susan can now know that Pauline can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pauline","Susan"],"index":56844,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9846040606,"difficulty":0.0153959394}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leo's card is shown to Jill. Bruce's card is shown to Bruce. Bruce's card is shown to Leo. It is publicly announced that someone picked a red card. It is publicly announced that Leo picked a red card. It is publicly announced that Denise knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Bruce can now know that Jill can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jill","Bruce","Denise","Leo"],"index":5132,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Kimberly's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Kimberly can now know whether Joseph can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Kimberly"],"index":31994,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9938588738,"difficulty":0.0061411262}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanne does not know whether Jeanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know whether Barbara can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Jeanne","James","Joseph"],"index":54257,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997615218,"difficulty":0.0002384782}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Donna is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Audrey can now know whether Donna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Audrey","David","Donna","Robert"],"index":40837,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8371164799,"difficulty":0.1628835201}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alisa's card is shown to Alisa. Josephine's card is shown to Alisa. Alisa's card is shown to Josephine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Alisa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alisa","Josephine"],"index":14755,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983550906,"difficulty":0.0016449094}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandon's card is shown to Felicia. Ruth's card is shown to Felicia. Felicia's card is shown to Felicia. It is publicly announced that someone picked a red card. It is publicly announced that Brandon knows whether Ruth picked a red card. It is publicly announced that Felicia picked a black card. It is publicly announced that Brandon knows whether Brandon picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Brandon can now know whether Felicia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brandon","Rodney","Ruth","Felicia"],"index":12584,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6297100186,"difficulty":0.3702899814}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernadine knows whether or not everyone is thirsty. It is publicly announced that Tim knows whether Tim is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Bernadine can now know that Tim is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tim","Bernadine"],"index":55796,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9614439607,"difficulty":1.9614439607}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Carolyn can now know whether Lisa can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Sheila","Lisa"],"index":19677,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995601773,"difficulty":0.0004398227}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lorenzo does not know whether Luis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Luis can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Luis","Hugh","Lorenzo"],"index":14878,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985937476,"difficulty":0.0014062524}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Apryl does not know whether Apryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lawrence can now know whether Apryl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lawrence","Justin","Apryl"],"index":65279,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994681478,"difficulty":0.0005318522}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicole can now know that Sarah can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["April","Eunice","Nicole","Sarah"],"index":51068,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983465672,"difficulty":0.0016534328}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is not muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Thomas can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thomas","Charles"],"index":45191,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979059696,"difficulty":0.0020940304}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michele's card is shown to Kenneth. Virginia's card is shown to Kenneth. Kenneth's card is shown to Michele. Virginia's card is shown to Michele. Michele's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know that Virginia can know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Michele","Virginia"],"index":62029,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9588502645,"difficulty":0.0411497355}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacy's card is shown to Terrell. Freddie's card is shown to Stacy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Terrell can now know that Freddie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terrell","Stacy","Catherine","Freddie"],"index":25534,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943401814,"difficulty":0.0056598186}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacklyn's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Jacklyn can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jacklyn","Leo"],"index":4995,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998403728,"difficulty":0.001596272}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelo's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Stephen can now know that Stephen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Angelo","Clarence","Bryan"],"index":46607,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9955872297,"difficulty":0.0044127703}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Hallie. Nathan's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nathan can now know whether Hallie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hallie","Nathan","Anna","Richard"],"index":48738,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9585729241,"difficulty":0.0414270759}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Richard is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Jeremy is thirsty. It is publicly announced that Gary knows whether Jeremy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Gary can now know whether Gary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Jeremy","Gary","Richard"],"index":56194,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992161989,"difficulty":0.0007838011}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Gary. Russell's card is shown to Gary. Russell's card is shown to Evan. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Gary can now know whether Russell picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gary","Evan","Russell"],"index":65682,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7900267839,"difficulty":1.7900267839}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joellen's card is shown to Joellen. Natasha's card is shown to Ken. Joellen's card is shown to Natasha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ken can now know that Mitchell can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joellen","Mitchell","Ken","Natasha"],"index":37525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9847352505,"difficulty":0.0152647495}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy. It is publicly announced that Joel knows whether Val's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agentb knows that (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Richard can now know that Hattie can know that Joel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hattie","Richard","Val","Joel"],"index":38777,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968660474,"difficulty":0.0031339526}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Floyd can now know that Maranda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amy","Floyd","Maranda"],"index":61233,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.960357666,"difficulty":0.039642334}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Norma is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ryan can now know whether Norma is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Norma","Ronald","Ryan"],"index":32889,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9912140965,"difficulty":0.0087859035}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Gary knows whether Keith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Mary can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Louis","Keith","Gary","Mary"],"index":26027,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9952456355,"difficulty":0.0047543645}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hazel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Victor can now know that Mary can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nathan","Victor","Hazel","Mary"],"index":26500,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9591878653,"difficulty":0.0408121347}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Jose is thirsty. It is publicly announced that Jose does not know whether Bryan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Bryan can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Jose","Bryan","James"],"index":11455,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964291453,"difficulty":0.0035708547}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Louis's card is shown to Louis. Louis's card is shown to Lois. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Louis can now know that Lois can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Louis","Lois"],"index":63115,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997708201,"difficulty":0.0002291799}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roger's card is shown to Kathryn. Susan's card is shown to Kathryn. Kathryn's card is shown to Roger. Roger's card is shown to Roger. Kathryn's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Susan knows whether Susan picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] [ ! (1&2&3) ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] [ ! (1&2&3) ] 0","hypothesis":"Roger can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathryn","Roger","Susan"],"index":56806,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848367572,"difficulty":0.0151632428}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Melissa can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Melissa","Anthony","Jeanette"],"index":18782,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6648094654,"difficulty":1.6648094654}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Sharon can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deborah","Nathan","Sharon"],"index":8293,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983546138,"difficulty":0.0016453862}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vonda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Gordon can now know whether Vonda can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Gordon","Fredrick","Vonda"],"index":46230,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9937269688,"difficulty":0.0062730312}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christina knows whether someone is thirsty. It is publicly announced that Sachiko is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"William can now know that Christina can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Christina","Sachiko"],"index":61008,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9623440504,"difficulty":0.0376559496}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"William can now know that Robert can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Robert"],"index":30933,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997790456,"difficulty":0.0002209544}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwina's card is shown to John. John's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Janice does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether Edwina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Janice","Edwina"],"index":26731,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8403966427,"difficulty":0.1596033573}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Harriet can now know whether Chad can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Harriet","Chad"],"index":18507,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9853261709,"difficulty":0.0146738291}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Donald's forehead is muddy. It is publicly announced that Antonio knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Micheal can now know that Susan can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Antonio","Donald","Micheal","Susan"],"index":1817,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997469783,"difficulty":0.0002530217}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Dennis picked a black card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] 0","hypothesis":"Dennis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dennis","Nancy"],"index":14543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983353019,"difficulty":0.0016646981}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Dung can now know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dung","William","Patricia"],"index":17734,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997435212,"difficulty":0.0002564788}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Jay","Mable"],"index":13343,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997630715,"difficulty":0.0002369285}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Jesse. Wilfred's card is shown to Jesse. Nancy's card is shown to Wilfred. Jesse's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Wilfred picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Nancy can now know whether Wilfred can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Jesse","Wilfred","Richard"],"index":12751,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995449185,"difficulty":0.0004550815}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Kristen can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cheryl","Kristen"],"index":3889,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996235311,"difficulty":0.003764689}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Robert can now know that Jose can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Robert","Shirley","Jose"],"index":3002,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983997941,"difficulty":0.0016002059}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Keith knows whether Keith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Rosalyn can now know that Rosalyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Keith","Rosalyn","Ruth","Bethel"],"index":56914,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9929651022,"difficulty":0.0070348978}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cory does not know whether Robert is thirsty. It is publicly announced that Lance is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! (1|2|3) ] 0","hypothesis":"Cory can now know that Robert can know whether Cory is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cory","Lance","Robert"],"index":63634,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7726441622,"difficulty":1.7726441622}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Tisha's card is shown to Richard. Richard's card is shown to Erica. Erica's card is shown to Tisha. Tisha's card is shown to Tisha. Tisha's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Thomas can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Erica","Tisha","Thomas"],"index":12634,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997755885,"difficulty":0.0002244115}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresa's card is shown to Theresa. Theresa's card is shown to Jose. David's card is shown to David. Jose's card is shown to Morris. It is publicly announced that someone picked a red card. It is publicly announced that Theresa does not know whether Morris picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Morris can now know that Theresa can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Theresa","Jose","David","Morris"],"index":30905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998219192,"difficulty":0.001780808}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Peggy's forehead is muddy. It is publicly announced that Peggy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"Serena can now know that Mary can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Serena","Mary","Peggy","Linda"],"index":63304,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977862835,"difficulty":0.0022137165}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Sarah's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Sarah can now know that Michael can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Sarah"],"index":44854,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.992739737,"difficulty":0.007260263}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Celia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Harriette can now know that Walter can know that Harriette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Celia","Amanda","Harriette"],"index":44369,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8886418939,"difficulty":0.1113581061}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Heather can now know whether Bruce can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Heather","Bruce"],"index":20601,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997432828,"difficulty":0.0002567172}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillie does not know whether Lillie's forehead is muddy. It is publicly announced that Garry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Garry can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nathan","Lillie","Robert","Garry"],"index":60286,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997132421,"difficulty":0.0002867579}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Angie. Angie's card is shown to Angie. Angie's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Angie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Angie can now know that Richard can know whether Angie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Angie","Kelly"],"index":47221,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8319690824,"difficulty":0.1680309176}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Sheena. Leroy's card is shown to Sheena. Elizabeth's card is shown to Joe. Joe's card is shown to Joe. Elizabeth's card is shown to Leroy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sheena can now know whether Joe can know whether Sheena picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Sheena","Joe","Leroy"],"index":44782,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982517362,"difficulty":0.0017482638}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tony's card is shown to Sherman. Scott's card is shown to Scott. Sherman's card is shown to Tony. It is publicly announced that someone picked a red card. It is publicly announced that Tony knows whether Sherman picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Sherman can now know that Scott can know whether Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sherman","Scott","Tony"],"index":52813,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8864437938,"difficulty":1.8864437938}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Fernando is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Fernando can now know that Fernando is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glenn","Thomas","Fernando"],"index":63585,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953965545,"difficulty":0.0046034455}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Christopher can now know whether David can know whether Josephine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Bernadine","Christopher","Josephine"],"index":65803,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997037053,"difficulty":0.0002962947}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dewey's card is shown to Dewey. Jill's card is shown to Dewey. Jill's card is shown to Jill. Dewey's card is shown to Ralph. Jill's card is shown to Ralph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jill can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dewey","Jill","Ralph"],"index":29690,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ellsworth can now know whether John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Ellsworth","Mary","John"],"index":62119,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996137023,"difficulty":0.0003862977}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether Howard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Howard","Joseph","Mary","Barbara"],"index":35621,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999424696,"difficulty":0.000575304}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eva knows whether or not nobody is thirsty. It is publicly announced that Eva does not know whether Jim is thirsty. It is publicly announced that Jim knows whether Eva is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Eva can now know that Jim can know whether Jim is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jim","Eva"],"index":55188,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982902408,"difficulty":0.0017097592}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Debora can now know that Katie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katie","Philip","Debora","Kevin"],"index":32055,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984055161,"difficulty":0.0015944839}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Alyssa can now know that Edward can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Ann","Elizabeth","Alyssa"],"index":11435,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998396337,"difficulty":0.001603663}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Duane can now know whether Brett can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Duane","Gabriel","Brett"],"index":50443,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.985678494,"difficulty":0.014321506}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lonnie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lonnie can now know whether Marvin can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lonnie","Marvin","Stephanie"],"index":54915,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995523095,"difficulty":0.0004476905}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laquanda knows whether Mary's forehead is muddy. It is publicly announced that Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Laquanda can now know that Laquanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Elizabeth","Ronald","Laquanda"],"index":730,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9803702831,"difficulty":0.0196297169}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Tim. Tim's card is shown to Carla. Tim's card is shown to Phillip. It is publicly announced that someone picked a red card. It is publicly announced that Phillip does not know whether Phillip picked a red card. It is publicly announced that Carla knows whether or not everyone picked a red card. It is publicly announced that Carla picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 2 ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Phillip can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tim","Carla","Phillip"],"index":56226,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8866236806,"difficulty":0.1133763194}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly is not thirsty. It is publicly announced that William knows whether Kimberly is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"William can now know that Kimberly is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kimberly","William","Deborah"],"index":6727,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9824169874,"difficulty":0.0175830126}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Claudette does not know whether Connie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Connie can now know that Joe is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Connie","Claudette","Joe"],"index":33217,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971072078,"difficulty":0.0028927922}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether Alberta is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"David can now know that Mark is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alberta","Richard","David","Mark"],"index":10003,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978352189,"difficulty":0.0021647811}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thelma does not know whether or not everyone is thirsty. It is publicly announced that James knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Thelma can now know whether Vicki is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Thelma","Vicki"],"index":38602,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.82348001,"difficulty":0.17651999}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Robert's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Sarah can now know whether Matthew can know that Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Robert","Matthew"],"index":42938,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996689558,"difficulty":0.0003310442}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Melissa can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Melissa","Edward","Maria"],"index":56168,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984176159,"difficulty":0.0015823841}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey does not know whether Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ernest can now know that Jeffrey can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marilyn","Ernest","Jeffrey","Jimmy"],"index":39215,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996850491,"difficulty":0.0003149509}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Nicholas. Nicholas's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Nicholas can now know whether Richard can know whether Nicholas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nicholas","Richard"],"index":26462,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981437922,"difficulty":0.0018562078}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Gertrude can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gertrude","Steven","Mark","Audrey"],"index":23913,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985659719,"difficulty":0.0014340281}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Haley knows whether or not everyone's forehead is muddy. It is publicly announced that Haley's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 1 ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Barbara can now know whether Haley can know whether Haley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Haley","Barbara"],"index":25251,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996569157,"difficulty":0.0003430843}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandon's card is shown to Jesse. Jesse's card is shown to Brandon. Brandon's card is shown to Brandon. It is publicly announced that someone picked a red card. It is publicly announced that Jesse knows whether or not everyone picked a red card. It is publicly announced that Brandon knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Brandon can now know whether Jesse can know that Jesse picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jesse","Brandon"],"index":61416,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9190450907,"difficulty":0.0809549093}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Wendy"],"index":4909,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982246757,"difficulty":0.0017753243}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Amy. Bud's card is shown to Bud. Amy's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Margaret does not know whether Bud picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Amy can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amy","Bud","Margaret"],"index":58523,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954564571,"difficulty":0.0045435429}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Paul can now know whether Toi can know that Toi's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Toi","Paul"],"index":31218,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7743218541,"difficulty":1.7743218541}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Gordon can now know whether Susan can know whether Gordon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gordon","Susan"],"index":49850,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982255101,"difficulty":0.0017744899}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Daniel's forehead is muddy. It is publicly announced that William knows whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sandra can now know whether William can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Daniel","Sandra","Laura"],"index":59596,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996137023,"difficulty":0.0003862977}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jordan can now know whether Julie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Julie","Allen","Jordan"],"index":52440,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9978474379,"difficulty":0.0021525621}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether Joan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Joan can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Don","Brandon","Joan"],"index":60900,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997220635,"difficulty":0.0002779365}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delores knows whether someone's forehead is muddy. It is publicly announced that Delores knows whether someone's forehead is muddy. It is publicly announced that Delores knows whether someone's forehead is muddy. It is publicly announced that Delores knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Delores can now know that Natasha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Delores","Jose","Natasha"],"index":28668,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7136976123,"difficulty":0.2863023877}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Francisco. Michelle's card is shown to Francisco. Joseph's card is shown to Joseph. Michelle's card is shown to Joseph. Francisco's card is shown to Michelle. Joseph's card is shown to Michelle. Michelle's card is shown to Michelle. It is publicly announced that someone picked a red card. It is publicly announced that Michelle picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Michelle can now know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Francisco","Joseph","Michelle"],"index":53567,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7384377718,"difficulty":0.2615622282}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. John's card is shown to Marvin. Marvin's card is shown to Marvin. John's card is shown to Dorothy. Marvin's card is shown to Dorothy. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"John can now know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Marvin","Dorothy"],"index":22523,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6486126781,"difficulty":0.3513873219}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louise does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Louise can now know whether George can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louise","Dorothy","George"],"index":30096,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994571805,"difficulty":0.0005428195}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert does not know whether Albert's forehead is muddy. It is publicly announced that Etta does not know whether Etta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Etta can now know that Albert can know whether Etta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Albert","Theodore","Etta"],"index":21698,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995337725,"difficulty":0.0004662275}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anna knows whether someone is thirsty. It is publicly announced that Arleen does not know whether Simon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Anna can now know that Simon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anna","Arleen","Simon"],"index":513,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979481101,"difficulty":0.0020518899}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Steven can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephany","Steven","Susan"],"index":36285,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979394078,"difficulty":0.0020605922}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Julie can now know whether Donna can know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julie","Donna","Ronnie"],"index":41934,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995701909,"difficulty":0.0004298091}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Marion. Marion's card is shown to Natalie. Natalie's card is shown to Natalie. It is publicly announced that someone picked a red card. It is publicly announced that Marion knows whether Stephen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Marion can now know whether Stephen can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephen","Marion","Natalie"],"index":1409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Peter. Carroll's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carroll can now know that Carroll picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peter","Carroll","Heather"],"index":64710,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965033531,"difficulty":0.0034966469}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicole can now know whether Nicole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Curt","Brian","Nicole","Donna"],"index":65288,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.998167634,"difficulty":0.001832366}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Casey does not know whether Lee is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Casey can now know whether Lyle can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lee","Lyle","Jessica","Casey"],"index":34140,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997170568,"difficulty":0.0002829432}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeff does not know whether Heather is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jeff can now know that Nancy can know whether Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeff","Heather","Nancy"],"index":13667,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9931789637,"difficulty":0.0068210363}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maynard's card is shown to Yolanda. Maynard's card is shown to Maynard. It is publicly announced that someone picked a red card. It is publicly announced that Yolanda does not know whether or not everyone picked a red card. It is publicly announced that Yolanda does not know whether Yolanda picked a red card. It is publicly announced that Yolanda does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Yolanda can now know whether Yolanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Yolanda","Maynard"],"index":3339,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9929555655,"difficulty":1.9929555655}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Calvin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Lucy can now know that Calvin can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Jesus","Lucy","Calvin"],"index":1847,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982727766,"difficulty":0.0017272234}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denise's card is shown to Denise. Denise's card is shown to Ronald. Denise's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Ronald can now know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Denise","Ronald","Tracy"],"index":38555,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9965795875,"difficulty":0.0034204125}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rodney does not know whether Mark is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Donald can now know that Rodney can know that Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rodney","Mark","Donald"],"index":57010,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980157614,"difficulty":0.0019842386}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elise knows whether or not nobody's forehead is muddy. It is publicly announced that Elise knows whether Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Sarah can now know whether Elise can know whether Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sarah","Elise"],"index":4317,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993323684,"difficulty":0.0006676316}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curt's card is shown to Martin. Katherine's card is shown to Martin. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that Curt knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Curt can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Curt","Martin","Katherine"],"index":55365,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997523427,"difficulty":0.0002476573}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mabel's card is shown to Alexandra. Carmelo's card is shown to Carmelo. Carmelo's card is shown to Mabel. Alexandra's card is shown to Justin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carmelo can now know that Alexandra can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alexandra","Carmelo","Mabel","Justin"],"index":51349,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983729124,"difficulty":0.0016270876}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne does not know whether Anne's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Angela can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barbara","Dorothy","Angela","Anne"],"index":48564,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Kenneth's card is shown to Charles. Brian's card is shown to Charles. Patrice's card is shown to Kenneth. Charles's card is shown to Brian. Charles's card is shown to Patrice. Kenneth's card is shown to Patrice. Brian's card is shown to Patrice. Patrice's card is shown to Patrice. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Brian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:1 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:1 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Patrice can now know whether Brian can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Kenneth","Brian","Patrice"],"index":66581,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997727275,"difficulty":0.0002272725}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Columbus knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Grace can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melinda","Columbus","Joseph","Grace"],"index":54836,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981567264,"difficulty":0.0018432736}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julia does not know whether Thomas is thirsty. It is publicly announced that Julia does not know whether James is thirsty. It is publicly announced that Julia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] 0","hypothesis":"Thomas can now know that James can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julia","Thomas","James"],"index":2068,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984850287,"difficulty":0.0015149713}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole knows whether Nicole's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jerry can now know whether Jerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nicole","Jerry"],"index":21376,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989651442,"difficulty":0.0010348558}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Larry. Larry's card is shown to Jeff. Jeff's card is shown to Jeff. Steven's card is shown to Jeff. Larry's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Larry","Jeff","Steven"],"index":38501,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997269511,"difficulty":0.0002730489}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ellen can now know whether Gerald can know that Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gerald","Brandon","Ellen"],"index":54500,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6060362458,"difficulty":1.6060362458}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jane does not know whether Maxine is thirsty. It is publicly announced that Maxine does not know whether Jane is thirsty. It is publicly announced that Jane does not know whether Maxine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jane can now know whether Maxine can know whether Jonathon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maxine","Jane","Sean","Jonathon"],"index":11578,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982869029,"difficulty":0.0017130971}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Yvonne. Yvonne's card is shown to Stephanie. Stephanie's card is shown to Stephanie. Sarah's card is shown to Stephanie. It is publicly announced that someone picked a red card. It is publicly announced that Sarah picked a black card. It is publicly announced that Sarah picked a black card. It is publicly announced that Yvonne does not know whether Stephanie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Yvonne can now know that Sarah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yvonne","Stephanie","Sarah"],"index":6544,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7144064903,"difficulty":0.2855935097}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Alan's forehead is muddy. It is publicly announced that Timothy's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Christine can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christine","Alan","Timothy"],"index":39654,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986802936,"difficulty":0.0013197064}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Michael's card is shown to Laurence. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card. It is publicly announced that Laurence does not know whether or not everyone picked a red card. It is publicly announced that Laurence does not know whether Laurence picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Laurence can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Laurence"],"index":30241,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979332685,"difficulty":0.0020667315}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is not muddy. It is publicly announced that Lelia does not know whether Lelia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lelia can now know that Lelia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Barry","Lelia"],"index":59546,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9740611911,"difficulty":0.0259388089}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Oliver's card is shown to Oliver. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Oliver"],"index":67285,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946311712,"difficulty":0.0053688288}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobby's card is shown to Bobby. Ariana's card is shown to Ariana. It is publicly announced that someone picked a red card. It is publicly announced that Bobby does not know whether Bobby picked a red card. It is publicly announced that Marty picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Marty can now know whether Bobby can know that Marty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marty","Bobby","Ariana","Christine"],"index":57139,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7615947127,"difficulty":0.2384052873}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William knows whether William is thirsty. It is publicly announced that Connie knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"William can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Connie","Stan","William"],"index":10919,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9867438078,"difficulty":0.0132561922}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Dorothy's card is shown to Gary. Kenneth's card is shown to Gary. Jennifer's card is shown to Jennifer. Kenneth's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Gary can know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Gary","Jennifer","Kenneth"],"index":49302,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8896104097,"difficulty":0.1103895903}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know that William can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Rodney","Rita","William"],"index":1934,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9958498478,"difficulty":0.0041501522}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Mitchell can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Mitchell","Mary"],"index":35996,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985356331,"difficulty":0.0014643669}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Micah knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ralph can now know that Micah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Micah","Richard"],"index":23880,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9119272232,"difficulty":0.0880727768}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Merle does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Merle can now know that John can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rick","John","Merle"],"index":6911,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. Frank's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether Angela picked a red card. It is publicly announced that Frank does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Frank can now know that Angela can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frank","Angela"],"index":37781,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999781549,"difficulty":0.000218451}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra knows whether Sandra is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Sandra can now know that Edward can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Frances","Sandra"],"index":5413,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997670054,"difficulty":0.0002329946}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Penny knows whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Jeffrey can now know that Jerry can know whether Angelo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Penny","Angelo","Jeffrey","Jerry"],"index":36387,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998873055,"difficulty":0.001126945}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Omar knows whether Christopher is thirsty. It is publicly announced that Omar knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Omar can now know whether Omar is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christopher","Omar"],"index":31257,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991699457,"difficulty":0.0008300543}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Thomas's card is shown to Barbara. James's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Barbara can now know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Barbara","James"],"index":57053,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9812605381,"difficulty":0.0187394619}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeff does not know whether Merle is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jeff can now know that Tammie can know that Tammie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tammie","Merle","Jeff"],"index":17788,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970811009,"difficulty":0.0029188991}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danny knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Danny knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Danny can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Danny","Annie"],"index":15549,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Jennifer can now know whether Sandy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sandy","Jennifer"],"index":19015,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997823834,"difficulty":0.0002176166}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brandon can now know that Tim can know that Tim's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tim","Brandon","Rosa"],"index":65008,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984677434,"difficulty":0.0015322566}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Penny's card is shown to Maria. Sigrid's card is shown to Penny. Maria's card is shown to Sigrid. It is publicly announced that someone picked a red card. It is publicly announced that Sigrid does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Maria can now know that Sigrid can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Penny","Sigrid"],"index":62426,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Kamala does not know whether Deborah is thirsty. It is publicly announced that Kamala does not know whether Deborah is thirsty. It is publicly announced that Kamala does not know whether Deborah is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Kamala can now know that Deborah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kamala","Deborah"],"index":46635,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.971880734,"difficulty":0.028119266}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kasandra does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Julie can now know that Walter can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julie","Walter","Kasandra","Charles"],"index":66651,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wesley knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Rayna can now know that Clifton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wesley","Rayna","Clifton"],"index":28991,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979764819,"difficulty":0.0020235181}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roger knows whether or not nobody is thirsty. It is publicly announced that Roger does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"James can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roger","Shirley","James"],"index":11021,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8700024486,"difficulty":0.1299975514}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Minnie's card is shown to Anthony. Minnie's card is shown to Minnie. Minnie's card is shown to Gerardo. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Anthony can now know that Gerardo can know whether Minnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Minnie","Gerardo"],"index":49741,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9715806842,"difficulty":0.0284193158}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Ralph can now know that Mark can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ralph","Joseph","Mark","Scott"],"index":34875,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982559085,"difficulty":0.0017440915}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know whether Mildred can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Patricia","Malka","Joseph"],"index":13718,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9849180579,"difficulty":0.0150819421}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lilly does not know whether Lilly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Laurel can now know whether Lilly can know whether Elmer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Blair","Laurel","Lilly","Elmer"],"index":41383,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993023872,"difficulty":0.0006976128}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy. It is publicly announced that Harry knows whether Harry's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Harry can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mark","Harry"],"index":27059,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997642636,"difficulty":0.0002357364}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ryan can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ryan","Stephanie","Boyd"],"index":9492,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995248318,"difficulty":0.0004751682}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Diane can now know whether Mary can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Mary","Diane","James"],"index":12573,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997807145,"difficulty":0.0002192855}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tameka can now know that Brandi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cecilia","Brandi","Tameka"],"index":53903,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986340404,"difficulty":0.0013659596}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine knows whether Catherine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Catherine can now know that Catherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Catherine","Jacqueline"],"index":2017,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997418046,"difficulty":0.002581954}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Shavon can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Shavon","Craig"],"index":29928,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7892805338,"difficulty":0.2107194662}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether Terry's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Anthony can now know that Terry can know whether Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Terry","Anthony"],"index":34338,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995951056,"difficulty":0.0004048944}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Robert can now know that Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Cruz","Teresa"],"index":6204,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983178377,"difficulty":0.0016821623}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Melissa's card is shown to Ofelia. Melissa's card is shown to James. Ofelia's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ofelia can now know that Melissa can know that Ofelia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joann","Melissa","Ofelia","James"],"index":52515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972202778,"difficulty":0.0027797222}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy. It is publicly announced that Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Daniel can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Daniel","Rose"],"index":51176,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997227788,"difficulty":0.0002772212}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy. It is publicly announced that Barbara's forehead is muddy. It is publicly announced that Edward's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Frank can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Frank","Stephen","Edward","Barbara"],"index":28565,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996498823,"difficulty":0.0003501177}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alfred's card is shown to Jose. Alfred's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jose can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jose","Alfred","Michael"],"index":62702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985095859,"difficulty":0.0014904141}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Matthew can now know whether David can know that Lisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Matthew","Catherine","Lisa"],"index":52902,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9925282001,"difficulty":0.0074717999}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Vickie can now know that Stephen can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Michael","John","Vickie"],"index":32734,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9548975825,"difficulty":0.0451024175}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Bridgett knows whether Bridgett is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Georgia can now know whether Eileen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bridgett","Eileen","Tonya","Georgia"],"index":24398,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954136014,"difficulty":0.0045863986}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Larry. Gary's card is shown to Gary. David's card is shown to Gary. Gary's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David picked a red card. It is publicly announced that David does not know whether Larry picked a red card. It is publicly announced that David knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Gary can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Gary","David"],"index":50522,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981681108,"difficulty":0.0018318892}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Pamela can now know that Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Abel","Clyde","Pamela","Kevin"],"index":40152,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936088324,"difficulty":0.0063911676}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah does not know whether Deborah's forehead is muddy. It is publicly announced that Greta does not know whether Greta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Deborah can now know whether Greta can know that Muriel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Greta","Muriel","Deborah"],"index":17756,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99586761,"difficulty":0.00413239}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Earl knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Earl can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shaquana","Michael","Earl"],"index":35157,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997044206,"difficulty":0.0002955794}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Julio's card is shown to Robert. Robert's card is shown to Carrie. Carrie's card is shown to Eugene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carrie can now know that Eugene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Carrie","Julio","Eugene"],"index":24466,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983897209,"difficulty":0.0016102791}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessie's card is shown to Roxanne. Roxanne's card is shown to Joe. Joe's card is shown to Joe. Jessie's card is shown to Jean. Jean's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Joe does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jessie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roxanne","Jessie","Joe","Jean"],"index":55825,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962332845,"difficulty":0.0037667155}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edna knows whether Darrell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Joann can now know that Darrell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joann","Carol","Edna","Darrell"],"index":51309,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977234006,"difficulty":0.0022765994}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall knows whether Randall's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Annie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Michael","Annie","Randall"],"index":36661,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982520938,"difficulty":0.0017479062}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether Kevin is thirsty. It is publicly announced that Rose does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Eric can now know that Kevin can know that Mark is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Rose","Mark","Eric"],"index":15864,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9455354214,"difficulty":0.0544645786}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Richard. Mark's card is shown to Lacresha. Richard's card is shown to Mark. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Lacresha can now know that Richard can know whether Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Lacresha","Mark","Sharon"],"index":48146,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7274039984,"difficulty":0.2725960016}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laurie's card is shown to Laurie. Regina's card is shown to Laurie. Regina's card is shown to Regina. It is publicly announced that someone picked a red card. It is publicly announced that Regina does not know whether Laurie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Regina can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Laurie","Regina"],"index":60569,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986178875,"difficulty":0.0013821125}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adriana's card is shown to Charles. Truman's card is shown to Truman. Adriana's card is shown to Truman. Grace's card is shown to Adriana. Grace's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Grace picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Grace can now know whether Adriana can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Truman","Adriana","Grace"],"index":57925,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9470048547,"difficulty":0.0529951453}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Barbara can now know whether Joseph can know whether Wendy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wendy","Joseph","Dolores","Barbara"],"index":31095,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997088313,"difficulty":0.0002911687}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to James. Donald's card is shown to Donald. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Richard picked a red card. It is publicly announced that James does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Donald","Richard"],"index":1235,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997208714,"difficulty":0.0002791286}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold knows whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kenneth can now know that Harold can know that Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darla","Harold","Kenneth","Debra"],"index":53979,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979037046,"difficulty":0.0020962954}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alvin is thirsty. It is publicly announced that Donald does not know whether Christopher is thirsty. It is publicly announced that Steven knows whether or not nobody is thirsty. It is publicly announced that Steven is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentb knows that (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Donald can now know that Alvin can know that Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Donald","Steven","Alvin"],"index":5415,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7537330389,"difficulty":0.2462669611}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Frank can now know that Mark can know that Deborah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Frank","Leonard","Deborah"],"index":47747,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965513945,"difficulty":0.0034486055}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Billy can now know that Billy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Billy","Gary"],"index":2567,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9900147915,"difficulty":1.9900147915}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Shelley can now know whether Jason can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shelley","Gilbert","Jason","Floyd"],"index":54991,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997175336,"difficulty":0.0002824664}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether Rosemary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Melissa can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Diane","Melissa","Lawrence","Rosemary"],"index":10603,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997174144,"difficulty":0.0002825856}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Velma does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Steven can now know whether Betty is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Velma","Betty","Junior"],"index":30604,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8363454938,"difficulty":0.1636545062}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul is not thirsty. It is publicly announced that Paul knows whether Paul is thirsty. It is publicly announced that Paul does not know whether Christina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Charles can now know whether Christina can know that Christina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paul","Christina","Charles"],"index":30847,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9244506955,"difficulty":1.9244506955}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhonda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Rhonda can now know that Adrienne can know that Adrienne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rhonda","Adrienne"],"index":11306,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9470514655,"difficulty":0.0529485345}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Clyde can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kathy","Clyde"],"index":66427,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9941732287,"difficulty":0.0058267713}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julianna does not know whether Brent is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Julianna can now know that Brent can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brent","Julianna"],"index":40399,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9892955422,"difficulty":0.0107044578}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brett's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Mary can now know whether Hilda can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Mary","Brett","Hilda"],"index":63904,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997841716,"difficulty":0.0002158284}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether or not nobody's forehead is muddy. It is publicly announced that Paul knows whether Paul's forehead is muddy. It is publicly announced that Gina's forehead is muddy. It is publicly announced that Roxanna knows whether Gina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Gina can now know that Paul can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gina","Paul","Roxanna","John"],"index":65933,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997547269,"difficulty":0.0002452731}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Kathleen can now know whether Andre can know whether Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andre","Kathleen"],"index":52368,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997312427,"difficulty":0.0002687573}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandy's card is shown to Sandy. Maria's card is shown to Sandy. Marie's card is shown to Marie. Sandy's card is shown to Maria. Marie's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Maria picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Sandy can now know whether Marie can know that Marie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sandy","Marie","Maria"],"index":13378,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8750285506,"difficulty":1.8750285506}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Philip knows whether Philip's forehead is muddy. It is publicly announced that Gerald knows whether Philip's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Vinita can now know that Joni can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gerald","Philip","Vinita","Joni"],"index":54629,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984362721,"difficulty":0.0015637279}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy. It is publicly announced that Stacey does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that Thea's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stacey","James","Scott","Thea"],"index":28626,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7306215763,"difficulty":1.7306215763}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita does not know whether Phillip is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Eric can now know that Anita can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Phillip","Anita"],"index":67517,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Parthenia can now know whether Luella's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Arnette","Luella","Parthenia"],"index":12986,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997370839,"difficulty":0.0002629161}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Roy can now know that Ethel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roy","Janet","Ethel"],"index":32934,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972894192,"difficulty":0.0027105808}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fannie knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Jason can now know that Arthur can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arthur","Fannie","Brittany","Jason"],"index":28741,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984265566,"difficulty":0.0015734434}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Jeannette. Scott's card is shown to Jeannette. Jose's card is shown to Scott. Anthony's card is shown to Scott. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeannette can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Jeannette","Scott","Anthony"],"index":54553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985758066,"difficulty":0.0014241934}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glenda's card is shown to Glenda. Glenda's card is shown to Sandy. Sandy's card is shown to Sandy. It is publicly announced that someone picked a red card. It is publicly announced that Sandy knows whether or not nobody picked a red card. It is publicly announced that Sandy knows whether Glenda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Sandy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Glenda","Sandy"],"index":11096,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997726083,"difficulty":0.0002273917}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Michael is thirsty. It is publicly announced that Michael is not thirsty. It is publicly announced that Ruth does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"James can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Ruth","Michael"],"index":37100,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985219836,"difficulty":0.0014780164}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. Cynthia's card is shown to Cynthia. Susan's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Gregory picked a red card. It is publicly announced that Gregory does not know whether Cynthia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gregory can now know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregory","Cynthia","Susan"],"index":39631,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7719113827,"difficulty":0.2280886173}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephenie's card is shown to Stephenie. Stephenie's card is shown to Grant. Stephenie's card is shown to Terry. Grant's card is shown to Terry. It is publicly announced that someone picked a red card. It is publicly announced that Stephenie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Terry can now know that Terry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephenie","Grant","Terry"],"index":50372,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6319549084,"difficulty":0.3680450916}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deanna knows whether Deanna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Timothy can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deanna","Timothy","Ryan","Richard"],"index":56748,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997490048,"difficulty":0.0002509952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"William can now know whether Freddie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","William","Stevie","Freddie"],"index":58918,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953705668,"difficulty":0.0046294332}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Kimberly's forehead is muddy. It is publicly announced that Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Kimberly can now know that Bill can know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bill","Linda","Kimberly"],"index":13248,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.5121356845,"difficulty":1.5121356845}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josefina does not know whether Cindy is thirsty. It is publicly announced that Brenda does not know whether Cindy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Cindy can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josefina","Brenda","Cindy","Lauren"],"index":18920,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997840524,"difficulty":0.0002159476}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcelina's card is shown to Dale. Jose's card is shown to Dale. Kim's card is shown to Marcelina. Marcelina's card is shown to Jose. Dale's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Marcelina does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kim can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dale","Marcelina","Jose","Kim"],"index":18220,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953898191,"difficulty":0.0046101809}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know whether Marcia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marcia","Coleen","Michael"],"index":4129,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997076392,"difficulty":0.0002923608}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Celeste does not know whether Celeste's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3&4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3&4) ] 0","hypothesis":"Dean can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Celeste","George","Dean"],"index":63769,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965643287,"difficulty":0.0034356713}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Traci. Betty's card is shown to Betty. Betty's card is shown to Carl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Traci can now know that Betty can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Traci","Betty","Carl"],"index":61584,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984840751,"difficulty":0.0015159249}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Buddy is thirsty. It is publicly announced that Woodrow is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(1) ] Agenta knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(1) ] 0","hypothesis":"Woodrow can now know that Buddy can know whether Jon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Woodrow","Buddy","Leona","Jon"],"index":13642,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8715657592,"difficulty":0.1284342408}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether Joshua's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Joshua can now know whether Erma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Erma","Joseph","Joshua"],"index":19496,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995979667,"difficulty":0.0004020333}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ted knows whether someone is thirsty. It is publicly announced that Rachel does not know whether Ted is thirsty. It is publicly announced that Rachel is thirsty. It is publicly announced that James does not know whether Ted is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jesse can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesse","Rachel","Ted","James"],"index":62630,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984785914,"difficulty":0.0015214086}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy. It is publicly announced that Alana's forehead is not muddy. It is publicly announced that David knows whether Dean's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that Dean's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","William","Dean","Alana"],"index":11359,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8494670987,"difficulty":0.1505329013}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Rose can now know whether Rose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rose","Michele"],"index":18085,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996638298,"difficulty":0.0003361702}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy. It is publicly announced that Shannon knows whether Mario's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Mario can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mario","Tanya","Robert","Shannon"],"index":59715,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982847571,"difficulty":0.0017152429}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diane knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Fred can now know whether Yon can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Diane","Edna","Fred","Yon"],"index":48708,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999563992,"difficulty":0.000436008}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jeffrey can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Jeffrey","Charles","Michael"],"index":20525,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984271526,"difficulty":0.0015728474}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy is not thirsty. It is publicly announced that Thomas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"William can now know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marsha","William","Timothy","Thomas"],"index":50651,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9829006791,"difficulty":0.0170993209}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Jamaal. Eva's card is shown to Jamaal. Deborah's card is shown to Deborah. Eva's card is shown to Deborah. Jamaal's card is shown to Eva. Deborah's card is shown to Eva. Eva's card is shown to Eva. It is publicly announced that someone picked a red card. It is publicly announced that Eva picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Jamaal can now know whether Deborah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jamaal","Deborah","Eva"],"index":41483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6396291256,"difficulty":0.3603708744}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margarite does not know whether Margarite's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Margarite can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Martha","Margarite"],"index":50043,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986048341,"difficulty":0.0013951659}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Therese does not know whether or not everyone's forehead is muddy. It is publicly announced that Therese knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Tom can now know that Tom's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anthony","Therese","Tom","David"],"index":4250,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5665898323,"difficulty":0.4334101677}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether or not everyone is thirsty. It is publicly announced that Paul does not know whether Clifton is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Clifton can now know whether Paul can know that Clifton is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Clifton"],"index":10869,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.987450242,"difficulty":0.012549758}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Maria can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Clinton","Rachel"],"index":16071,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982085228,"difficulty":0.0017914772}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Blanche does not know whether Andrea is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Cora can now know whether Andrea can know that Cora is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Blanche","Cora","Andrea"],"index":55423,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9705045819,"difficulty":0.0294954181}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Holli's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Adam can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adam","Elizabeth","Holli"],"index":13342,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983307719,"difficulty":0.0016692281}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vicente knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Vicente can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Victoria","Vicente"],"index":51353,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972086549,"difficulty":0.0027913451}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sidney's card is shown to Sidney. Anthony's card is shown to Anthony. Kelly's card is shown to Anthony. Sidney's card is shown to Kelly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kelly can now know whether Anthony can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sidney","Anthony","Kelly"],"index":20356,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997134805,"difficulty":0.0002865195}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Rose. Helen's card is shown to Helen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Helen can now know whether Adam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rose","Helen","Adam"],"index":6431,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.963357389,"difficulty":0.036642611}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Patricia can now know that Lou's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Lou","Henry","Howard"],"index":24633,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983797073,"difficulty":0.0016202927}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rey does not know whether Rey's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rey knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Rey can now know whether Miguel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rey","Miguel","Jordan"],"index":17292,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995131493,"difficulty":0.0004868507}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Jennifer's card is shown to Carmen. Marguerite's card is shown to Marguerite. Jennifer's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether Carmen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Carmen","Marguerite","Jennifer"],"index":647,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9233222604,"difficulty":0.0766777396}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Roberta can now know that Doris can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Roberta","Terry","Debra"],"index":4508,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983935952,"difficulty":0.0016064048}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa does not know whether or not everyone's forehead is muddy. It is publicly announced that Lisa does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Lisa can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lisa","Rogelio"],"index":44304,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975800514,"difficulty":0.0024199486}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Peggy can now know that Bonnie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Peggy","Bonnie"],"index":30456,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983235002,"difficulty":0.0016764998}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether or not everyone's forehead is muddy. It is publicly announced that Leslie does not know whether Leslie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Diane can now know whether Thomas can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marilyn","Thomas","Leslie","Diane"],"index":40117,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997091889,"difficulty":0.0002908111}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melisa knows whether Kim's forehead is muddy. It is publicly announced that Kim knows whether Melisa's forehead is muddy. It is publicly announced that Glenn does not know whether Glenn's forehead is muddy. It is publicly announced that Melisa knows whether Melisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Glenn can now know that Melisa can know that Melisa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Glenn","Melisa","Kim"],"index":7642,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9914503694,"difficulty":1.9914503694}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Vicky. Vicky's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Vicky knows whether Vicky picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"James can now know that Vicky can know whether Vicky picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vicky","James"],"index":1975,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9185154438,"difficulty":0.0814845562}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether or not everyone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Linda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Linda","Paula"],"index":52193,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937692285,"difficulty":0.0062307715}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"James can now know that Clay can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Clay"],"index":53081,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998298943,"difficulty":0.001701057}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Natasha's card is shown to Monica. Teri's card is shown to Natasha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Monica can now know whether Teri can know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Teri","Monica","Natasha","Kenneth"],"index":48751,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9270102978,"difficulty":0.0729897022}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis knows whether Francis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Tina can now know that Francis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vernon","Tina","Francis","Herbert"],"index":50291,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978564382,"difficulty":0.0021435618}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Brian can now know whether William can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Brian","Matthew","William"],"index":5082,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997819066,"difficulty":0.0002180934}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. Daniel's card is shown to Junior. Junior's card is shown to Junior. Wilma's card is shown to Junior. Junior's card is shown to Wilma. Junior's card is shown to Bruce. Bruce's card is shown to Bruce. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that Bruce can know whether Wilma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Junior","Wilma","Bruce"],"index":61736,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5890257955,"difficulty":0.4109742045}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy. It is publicly announced that Daniel knows whether or not nobody's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Daniel can now know that Richard can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daniel","Richard"],"index":47512,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9904056191,"difficulty":0.0095943809}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raul does not know whether Ronald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Raul can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Antonia","Raul","Ronald","Elizabeth"],"index":64071,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997707009,"difficulty":0.0002292991}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne knows whether Joanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Joanne can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frank","Margaret","Joanne"],"index":38316,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984771609,"difficulty":0.0015228391}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Peggy is thirsty. It is publicly announced that Peggy is not thirsty. It is publicly announced that Thomas is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] Agentd knows whether (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] 0","hypothesis":"Billy can now know whether Lena can know that Billy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Peggy","Thomas","Lena","Billy"],"index":51630,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9708569646,"difficulty":1.9708569646}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Juan can now know whether Juan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jamie","Juan","Ralph"],"index":23109,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996402264,"difficulty":0.0003597736}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ericka can now know that Eddie can know that Jane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eddie","Ericka","Jane"],"index":65110,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986454844,"difficulty":0.0013545156}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dustin's card is shown to Dustin. It is publicly announced that someone picked a red card. It is publicly announced that Dustin knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Dustin can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dustin","Andrew"],"index":18222,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9906734824,"difficulty":0.0093265176}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether or not everyone is thirsty. It is publicly announced that Kimberly does not know whether or not everyone is thirsty. It is publicly announced that Kimberly does not know whether Lisa is thirsty. It is publicly announced that Kimberly knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Kimberly can now know whether Lisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lisa","Kimberly"],"index":47849,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7559395432,"difficulty":1.7559395432}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Albert can now know that Gregg can know that Gregg's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Allene","Albert","Anna","Gregg"],"index":44649,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984908104,"difficulty":0.0015091896}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanette knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Jeanette can now know that Ivan can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jay","Ivan","Jeanette"],"index":3621,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997665286,"difficulty":0.0002334714}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Shelly can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Larry","Shelly"],"index":3409,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997379184,"difficulty":0.0002620816}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Helen can now know whether Beverly can know whether Helen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beverly","Helen","Dale"],"index":16604,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980899692,"difficulty":0.0019100308}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Treena can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","Candance","John","Treena"],"index":35147,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980868101,"difficulty":0.0019131899}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joan knows whether Joan is thirsty. It is publicly announced that Joan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 3 ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 3 ] 0","hypothesis":"Joan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leonard","Michael","Joan"],"index":40743,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984852672,"difficulty":0.0015147328}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Gary. Moises's card is shown to Gary. Moises's card is shown to Moises. Gary's card is shown to Deborah. Deborah's card is shown to Deborah. Moises's card is shown to Clyde. Clyde's card is shown to Clyde. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Moises picked a red card. It is publicly announced that Moises knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Deborah can now know that Gary can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Moises","Deborah","Clyde"],"index":22907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997790456,"difficulty":0.0002209544}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemarie's card is shown to Eva. Eva's card is shown to Rosemarie. Rosemarie's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Eva picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Donna picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Rosemarie can now know that Donna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Santiago","Eva","Rosemarie","Donna"],"index":54022,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9330555797,"difficulty":0.0669444203}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether Sheila is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Anthony can now know that Sheila can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Sheila","Philip","Anthony"],"index":46533,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997026324,"difficulty":0.0002973676}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Debbie can now know that Carlo can know that Debbie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carlo","Debbie","Mark"],"index":52823,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940719008,"difficulty":0.0059280992}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon's forehead is not muddy. It is publicly announced that Soila knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Soila can now know that Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daniel","Neva","Brandon","Soila"],"index":51543,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8414357901,"difficulty":0.1585642099}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nathan does not know whether Claude is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Richard does not know whether Nathan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Richard can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Claude","Julie","Richard","Nathan"],"index":40624,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Timothy. Robert's card is shown to Timothy. Timothy's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Timothy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Robert can now know that Timothy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Timothy","Robert"],"index":61668,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6504498124,"difficulty":1.6504498124}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Lucas. Lucas's card is shown to Lucas. Rachel's card is shown to Rachel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lucas can now know that Mary can know whether Lorraine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Lucas","Lorraine","Rachel"],"index":64736,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.890239656,"difficulty":0.109760344}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelic's card is shown to Angelic. Angelic's card is shown to Katherine. Angelic's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card. It is publicly announced that Angelic picked a red card. It is publicly announced that Katherine does not know whether Katherine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know that Angelic can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angelic","Katherine","James"],"index":56013,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981904626,"difficulty":0.0018095374}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rudolph knows whether Lauren's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mary can now know that Lauren can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Rudolph","Lauren"],"index":57091,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983491898,"difficulty":0.0016508102}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Estelle's card is shown to Patricia. Susan's card is shown to Estelle. Estelle's card is shown to Estelle. It is publicly announced that someone picked a red card. It is publicly announced that Susan knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Susan can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Patricia","Estelle"],"index":44117,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8670428395,"difficulty":0.1329571605}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Marguerite. Marguerite's card is shown to Thelma. Marguerite's card is shown to Laura. Thelma's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thelma can now know whether Marguerite can know that Thelma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marguerite","Thelma","Laura"],"index":51923,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8637832999,"difficulty":1.8637832999}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether Kathryn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Heather can now know that Margaret can know that Heather is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathryn","Margaret","Heather"],"index":63613,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978047013,"difficulty":0.0021952987}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary's forehead is muddy. It is publicly announced that Edward knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Edward can now know that Gary can know that Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Edward","Gary"],"index":22477,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9905481935,"difficulty":0.0094518065}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clara knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Melissa can now know that Clara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clara","Debra","Melissa"],"index":9776,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982074499,"difficulty":0.0017925501}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernie's card is shown to Dianne. Ernie's card is shown to Roger. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Dianne can now know that Ernie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dianne","Roger","Ernie"],"index":28458,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945856929,"difficulty":0.0054143071}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon is not thirsty. It is publicly announced that Jocelyn knows whether Sharon is thirsty. It is publicly announced that Jocelyn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! 1 ] Agentb knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! 1 ] 0","hypothesis":"Rose can now know whether Beth can know whether Jocelyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jocelyn","Rose","Beth","Sharon"],"index":38597,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988970757,"difficulty":0.0011029243}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Kimberly. Kyle's card is shown to Kimberly. Kimberly's card is shown to Laura. Laura's card is shown to Laura. Kyle's card is shown to Laura. Kimberly's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that Laura knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Laura can now know whether Kyle can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","Laura","Kyle"],"index":16602,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9951598048,"difficulty":0.0048401952}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Connie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Gloria can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gloria","Lawrence","Susan","Connie"],"index":15865,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982466698,"difficulty":0.0017533302}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Donald can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joshua","Randall","Donald"],"index":66025,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981895089,"difficulty":0.0018104911}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Brian. James's card is shown to Brian. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Brian can now know whether James can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brian","James"],"index":35336,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9733012319,"difficulty":0.0266987681}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Samuel can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Samuel","Michelle","Thomas"],"index":12295,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982699156,"difficulty":0.0017300844}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel is thirsty. It is publicly announced that Billy does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Maurice can now know that Joseph can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Billy","Maurice","Joseph","Daniel"],"index":47534,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984140396,"difficulty":0.0015859604}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Danielle does not know whether or not everyone is thirsty. It is publicly announced that Danielle does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Eric can now know that Mary can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danielle","Eric","Mary","David"],"index":43249,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997153878,"difficulty":0.0002846122}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Joshua. Mary's card is shown to Hugh. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Mary can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Joshua","Hugh"],"index":9427,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9933425784,"difficulty":0.0066574216}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josh's card is shown to Josh. Joshua's card is shown to Josh. Joshua's card is shown to Joshua. Vonda's card is shown to Joshua. Josh's card is shown to James. Joshua's card is shown to James. Josh's card is shown to Vonda. Vonda's card is shown to Vonda. It is publicly announced that someone picked a red card. It is publicly announced that Josh knows whether Josh picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"James can now know whether Vonda can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josh","Joshua","James","Vonda"],"index":39259,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ben does not know whether or not everyone is thirsty. It is publicly announced that Alfonso knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Alfonso can now know that Alfonso is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ben","Alfonso"],"index":2640,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9871929884,"difficulty":1.9871929884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michelle","Christopher","James"],"index":1720,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979321957,"difficulty":0.0020678043}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether Cedric's forehead is muddy. It is publicly announced that Cedric does not know whether Cedric's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Betty can now know whether Elisabeth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elisabeth","Betty","Cedric"],"index":18779,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8002464175,"difficulty":0.1997535825}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen does not know whether Marion is thirsty. It is publicly announced that Helen does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Johanna can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Johanna","Carrie","Marion"],"index":57074,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962952733,"difficulty":0.0037047267}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittany's card is shown to Dennis. Marshall's card is shown to Brittany. Dennis's card is shown to Marshall. Marshall's card is shown to Marshall. It is publicly announced that someone picked a red card. It is publicly announced that Brittany does not know whether Dennis picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Marshall can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Brittany","Marshall"],"index":12365,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986074567,"difficulty":0.0013925433}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Jerry does not know whether Theresa is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Theresa can now know whether Jerry can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Theresa","Jerry"],"index":18161,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997802377,"difficulty":0.0002197623}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Debby can now know whether Randall is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Franklin","Randall","Chrystal","Debby"],"index":25411,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971513152,"difficulty":0.0028486848}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Farrah can now know that Mario can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angelique","Farrah","Mario"],"index":6980,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983287454,"difficulty":0.0016712546}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marilyn does not know whether Anthony is thirsty. It is publicly announced that Nick knows whether someone is thirsty. It is publicly announced that Marilyn does not know whether or not everyone is thirsty. It is publicly announced that Marlene does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nick can now know that Anthony can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nick","Marilyn","Anthony","Marlene"],"index":54225,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997825027,"difficulty":0.0002174973}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwight's card is shown to Sandra. Sandra's card is shown to Dwight. Sandra's card is shown to Cathy. Dwight's card is shown to Cathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sandra can now know whether Cathy can know whether Dwight picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Dwight","Cathy"],"index":2283,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989504814,"difficulty":0.0010495186}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Helena can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julia","Patricia","Helena"],"index":37589,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996738434,"difficulty":0.0003261566}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelby knows whether Frank's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy. It is publicly announced that Frank knows whether Shelby's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Frank can now know that Shelby can know that Frank's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Shelby","Frank"],"index":14102,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9450222254,"difficulty":0.0549777746}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Denis does not know whether Ellen is thirsty. It is publicly announced that Ellen does not know whether Denis is thirsty. It is publicly announced that Denis does not know whether Ellen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Edna can now know that Denis can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ellen","Denis","Edna","Michael"],"index":49867,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9753608704,"difficulty":0.0246391296}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Justin can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Justin","Charles","Patricia"],"index":5845,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993330836,"difficulty":0.0006669164}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tomas knows whether Miguel's forehead is muddy. It is publicly announced that Tomas knows whether or not everyone's forehead is muddy. It is publicly announced that Miguel knows whether Tomas's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Tomas can now know that Miguel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tomas","Miguel"],"index":35845,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981683493,"difficulty":0.0018316507}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy. It is publicly announced that Trina's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Trina can now know whether Steven can know whether Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Trina","Steven"],"index":21081,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9451447725,"difficulty":0.0548552275}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jody knows whether Jody is thirsty. It is publicly announced that Nancy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Jody","John","Nancy"],"index":4953,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9403415322,"difficulty":0.0596584678}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rick does not know whether Rick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"William can now know that Danielle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rick","Jason","Danielle","William"],"index":60751,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978474379,"difficulty":0.0021525621}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberley can now know that Tabatha can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ryan","Tabatha","Kimberley","Mary"],"index":48981,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986549616,"difficulty":0.0013450384}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Martha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Martha","Mary","Joshua"],"index":62878,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986316562,"difficulty":0.0013683438}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernice's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Cora can now know that Bernice can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cora","Bernice","Jim"],"index":42816,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984305501,"difficulty":0.0015694499}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dallas knows whether Dallas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Tami can now know that Dallas can know that Tami's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dallas","Cynthia","Harold","Tami"],"index":53811,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978590608,"difficulty":0.0021409392}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Modesto does not know whether Clarence is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Mckinley can now know whether Susan can know whether Susan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mckinley","Modesto","Susan","Clarence"],"index":57451,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974765182,"difficulty":0.0025234818}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"George can now know whether Jacob can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Jacob","Andy","George"],"index":55273,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997832179,"difficulty":0.0002167821}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Flossie can now know that Norma can know that Norma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Flossie","Lupe","Zackary","Norma"],"index":31210,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985772371,"difficulty":0.0014227629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Chester is thirsty. It is publicly announced that Chester does not know whether Savannah is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Chester can now know whether Chester is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Savannah","Michael","Chester","Mary"],"index":32951,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989187717,"difficulty":0.0010812283}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Robert can now know that Charles can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Robert","Edith","Jackie"],"index":9935,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983336329,"difficulty":0.0016663671}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Risa's forehead is muddy. It is publicly announced that Risa's forehead is muddy. It is publicly announced that Diane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Risa can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Percy","Diane","Risa"],"index":14030,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8374971747,"difficulty":0.1625028253}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether Lettie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Deborah can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deborah","Lettie","Mary"],"index":8522,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9881783128,"difficulty":0.0118216872}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ryan does not know whether Mark is thirsty. It is publicly announced that Joyce does not know whether Walter is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ryan can now know that Walter can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Mark","Ryan","Walter"],"index":44297,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983972907,"difficulty":0.0016027093}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina's forehead is not muddy. It is publicly announced that Clinton knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Tina can now know that Keith's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clinton","Tina","Keith"],"index":30983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.995256722,"difficulty":0.004743278}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alejandrina does not know whether Lela is thirsty. It is publicly announced that Paul does not know whether Alejandrina is thirsty. It is publicly announced that Paul knows whether or not nobody is thirsty. It is publicly announced that Lela does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Paul can now know whether Alejandrina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lela","Paul","James","Alejandrina"],"index":53905,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8562127948,"difficulty":0.1437872052}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Florentina's forehead is muddy. It is publicly announced that Melissa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Florentina can now know that Kelvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Kelvin","Florentina","Melissa"],"index":57929,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99746418,"difficulty":0.00253582}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Megan. Burton's card is shown to Francis. Francis's card is shown to Francis. It is publicly announced that someone picked a red card. It is publicly announced that Megan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Megan can now know whether Burton can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Megan","Burton","Francis"],"index":65009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996830225,"difficulty":0.0003169775}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Larry can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Larry","Deborah"],"index":44708,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981740713,"difficulty":0.0018259287}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Cathy can now know that Kevin can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Bobbie","Cathy"],"index":58007,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997100234,"difficulty":0.0002899766}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jackie's card is shown to Sarah. Jackie's card is shown to Jackie. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Sarah can now know that Jackie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sarah","Jackie"],"index":44145,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986227751,"difficulty":0.0013772249}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Reynaldo is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Joyce can now know whether Randal can know that Randal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Randal","Theodore","Joyce","Reynaldo"],"index":1497,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.520440042,"difficulty":0.479559958}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Velma. Velma's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Dana knows whether Velma picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Velma can now know that Velma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Velma","Dana","Ronald"],"index":52664,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917347431,"difficulty":0.0082652569}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edna does not know whether Brian is thirsty. It is publicly announced that Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Edna can now know that Agnes is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Agnes","Edna","Brian"],"index":32503,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9872307181,"difficulty":0.0127692819}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Maire's card is shown to Maire. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Maire picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Maire can now know that James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Maire"],"index":40769,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982481003,"difficulty":0.0017518997}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Wayne is thirsty. It is publicly announced that Maria does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Maria can now know that Wayne can know that Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Wayne","Veronica"],"index":27069,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.778331399,"difficulty":0.221668601}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wayne can now know that Carl can know whether Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","Ben","Betty","Carl"],"index":1601,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995977283,"difficulty":0.0004022717}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Edward. Thomas's card is shown to Edward. Roosevelt's card is shown to Edward. Janet's card is shown to Thomas. Janet's card is shown to Roosevelt. Roosevelt's card is shown to Roosevelt. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janet can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edward","Thomas","Janet","Roosevelt"],"index":1490,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984554052,"difficulty":0.0015445948}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Krista does not know whether Kristy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Kristy can now know whether Krista is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Juan","Krista","Kristy","Margie"],"index":49436,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6982576847,"difficulty":1.6982576847}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"David can now know that Madie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Opal","David","Madie"],"index":935,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997482896,"difficulty":0.0002517104}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Karen can now know whether Shirley can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Karen","Shirley"],"index":58642,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995798469,"difficulty":0.0004201531}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Amanda can now know that Katrina can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katrina","Amanda","Eloise","Genevieve"],"index":33626,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.682893455,"difficulty":1.682893455}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shanda's card is shown to Dale. Shanda's card is shown to Shanda. It is publicly announced that someone picked a red card. It is publicly announced that Dale knows whether Shanda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Dale can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dale","Shanda"],"index":51747,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leonard's card is shown to Leonard. Leonard's card is shown to Katherine. Katherine's card is shown to Katherine. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leonard can now know that Katherine can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leonard","Katherine","Kevin","Hang"],"index":3638,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997768998,"difficulty":0.0002231002}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Johnnie does not know whether Johnnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Johnnie can now know whether Marilyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diane","Marilyn","Johnnie"],"index":37761,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994843006,"difficulty":0.0005156994}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Aaron. Aaron's card is shown to Tony. Gwendolyn's card is shown to Gwendolyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tony can now know that Deborah can know whether Aaron picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Aaron","Tony","Deborah","Gwendolyn"],"index":65605,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6892246604,"difficulty":0.3107753396}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelly's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Katherine can now know whether Shelly can know that Katherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christine","Shelly","Katherine"],"index":33256,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6890009046,"difficulty":0.3109990954}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julian does not know whether or not everyone is thirsty. It is publicly announced that Jose knows whether someone is thirsty. It is publicly announced that Jose is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] (Agentd knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Esther can now know whether Ruby is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruby","Jose","Julian","Esther"],"index":21065,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9037648439,"difficulty":0.0962351561}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Paul can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Paul","Alton","Donna"],"index":55540,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983439445,"difficulty":0.0016560555}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Rodney can now know that Michael can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rodney","Deborah","Michael"],"index":2544,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996664524,"difficulty":0.0003335476}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Dylan. Dylan's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Dylan does not know whether Dylan picked a red card. It is publicly announced that Dylan does not know whether Dylan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dylan can now know that Dylan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dylan","Gary"],"index":43667,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8753803372,"difficulty":0.1246196628}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] 0","hypothesis":"Joseph can now know that Laura can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Laura","Joseph"],"index":47138,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980193377,"difficulty":0.0019806623}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christa's card is shown to Christa. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Christa picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Christa can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christa","Juanita","Robert"],"index":38497,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997250438,"difficulty":0.0002749562}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Ross. Mary's card is shown to Helen. George's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether Ross can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Ross","Helen","Mary"],"index":40204,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Albert does not know whether Barbara is thirsty. It is publicly announced that Douglas does not know whether Albert is thirsty. It is publicly announced that Barbara does not know whether Douglas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Barbara can now know whether Barbara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clyde","Douglas","Barbara","Albert"],"index":23405,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985827208,"difficulty":0.0014172792}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremiah does not know whether Jeremiah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Richard can now know that Christopher can know whether Jacque's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Jacque","Christopher","Jeremiah"],"index":2774,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996345043,"difficulty":0.0003654957}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Walter can now know whether Shelley can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Walter","Ismael","Shelley","Kristy"],"index":64345,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997181296,"difficulty":0.0002818704}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Larry can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Larry","Jeffrey"],"index":65070,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997637868,"difficulty":0.0002362132}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Christine. Christine's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Timothy can now know that Christine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Christine","Timothy"],"index":58503,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984773993,"difficulty":0.0015226007}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqueline's card is shown to James. Eldon's card is shown to Eldon. Paul's card is shown to Eldon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eldon can now know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Eldon","Jacqueline","Paul"],"index":49792,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8411147594,"difficulty":1.8411147594}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Alfred can now know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alfred","Donald","Sandy","Jane"],"index":6017,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968253374,"difficulty":0.0031746626}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Doretha's forehead is muddy. It is publicly announced that Doretha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Douglas can now know that Doretha can know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cameron","Douglas","Doretha"],"index":63222,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9333751202,"difficulty":0.0666248798}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Debra. Charles's card is shown to Evelyn. Evelyn's card is shown to Lezlie. Lezlie's card is shown to Lezlie. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Lezlie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Debra can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Debra","Charles","Evelyn","Lezlie"],"index":13346,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997196794,"difficulty":0.0002803206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Henry can now know that Martin can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Martin","Naomi","Evelyn"],"index":40543,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983673692,"difficulty":0.0016326308}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene knows whether Arlene's forehead is muddy. It is publicly announced that Arlene knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Kathleen can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arlene","Carl","Kathleen","Luz"],"index":28053,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997749269,"difficulty":0.002250731}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Blanche's card is shown to Carroll. Carroll's card is shown to Blanche. Blanche's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carroll can now know whether Blanche can know whether Blanche picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carroll","Blanche","Brian"],"index":66964,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9922661185,"difficulty":0.0077338815}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester's forehead is not muddy. It is publicly announced that Hae's forehead is muddy. It is publicly announced that Hae's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Hae can now know that Abby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Abby","Hae","Lester"],"index":24189,"s-l":"forehead_mirror-0","deberta_pred":1,"deberta_confidence":0.7384437323,"difficulty":1.7384437323}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Cynthia can know that Cynthia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Cynthia","Robert"],"index":2489,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995809197,"difficulty":0.0004190803}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Joanne can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Joanne"],"index":28556,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Geraldine does not know whether Joann is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Joann can now know that Mary can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Geraldine","Joann","Mary"],"index":49566,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.994818151,"difficulty":0.005181849}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Robert can now know that Shaina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alicia","Shaina","Robert"],"index":55309,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9778174758,"difficulty":0.0221825242}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danny knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Danny can now know whether Sharon can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Danny","Brian","Sharon"],"index":54307,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997621179,"difficulty":0.0002378821}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lawrence does not know whether Hazel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Elmer can now know that Elmer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Elmer","Lawrence","Hazel"],"index":30316,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997892797,"difficulty":0.002107203}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Dannie can now know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dannie","Martha","Patrick"],"index":47453,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994204044,"difficulty":0.0005795956}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl knows whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Casey can now know that Casey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carl","Casey","Colleen"],"index":36021,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981188178,"difficulty":0.0018811822}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Annette can now know that Joe can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","Allen","Joe","Annette"],"index":26002,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984771609,"difficulty":0.0015228391}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mandy's card is shown to Mandy. Mary's card is shown to Mandy. Rodney's card is shown to Mandy. Del's card is shown to Rodney. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mandy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Del","Mandy","Mary","Rodney"],"index":4385,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985204339,"difficulty":0.0014795661}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. David's card is shown to Paul. Paul's card is shown to David. Raymond's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Raymond can now know that Paul can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Raymond","David"],"index":37926,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9722161889,"difficulty":0.0277838111}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lenore knows whether or not nobody's forehead is muddy. It is publicly announced that Quintin's forehead is not muddy. It is publicly announced that Doris does not know whether Doris's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Quintin can now know whether Doris can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Quintin","Lenore"],"index":45410,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999781549,"difficulty":0.000218451}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jean does not know whether James is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] 0","hypothesis":"James can now know that Jean can know whether Jean is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jean","James"],"index":40305,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992300272,"difficulty":0.0007699728}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sam's card is shown to Rodney. Joanne's card is shown to Sam. Sam's card is shown to Joanne. It is publicly announced that someone picked a red card. It is publicly announced that Rodney knows whether someone picked a red card. It is publicly announced that Sam does not know whether Rodney picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Sam can now know that Sam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rodney","Sam","Joanne"],"index":3942,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8127759099,"difficulty":0.1872240901}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nikki's card is shown to Ruth. Ruth's card is shown to Nikki. Nikki's card is shown to Nikki. It is publicly announced that someone picked a red card. It is publicly announced that Ruth knows whether Ruth picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ruth can now know whether Nikki can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ruth","Nikki"],"index":20588,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995234013,"difficulty":0.0004765987}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank does not know whether Alfred is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Frank can now know that Delmer can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Delmer","Alfred","John","Frank"],"index":62962,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983482361,"difficulty":0.0016517639}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dave's card is shown to Robert. Alvin's card is shown to Robert. Dave's card is shown to Alvin. It is publicly announced that someone picked a red card. It is publicly announced that Dave does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dave can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dave","Robert","Alvin"],"index":33430,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9853643775,"difficulty":0.0146356225}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terrance's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Sean can now know that Margaret can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathy","Terrance","Margaret","Sean"],"index":61739,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9895139933,"difficulty":0.0104860067}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth does not know whether Lara is thirsty. It is publicly announced that Kenneth does not know whether Morton is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lara can now know whether Morton can know that Lara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Morton","Lara","Alecia"],"index":31968,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9871039987,"difficulty":0.0128960013}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gladys's card is shown to Anthony. Anthony's card is shown to Gladys. Gladys's card is shown to Gladys. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Gladys does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Anthony can now know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Gladys","Robert"],"index":26698,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9872729182,"difficulty":1.9872729182}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Rory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Rory can now know that Erwin can know that Rory's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rory","Matthew","Michael","Erwin"],"index":33084,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970725775,"difficulty":0.0029274225}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Julius can now know that Patricia can know whether Brandon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Willie","Patricia","Brandon","Julius"],"index":10909,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978867173,"difficulty":0.0021132827}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Velma does not know whether or not everyone is thirsty. It is publicly announced that Jerry does not know whether Pearl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jerry can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tim","Jerry","Pearl","Velma"],"index":33624,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977320433,"difficulty":0.0022679567}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timmy does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mary can now know whether Carmen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carmen","Mary","Timmy"],"index":1069,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972106814,"difficulty":0.0027893186}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Damien does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether Omar can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","Damien","Omar","Natasha"],"index":25723,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8708069921,"difficulty":0.1291930079}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy. It is publicly announced that Rosa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] 0","hypothesis":"Rosa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Rose","Rosa"],"index":56651,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956978559,"difficulty":0.0043021441}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rene's forehead is muddy. It is publicly announced that Joseph does not know whether Joseph's forehead is muddy. It is publicly announced that Joseph knows whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Rene can now know whether Joseph can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rene","Henry","Mark","Joseph"],"index":34661,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sally is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"George can now know that Sally can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sally","George","Clarence","William"],"index":38869,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9836981297,"difficulty":0.0163018703}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know whether Deborah can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Frank","Deborah","Arthur"],"index":4021,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995910525,"difficulty":0.0004089475}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Johnny can now know whether Robert can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cindy","Johnny","Ray","Robert"],"index":45451,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999702394,"difficulty":0.000297606}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louis does not know whether Olive is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Louis can now know that James can know whether Olive is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Olive","Louis","James"],"index":17838,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975474477,"difficulty":0.0024525523}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest does not know whether Ernest's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ernest","Jeffrey","James","Donna"],"index":32800,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982771873,"difficulty":0.0017228127}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to Donald. Connie's card is shown to Connie. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether Donald picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Donald can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Donald","Connie"],"index":20349,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997193217,"difficulty":0.0002806783}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Socorro knows whether Catherine's forehead is muddy. It is publicly announced that Socorro knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Socorro can now know whether Catherine can know whether Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Catherine","Socorro"],"index":60527,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6030465364,"difficulty":1.6030465364}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Paula. Cathy's card is shown to Paula. Paula's card is shown to Nancy. Stephanie's card is shown to Cathy. It is publicly announced that someone picked a red card. It is publicly announced that Paula does not know whether Nancy picked a red card. It is publicly announced that Nancy does not know whether Nancy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Paula can now know that Stephanie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paula","Stephanie","Nancy","Cathy"],"index":239,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9838543534,"difficulty":0.0161456466}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda does not know whether Amanda's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda knows whether Arden's forehead is muddy. It is publicly announced that Amanda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Arden can now know that Amanda can know that Arden's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amanda","Misty","Arden"],"index":14365,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9911482334,"difficulty":0.0088517666}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Sheila can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sheila","Lucille","Barbara"],"index":27573,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982911944,"difficulty":0.0017088056}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack knows whether or not everyone's forehead is muddy. It is publicly announced that Kaitlyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"George can now know that Samuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Samuel","George","Kaitlyn","Jack"],"index":28624,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9715923667,"difficulty":0.0284076333}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lesley does not know whether or not everyone's forehead is muddy. It is publicly announced that Marcella knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lesley can now know whether Lesley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lesley","Cynthia","Marcella","Sheryl"],"index":37600,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6794804931,"difficulty":0.3205195069}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brunilda's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Tarsha can now know that Brunilda can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tarsha","Brunilda"],"index":5399,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983910918,"difficulty":0.0016089082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Darcel can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Darcel","Donald","James"],"index":63021,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989373088,"difficulty":0.0010626912}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Madelyn knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know whether Madelyn can know whether Daniela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Madelyn","Daniela"],"index":26160,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996997118,"difficulty":0.0003002882}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Linda can now know whether Arthur's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Michael","Harold","Linda"],"index":40840,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999435246,"difficulty":0.000564754}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Amber. Amber's card is shown to Dora. Dora's card is shown to Dora. Amber's card is shown to David. Dora's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Dora knows whether Dora picked a red card. It is publicly announced that Amber does not know whether Dora picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"David can now know that Amber picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amber","Dora","David"],"index":38060,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9839443564,"difficulty":0.0160556436}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cristobal knows whether Deborah's forehead is muddy. It is publicly announced that Cristobal knows whether Cristobal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Carol can now know that Cristobal can know that Deborah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carol","Cristobal","Deborah"],"index":20116,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977338314,"difficulty":0.0022661686}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Olivia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Marva can now know whether Olivia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Peggy","Marva","Olivia"],"index":46944,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997140765,"difficulty":0.0002859235}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Dorothy. Brian's card is shown to Dorothy. Angela's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Angela can now know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Angela","Brian"],"index":11266,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6992571354,"difficulty":1.6992571354}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Shawn. Shawn's card is shown to Burton. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Burton does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Burton can now know whether Shawn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shawn","Burton","Paul"],"index":41454,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9739708304,"difficulty":0.0260291696}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Howard can now know that Nancy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Howard","Nancy","Andrea"],"index":16847,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997839332,"difficulty":0.0002160668}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lela does not know whether Rachelle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jaime can now know whether Lela can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christy","Jaime","Rachelle","Lela"],"index":22185,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7767589092,"difficulty":0.2232410908}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hugo does not know whether Hugo's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Maurice can now know whether Bernard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Maurice","Bernard","Hugo"],"index":42127,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994289279,"difficulty":0.0005710721}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilbur's card is shown to Roberta. Aaron's card is shown to Roberta. Sandra's card is shown to Sandra. Roberta's card is shown to Wilbur. Sandra's card is shown to Wilbur. Roberta's card is shown to Aaron. It is publicly announced that someone picked a red card. It is publicly announced that Wilbur does not know whether Wilbur picked a red card. It is publicly announced that Wilbur does not know whether Wilbur picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Aaron can now know whether Sandra can know that Aaron picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roberta","Sandra","Wilbur","Aaron"],"index":11775,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.914177537,"difficulty":0.085822463}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lillian can now know that Carolyn can know whether Carolyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Lillian","James"],"index":2875,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995180368,"difficulty":0.0004819632}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Tricia's card is shown to Christopher. Paul's card is shown to Christopher. Christopher's card is shown to Joseph. Tricia's card is shown to Joseph. Paul's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that Joseph can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Joseph","Tricia","Paul"],"index":22890,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974822402,"difficulty":0.0025177598}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley knows whether Eunice's forehead is muddy. It is publicly announced that Stanley's forehead is not muddy. It is publicly announced that Irene knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows whether (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Eunice can now know whether Rose can know that Eunice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irene","Eunice","Rose","Stanley"],"index":58517,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5951477885,"difficulty":1.5951477885}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Cassondra. Beverly's card is shown to Cassondra. Linda's card is shown to Carol. Cassondra's card is shown to Carol. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cassondra can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Cassondra","Carol","Beverly"],"index":17104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerald does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mary can now know that Tim can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gerald","Leon","Mary","Tim"],"index":14817,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983209968,"difficulty":0.0016790032}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Kristin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Robert","Kristin","Joseph"],"index":6239,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985520244,"difficulty":0.0014479756}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clayton's card is shown to Alvin. Charles's card is shown to Alvin. Alvin's card is shown to Stephanie. Alvin's card is shown to Clayton. Stephanie's card is shown to Charles. Clayton's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stephanie can now know that Charles can know whether Clayton picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alvin","Stephanie","Clayton","Charles"],"index":50736,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6507501602,"difficulty":1.6507501602}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Barbara. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know whether Rosa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosa","Barbara","Richard"],"index":26483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997677207,"difficulty":0.0002322793}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nelly does not know whether Nelly's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Delores can now know that Delores's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Constance","Nelly","Delores"],"index":56287,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970159531,"difficulty":0.0029840469}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Delores knows whether Juanita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"George can now know whether Juanita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Delores","Juanita","Dawn"],"index":34697,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997491241,"difficulty":0.0002508759}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","David"],"index":44710,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976454377,"difficulty":0.0023545623}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Thomas can now know whether Penny can know that Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Timothy","Thomas","Penny"],"index":13333,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9868805408,"difficulty":1.9868805408}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Ronald can know that Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amanda","Ronald","Mary"],"index":3009,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7620456219,"difficulty":0.2379543781}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey does not know whether or not everyone is thirsty. It is publicly announced that Donald knows whether someone is thirsty. It is publicly announced that Katherine does not know whether Donald is thirsty. It is publicly announced that Katherine does not know whether Germaine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Donald can now know that Germaine can know whether Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Germaine","Katherine","Jeffrey"],"index":8966,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7212642431,"difficulty":0.2787357569}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know whether Rebekah can know that Rebekah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rebekah","Margaret","Linda"],"index":5992,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7946627736,"difficulty":0.2053372264}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roberta's card is shown to David. Roberta's card is shown to Jocelyn. Jocelyn's card is shown to Roberta. It is publicly announced that someone picked a red card. It is publicly announced that Roberta picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"David can now know that Roberta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Jocelyn","Roberta"],"index":65487,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6641392708,"difficulty":0.3358607292}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julius knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"William can now know that Julius can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julius","Robin","William"],"index":28262,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971068501,"difficulty":0.0028931499}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miriam's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Gary can now know that Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Miriam","Gary","Michael"],"index":17629,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.965862453,"difficulty":0.034137547}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Violet's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"James can now know whether Belinda can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Violet","James","Belinda"],"index":8043,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997220635,"difficulty":0.0002779365}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lane's card is shown to Lane. Anna's card is shown to Lane. Sarah's card is shown to Lane. Anna's card is shown to Ruth. Sarah's card is shown to Ruth. Anna's card is shown to Anna. Sarah's card is shown to Anna. Lane's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Ruth knows whether or not everyone picked a red card. It is publicly announced that Sarah picked a black card. It is publicly announced that Lane picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Lane can now know whether Ruth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lane","Ruth","Anna","Sarah"],"index":35168,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997768998,"difficulty":0.0002231002}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Danielle is not thirsty. It is publicly announced that Danielle does not know whether Ralph is thirsty. It is publicly announced that Howard does not know whether Ralph is thirsty. It is publicly announced that Howard knows whether Howard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Danielle can now know that Howard can know that Danielle is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Danielle","Howard","Ralph","John"],"index":37364,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9115883112,"difficulty":0.0884116888}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ezekiel knows whether Ezekiel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ezekiel can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deborah","James","Ezekiel"],"index":12688,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982001781,"difficulty":0.0017998219}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty. It is publicly announced that Richard knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Shante can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shante","Richard"],"index":38784,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997380376,"difficulty":0.0002619624}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Jean. Victoria's card is shown to Jean. Thomas's card is shown to Jean. Jaime's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Victoria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Jean can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jean","Victoria","Jaime","Thomas"],"index":36201,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985230565,"difficulty":0.0014769435}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry does not know whether Sherry's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] 0","hypothesis":"Daniel can now know whether Sherry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alfredo","Daniel","Barbara","Sherry"],"index":7352,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996163845,"difficulty":0.0003836155}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Lucila can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patrick","Sean","Nancy","Lucila"],"index":58745,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997306466,"difficulty":0.0002693534}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Elden can now know whether Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Walter","Elden"],"index":8409,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997443557,"difficulty":0.0002556443}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Bryan is thirsty. It is publicly announced that Bryan does not know whether Charles is thirsty. It is publicly announced that Charles is thirsty. It is publicly announced that Robert does not know whether Bryan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] [ ! ~(Agentc knows whether 2) ] (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Bryan can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Bryan","Robert","Tonya"],"index":43145,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8941420317,"difficulty":0.1058579683}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandon's card is shown to Arthur. Arthur's card is shown to Arthur. Betty's card is shown to Arthur. Brandon's card is shown to Betty. Patrick's card is shown to Betty. Patrick's card is shown to Patrick. It is publicly announced that someone picked a red card. It is publicly announced that Patrick picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Arthur can now know that Betty can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandon","Arthur","Betty","Patrick"],"index":21892,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997166991,"difficulty":0.0002833009}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to William. William's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether Jeffrey picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jeffrey can now know that William can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Jeffrey"],"index":39296,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9268274903,"difficulty":0.0731725097}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia's forehead is muddy. It is publicly announced that Cynthia knows whether someone's forehead is muddy. It is publicly announced that Fred's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Fred can now know whether Cynthia can know that Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Fred","Cynthia"],"index":44625,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995069504,"difficulty":0.0004930496}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether Aaron is thirsty. It is publicly announced that Barbara knows whether or not nobody is thirsty. It is publicly announced that Barbara does not know whether Aaron is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Barbara can now know that David can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Barbara","Aaron"],"index":2445,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9931681156,"difficulty":0.0068318844}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Pamela. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Pamela knows whether Pamela picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Pamela can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Pamela","Daniel"],"index":21306,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998428762,"difficulty":0.001571238}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Ashley. Kenneth's card is shown to Ashley. Kenneth's card is shown to Maria. Thomas's card is shown to Maria. Kenneth's card is shown to Kenneth. Maria's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kenneth can now know that Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ashley","Maria","Kenneth","Thomas"],"index":24692,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7281561494,"difficulty":0.2718438506}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Irene can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Michael","Richard","Irene"],"index":42746,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983752966,"difficulty":0.0016247034}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Naomi knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Claude can now know that Carol can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Claude","David","Naomi"],"index":63371,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9511350393,"difficulty":0.0488649607}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Christopher. Barbara's card is shown to Barbara. Jason's card is shown to Barbara. Christopher's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Jason can know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Barbara","Jason"],"index":66320,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9037210345,"difficulty":0.0962789655}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Alvin can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sharon","Alvin"],"index":45398,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999735415,"difficulty":0.000264585}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether Carolyn's forehead is muddy. It is publicly announced that Edward does not know whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Edward can now know that Carolyn can know that Mandy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mandy","Carolyn","Edward"],"index":39122,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.991067946,"difficulty":1.991067946}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Graig's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Lois can now know whether Jack can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Antonio","Jack","Lois","Graig"],"index":43920,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997316003,"difficulty":0.0002683997}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mae does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Mae can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gabriela","Mae"],"index":55726,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9969034791,"difficulty":0.0030965209}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frederick's card is shown to Elizabeth. Imogene's card is shown to Elizabeth. Imogene's card is shown to Frederick. Elizabeth's card is shown to Daniel. Imogene's card is shown to Imogene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know whether Imogene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Frederick","Daniel","Imogene"],"index":54552,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8640942574,"difficulty":0.1359057426}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Christina is thirsty. It is publicly announced that Mafalda knows whether or not nobody is thirsty. It is publicly announced that Christina does not know whether Mafalda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Christina can now know that Joseph can know whether Christina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christina","Mafalda","Joseph"],"index":22808,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9768810868,"difficulty":0.0231189132}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessica can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Monica","Matthew","Leonard"],"index":61310,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997683167,"difficulty":0.0002316833}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Gladys can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Gladys","Bobby"],"index":10432,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997586608,"difficulty":0.0002413392}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hester does not know whether or not everyone is thirsty. It is publicly announced that Hester knows whether or not nobody is thirsty. It is publicly announced that Shirley knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Hester can now know whether Louis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Abraham","Shirley","Louis","Hester"],"index":38183,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7005473375,"difficulty":0.2994526625}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frederick knows whether Vicki is thirsty. It is publicly announced that Frederick knows whether Vicki is thirsty. It is publicly announced that Vicki knows whether Frederick is thirsty. It is publicly announced that Frederick knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Vicki can now know whether Frederick can know that Vicki is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frederick","Vicki"],"index":6720,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9855749607,"difficulty":0.0144250393}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Thomas can now know whether Karen can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Karen"],"index":13919,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brad knows whether someone's forehead is muddy. It is publicly announced that Brad knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Brad can now know whether Edna can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brad","Edna"],"index":10127,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999742806,"difficulty":0.000257194}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa knows whether or not nobody is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Melissa can now know that Charles can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melissa","Charles"],"index":6921,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999766767,"difficulty":0.000233233}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Seth's card is shown to James. James's card is shown to Timothy. Timothy's card is shown to Debra. James's card is shown to Seth. Seth's card is shown to Seth. It is publicly announced that someone picked a red card. It is publicly announced that Debra does not know whether Debra picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Seth can now know that Seth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Timothy","Debra","Seth"],"index":60043,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6619893909,"difficulty":0.3380106091}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Kevin can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","James","Kevin"],"index":24266,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983885288,"difficulty":0.0016114712}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Bruce is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Curtis","Nicole","Bruce"],"index":38105,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984099865,"difficulty":0.0015900135}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Randy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jennifer can now know whether Randy can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randy","Jennifer"],"index":43571,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997809529,"difficulty":0.0002190471}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reginald's card is shown to Reginald. Kyle's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that Kyle does not know whether Reginald picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kyle can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Reginald","Kyle"],"index":55095,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that Andrea can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ann","Kenny","Andrea","Christopher"],"index":67336,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997709394,"difficulty":0.0002290606}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Santiago does not know whether Santiago's forehead is muddy. It is publicly announced that Brad knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Douglas can now know that Benjamin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brad","Santiago","Benjamin","Douglas"],"index":63372,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9975625277,"difficulty":0.0024374723}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula knows whether someone is thirsty. It is publicly announced that Jeremy does not know whether Benjamin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Paula can now know that Benjamin can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Benjamin","Paula","Jeremy"],"index":62773,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cori is thirsty. It is publicly announced that Cori does not know whether Arnold is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Arnold can now know that Cori can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cori","Arnold"],"index":52206,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Geoffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Geoffrey can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Geoffrey","Mark","Janice","Robert"],"index":19349,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998434484,"difficulty":0.001565516}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tillie knows whether someone is thirsty. It is publicly announced that Susan does not know whether Maryland is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Maryland can now know whether Maryland is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tillie","Susan","Maryland"],"index":10265,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990492463,"difficulty":0.0009507537}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Essie's card is shown to Essie. Irene's card is shown to Essie. Daniel's card is shown to Essie. Essie's card is shown to Irene. Daniel's card is shown to Irene. Irene's card is shown to Daniel. Daniel's card is shown to Alejandro. Alejandro's card is shown to Alejandro. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,3 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,3 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Essie can now know whether Irene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Essie","Irene","Daniel","Alejandro"],"index":60693,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5824351311,"difficulty":1.5824351311}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carolyn knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Susana can now know that Theresa can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susana","Carolyn","Theresa"],"index":36716,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997625947,"difficulty":0.0002374053}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eneida knows whether Eneida is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jeremy can now know whether Corey can know that Corey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Corey","Eneida","Jeremy"],"index":42345,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.776689887,"difficulty":0.223310113}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Richard. Richard's card is shown to Fred. Fred's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Roy does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Richard can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Roy","James","Fred"],"index":20248,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997187257,"difficulty":0.0002812743}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Alice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Alice","Linda","Avery"],"index":47646,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986547232,"difficulty":0.0013452768}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Thomas can now know that Ida's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thomas","Ida"],"index":65167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998293221,"difficulty":0.001706779}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Donald knows whether Donald is thirsty. It is publicly announced that Donald knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Kellie can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Kellie","Donald"],"index":46596,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997310042,"difficulty":0.0002689958}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Joanne. Joanne's card is shown to Maria. Maria's card is shown to Maria. Maria's card is shown to Alice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know that Catherine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joanne","Maria","Alice","Catherine"],"index":4222,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983199239,"difficulty":0.0016800761}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vickie knows whether or not everyone's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Thomas can now know whether Vickie can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vickie","Thomas"],"index":17187,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997472167,"difficulty":0.0002527833}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether someone's forehead is muddy. It is publicly announced that Jacklyn knows whether Don's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jacklyn can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Don","Jacklyn","Jean"],"index":25061,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981830716,"difficulty":0.0018169284}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Effie's card is shown to James. Pauline's card is shown to Pauline. James's card is shown to Effie. It is publicly announced that someone picked a red card. It is publicly announced that Pauline does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Pauline can now know whether James can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Pauline","Effie"],"index":60525,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996960163,"difficulty":0.0003039837}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether or not nobody's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"James can now know that Arthur can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Arthur"],"index":3320,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975377321,"difficulty":0.0024622679}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret is thirsty. It is publicly announced that Suzanne knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Wayne can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Suzanne","Wayne","Margaret"],"index":63863,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997294545,"difficulty":0.0002705455}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Anne can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","William","Anne","Anna"],"index":1565,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986133575,"difficulty":0.0013866425}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Grace knows whether or not everyone's forehead is muddy. It is publicly announced that Katherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Joy can now know whether Grace's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katherine","Jean","Grace","Joy"],"index":59093,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997027516,"difficulty":0.0002972484}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Melanie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kevin can now know whether Denver can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melanie","Kevin","Denver","Matthew"],"index":1629,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994858503,"difficulty":0.0005141497}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Allen can now know whether Whitney can know whether Whitney's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allen","Kevin","Whitney","Nicholas"],"index":24324,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996782541,"difficulty":0.0003217459}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathleen does not know whether Stefanie is thirsty. It is publicly announced that Liza is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agentb knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Liza can now know whether Vivian can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vivian","Liza","Kathleen","Stefanie"],"index":11704,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994559884,"difficulty":0.0005440116}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry does not know whether Terry's forehead is muddy. It is publicly announced that Melissa knows whether or not everyone's forehead is muddy. It is publicly announced that Terry's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] 0","hypothesis":"Terry can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Melissa","Terry"],"index":10804,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997809529,"difficulty":0.0002190471}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Florence can now know that John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Florence","Patricia"],"index":48911,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974330068,"difficulty":0.0025669932}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Carolyn knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Carolyn can now know that Steven can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steven","Carolyn","Kimbery"],"index":32929,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985753298,"difficulty":0.0014246702}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Pauline can now know whether Ashley can know that Pauline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laura","Ashley","Sandra","Pauline"],"index":46181,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999550879,"difficulty":0.000449121}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashli does not know whether or not everyone's forehead is muddy. It is publicly announced that Sylvia knows whether Ashli's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Linda can now know that Sylvia can know that Sylvia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvia","Debra","Linda","Ashli"],"index":59564,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5205910206,"difficulty":1.5205910206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Eva's forehead is muddy. It is publicly announced that Joseph knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Eva can now know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Susan","Eva","Joseph"],"index":45714,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997862637,"difficulty":0.002137363}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lydia does not know whether Ira is thirsty. It is publicly announced that Doris knows whether someone is thirsty. It is publicly announced that Doris does not know whether Lydia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Lydia can now know that Ira can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lydia","Doris","Ira","Norma"],"index":56518,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985122085,"difficulty":0.0014877915}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Marjorie can now know whether David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Marjorie","David","Kathy"],"index":13717,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9908251166,"difficulty":0.0091748834}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin knows whether someone's forehead is muddy. It is publicly announced that Candice's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Erin can now know that Erin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wallace","Candice","Erin"],"index":54376,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9472407699,"difficulty":0.0527592301}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Sharon. Erin's card is shown to Sharon. Beatrice's card is shown to Beatrice. Sharon's card is shown to Erin. Erin's card is shown to Erin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Erin can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Beatrice","Erin"],"index":57415,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983496666,"difficulty":0.0016503334}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Rhona can now know whether Eugenia can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rhona","Delia","Eddie","Eugenia"],"index":4132,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997658134,"difficulty":0.0002341866}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Penny. Jason's card is shown to Martin. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Martin knows whether Robert picked a red card. It is publicly announced that Jason does not know whether Penny picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Martin can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Penny","Jason","Martin","Robert"],"index":11592,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6961813569,"difficulty":0.3038186431}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vera's card is shown to Vera. Vera's card is shown to Diane. Diane's card is shown to Diane. Diane's card is shown to Gail. Gail's card is shown to Gail. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vera","Diane","Barbara","Gail"],"index":17379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8948226571,"difficulty":0.1051773429}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ann can now know whether Kenneth can know whether Shaun's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Ann","Robert","Shaun"],"index":44543,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992659688,"difficulty":0.0007340312}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony does not know whether Anthony's forehead is muddy. It is publicly announced that Anthony does not know whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Fred can now know that Anthony can know that Luke's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rick","Luke","Anthony","Fred"],"index":35254,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9859798551,"difficulty":0.0140201449}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Leon's card is shown to Joan. Sherri's card is shown to Leon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leon can now know that Joan can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joan","Leon","Sherri"],"index":18019,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.98451823,"difficulty":0.01548177}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Thomas can now know whether Lala can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lala","Paul","Thomas"],"index":64473,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999755919,"difficulty":0.000244081}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Todd. Todd's card is shown to Timothy. Timothy's card is shown to Timothy. Todd's card is shown to Darrin. Darrin's card is shown to Darrin. It is publicly announced that someone picked a red card. It is publicly announced that Todd knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Todd can now know whether Todd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Todd","Timothy","Darrin"],"index":23420,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9911109209,"difficulty":0.0088890791}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fred does not know whether Claudio is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Claudio can now know whether Fred is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Claudio","Fred","Zaida","Ray"],"index":17371,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9921207428,"difficulty":0.0078792572}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cecelia's card is shown to Jame. Joe's card is shown to Joe. Cecelia's card is shown to Cecelia. It is publicly announced that someone picked a red card. It is publicly announced that Cecelia does not know whether Joe picked a red card. It is publicly announced that Joe does not know whether Cecelia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Cecelia can now know whether Joe can know that Jame picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jame","Joe","Cecelia"],"index":63738,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9571020603,"difficulty":0.0428979397}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Kelly can now know whether Ruth can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelly","Ronald","Ruth"],"index":35159,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997847676,"difficulty":0.0002152324}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virgilio does not know whether Kimberly is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Frank can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frank","Virgilio","Kimberly"],"index":17483,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982768297,"difficulty":0.0017231703}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Susan can now know that Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Susan","Mary","Billy"],"index":27447,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9773921371,"difficulty":0.0226078629}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gina knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Will can now know that Gina can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gina","Will"],"index":41630,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985088706,"difficulty":0.0014911294}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Steven can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maria","Steven"],"index":64700,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985392094,"difficulty":0.0014607906}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy. It is publicly announced that Billy knows whether or not everyone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"John can now know whether Billy can know whether Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Billy","Elizabeth","John"],"index":62796,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990605712,"difficulty":0.0009394288}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Earl. Brian's card is shown to Charles. Betty's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earl","Betty","Charles","Brian"],"index":9214,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993963778,"difficulty":0.006036222}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dollie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Kiersten can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joesph","Kiersten","Dollie"],"index":38917,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997884631,"difficulty":0.0002115369}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Eleanor can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tasha","Ellis","Eleanor"],"index":55871,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985541701,"difficulty":0.0014458299}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Denise can now know whether Becky's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Greg","Becky","Denise","Kevin"],"index":27996,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997201562,"difficulty":0.0002798438}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julius knows whether or not nobody is thirsty. It is publicly announced that Julius knows whether Julius is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mildred can now know that Julius can know whether Mildred is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mildred","Julius"],"index":13216,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9610822201,"difficulty":0.0389177799}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Harriet can now know whether Larry can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Larry","Harriet"],"index":33899,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9854627848,"difficulty":0.0145372152}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Lena. Michael's card is shown to Ian. Lena's card is shown to Beverly. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Lena can know that Beverly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lena","Ian","Michael","Beverly"],"index":1855,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978393316,"difficulty":0.0021606684}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy. It is publicly announced that Brandy knows whether Brandy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"David can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brandy","David","John","Violet"],"index":49304,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985155463,"difficulty":0.0014844537}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"George can now know that Brian can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Brian","Christopher"],"index":6854,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997856021,"difficulty":0.0002143979}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Allen. Charles's card is shown to Allen. Allen's card is shown to Raymundo. Allen's card is shown to Karen. Raymundo's card is shown to Charles. Karen's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymundo can now know whether Charles can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allen","Raymundo","Karen","Charles"],"index":58422,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9935147762,"difficulty":0.0064852238}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether Catherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Rita can now know that Donald can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Catherine","Rita"],"index":60431,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984369874,"difficulty":0.0015630126}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Kevin can now know whether George can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amy","Kevin","Lauren","George"],"index":19948,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997643828,"difficulty":0.0002356172}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"John can now know that Willie can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Willie","Jeffrey","Michael","John"],"index":147,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948535562,"difficulty":0.0051464438}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dexter does not know whether or not everyone's forehead is muddy. It is publicly announced that Dexter does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Dexter can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dexter","Kenneth"],"index":52820,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Patricia. Margie's card is shown to Patricia. Samuel's card is shown to Patricia. Patricia's card is shown to Margie. Cynthia's card is shown to Margie. Samuel's card is shown to Margie. Cynthia's card is shown to Samuel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know that Samuel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Cynthia","Margie","Samuel"],"index":14043,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979896545,"difficulty":0.0020103455}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Dana. Mary's card is shown to Dana. Christopher's card is shown to Christopher. Mary's card is shown to Christopher. Mary's card is shown to Alice. Christopher's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether Christopher picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Alice can now know that Mary can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dana","Christopher","Alice","Mary"],"index":26198,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.952221632,"difficulty":0.047778368}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Sheryl's forehead is muddy. It is publicly announced that Vito's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Barbara can now know that David can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vito","Barbara","Sheryl","David"],"index":66600,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984254837,"difficulty":0.0015745163}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Carolyn. Carolyn's card is shown to Jose. Jose's card is shown to Jose. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn picked a red card. It is publicly announced that Jose picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] 0","hypothesis":"Jose can now know that Carolyn can know whether Jose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carolyn","Jose"],"index":4643,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9727957845,"difficulty":0.0272042155}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Andrew can now know that Stephanie can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrew","Mary","Sharon","Stephanie"],"index":3874,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9938064814,"difficulty":0.0061935186}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobby's card is shown to Bobby. Lucien's card is shown to Bobby. Richard's card is shown to Bobby. Lucien's card is shown to Lucien. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Lucien does not know whether Bobby picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Lucien can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bobby","Lucien","Richard"],"index":22254,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984752536,"difficulty":0.0015247464}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darrin knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Christopher can now know that Darrin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christi","Christopher","Max","Darrin"],"index":5268,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998470366,"difficulty":0.001529634}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anastasia knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anastasia","Jay","James"],"index":57454,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983052015,"difficulty":0.0016947985}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Danielle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Fernando can now know whether Danielle can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Fernando","Linda","Danielle"],"index":43540,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996733665,"difficulty":0.0003266335}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie does not know whether Marie's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Marie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","John","James","Jona"],"index":64634,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986317754,"difficulty":0.0013682246}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to William. Johnnie's card is shown to William. William's card is shown to Shirley. Shirley's card is shown to Shirley. Johnnie's card is shown to Shirley. William's card is shown to Johnnie. It is publicly announced that someone picked a red card. It is publicly announced that Shirley knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"William can now know that Johnnie can know whether Johnnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Shirley","Johnnie"],"index":19354,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9711692929,"difficulty":1.9711692929}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Ruby. Andrea's card is shown to Ruby. Ruby's card is shown to Bradley. Andrea's card is shown to Bradley. Bradley's card is shown to Andrea. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bradley can now know whether Ruby can know that Ruby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Bradley","Andrea"],"index":566,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7936102748,"difficulty":0.2063897252}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Edward can now know that Jacquelin can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Jacquelin","Ann","Robert"],"index":45671,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999761045,"difficulty":0.000238955}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristopher's card is shown to Mary. Kristopher's card is shown to Lela. Candis's card is shown to Lela. Lela's card is shown to Kristopher. Lela's card is shown to Candis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Lela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Lela","Kristopher","Candis"],"index":17819,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980169535,"difficulty":0.0019830465}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Andrew can now know whether Lucille can know whether Lucille's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Andrew","Lucille","Hector"],"index":45594,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7353332043,"difficulty":0.2646667957}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rolando's card is shown to Rolando. Rolando's card is shown to Phillip. Katherine's card is shown to Phillip. Phillip's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that Rolando knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Katherine can now know that Phillip picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rolando","Phillip","Katherine"],"index":63288,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8491322994,"difficulty":0.1508677006}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Jessica knows whether Jessica is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Javier can now know that Kathleen can know whether Javier is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Javier","Jessica"],"index":15924,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9697626829,"difficulty":0.0302373171}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Nathan knows whether Nathan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Nathan can now know that Jennifer can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Jennifer","Nathan"],"index":13408,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9952736497,"difficulty":0.0047263503}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louis knows whether Louis is thirsty. It is publicly announced that Louis does not know whether Eli is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Louis can now know whether Eli can know that Eli is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Eli","Louis"],"index":54135,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9120587111,"difficulty":1.9120587111}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether Felicia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Felicia can now know that Felicia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Felicia","Barbara"],"index":57507,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942060113,"difficulty":0.0057939887}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether someone's forehead is muddy. It is publicly announced that Marcella's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Annette can now know that Annette's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Annette","Christi","Marcella"],"index":41527,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937451482,"difficulty":0.0062548518}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Lloyd is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty. It is publicly announced that David does not know whether Margaret is thirsty. It is publicly announced that Lloyd does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"David can now know whether Margaret can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Cora","Lloyd","David"],"index":52065,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric does not know whether Eric's forehead is muddy. It is publicly announced that Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agentc knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Karen can now know that Terrance can know whether Terrance's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eric","Terrance","Karen"],"index":56522,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9132595658,"difficulty":0.0867404342}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Artie's card is shown to Donald. Artie's card is shown to Artie. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Artie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Artie can now know that Donald can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donald","Artie"],"index":52308,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9548256397,"difficulty":0.0451743603}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rebecca does not know whether Todd is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Lia can now know that Rebecca can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lia","Todd","Charles","Rebecca"],"index":16415,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9825750589,"difficulty":0.0174249411}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Terri does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Anna can now know that Kelly can know that Kelly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Terri","Kelly","Anna"],"index":42373,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.577265501,"difficulty":0.422734499}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Nathaniel. Jeannetta's card is shown to Jeannetta. Christopher's card is shown to Jeannetta. Nathaniel's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Jeannetta can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nathaniel","Jeannetta","Christopher"],"index":53194,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997733235,"difficulty":0.0002266765}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy. It is publicly announced that Ellen knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ellen can now know whether Larue can know that Ellen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Ellen","Marietta","Larue"],"index":34228,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5507007241,"difficulty":0.4492992759}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Randal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Bernie can now know that Randal can know that Bernie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Bernie","Randal"],"index":52296,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983894825,"difficulty":0.0016105175}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Susan knows whether Alan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Susan can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alan","Susan","Thomas"],"index":54846,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982794523,"difficulty":0.0017205477}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shari knows whether Valerie's forehead is muddy. It is publicly announced that Shari knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Shari can now know that Valerie can know that Shari's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Valerie","Shari","Toby"],"index":64670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976112843,"difficulty":0.0023887157}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louis knows whether someone is thirsty. It is publicly announced that Julie does not know whether or not everyone is thirsty. It is publicly announced that Julie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Julie can now know whether John can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julie","John","Louis"],"index":11200,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994520545,"difficulty":0.0005479455}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Takisha does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Takisha can now know whether Charles can know that Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Takisha","David","Charles"],"index":28754,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6914104223,"difficulty":0.3085895777}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kathleen can now know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","Kurtis","Harold","Kathleen"],"index":63080,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985184073,"difficulty":0.0014815927}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Frank knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Frank can now know whether Annabelle can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Annabelle","Frank"],"index":11715,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994208813,"difficulty":0.0005791187}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Evelyn can now know that Catherine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Evelyn","Catherine"],"index":19866,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9870043397,"difficulty":0.0129956603}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly's forehead is muddy. It is publicly announced that Melanie does not know whether Melanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Beverly can now know whether Alice can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Benny","Melanie","Alice"],"index":18982,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Margaret can now know whether Christopher can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Christopher","Daniel"],"index":37560,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9480707645,"difficulty":0.0519292355}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Wayne. William's card is shown to Wayne. Gregory's card is shown to Gregory. William's card is shown to Gregory. Wayne's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gregory can now know that William can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wayne","Gregory","William"],"index":47588,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Esther does not know whether Eric is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentd knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Dale can now know whether Eric can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Esther","David","Eric","Dale"],"index":58753,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976183772,"difficulty":0.0023816228}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Darron. William's card is shown to Darron. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leah can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Leah","William","Darron"],"index":9147,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981102943,"difficulty":0.0018897057}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Berenice can now know that Darren can know that Berenice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Berenice","Matthew","Nancy","Darren"],"index":19034,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980966449,"difficulty":0.0019033551}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacey does not know whether Adam is thirsty. It is publicly announced that Cassandra knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Stacey can now know whether Cassandra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adam","Cassandra","Willis","Stacey"],"index":50134,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941543937,"difficulty":0.0058456063}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monique knows whether Monique is thirsty. It is publicly announced that Monique does not know whether Suzanne is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Monique can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Suzanne","Willie","Monique"],"index":49325,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997161031,"difficulty":0.0002838969}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua does not know whether Joseph is thirsty. It is publicly announced that Barbara does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Joseph can now know whether Barbara can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Barbara","Joseph"],"index":31393,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5808529854,"difficulty":0.4191470146}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathryn knows whether Constance's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Kathryn can now know whether Constance can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathryn","Arthur","Constance"],"index":44975,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996850491,"difficulty":0.0003149509}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Eugene can now know whether James can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Eugene","James"],"index":55963,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996714592,"difficulty":0.0003285408}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Kevin can now know whether Kent can know that Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kent","Thomas","Anita","Kevin"],"index":7026,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6318389177,"difficulty":1.6318389177}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Joyce can now know whether Fred can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marry","Fred","Joyce"],"index":21362,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997594953,"difficulty":0.0002405047}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverlee's card is shown to Beverlee. Beverlee's card is shown to Charles. Beverlee's card is shown to Antoinette. It is publicly announced that someone picked a red card. It is publicly announced that Antoinette does not know whether or not everyone picked a red card. It is publicly announced that Beverlee picked a red card. It is publicly announced that Charles does not know whether Charles picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Beverlee can now know that Antoinette can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Beverlee","Charles","Antoinette"],"index":35842,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982066154,"difficulty":0.0017933846}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy. It is publicly announced that Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] Agentc knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"John can now know whether Patrick can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patrick","Wanda","John","Debra"],"index":37961,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994531274,"difficulty":0.0005468726}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether Gene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Gene can now know that Margaret can know that Gene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","James","Gertrudis","Gene"],"index":33297,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974790215,"difficulty":0.0025209785}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Gregory can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vanessa","Gregory"],"index":44108,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996929169,"difficulty":0.0003070831}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Norman. Craig's card is shown to Craig. Norman's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Norman picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"William can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norman","Craig","William","Terry"],"index":23705,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9509490728,"difficulty":1.9509490728}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","Edward","Mark","Eugene"],"index":14598,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9742618799,"difficulty":0.0257381201}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether or not everyone's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dorothy can now know that Christine can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","Billy","Christine"],"index":11405,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984055161,"difficulty":0.0015944839}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nick knows whether Isaac's forehead is muddy. It is publicly announced that Nick's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Nick can now know that Isaac can know that Isaac's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Isaac","Nick"],"index":30478,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8505727649,"difficulty":0.1494272351}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Wayne can now know that Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Mary","Diane","Wayne"],"index":32349,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966037273,"difficulty":0.0033962727}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Timothy can now know that Ben can know that Ben's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Timothy","Ben","Nicholas"],"index":5759,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985260963,"difficulty":0.0014739037}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lanette's card is shown to Lanette. Kenneth's card is shown to Lanette. Lanette's card is shown to Kenneth. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Lanette can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lanette","Kenneth"],"index":33337,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997715354,"difficulty":0.0002284646}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Brett. Brett's card is shown to Ann. Stephen's card is shown to Ann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brett can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Homer","Brett","Ann","Stephen"],"index":65516,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997233748,"difficulty":0.0002766252}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty does not know whether Sharon is thirsty. It is publicly announced that Johnny knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Betty can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Sharon","Johnny"],"index":19302,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997128844,"difficulty":0.0002871156}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Rachell can now know whether Jimmie can know that Rachell's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roy","Rachell","Jimmie","William"],"index":66263,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5296257138,"difficulty":0.4703742862}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Geoffrey can now know that Christa can know whether Christa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Krystal","Geoffrey","Rex","Christa"],"index":46375,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948502183,"difficulty":0.0051497817}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Eric can now know whether Jessica can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Eric","Jessica"],"index":13890,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996656179,"difficulty":0.0003343821}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeanette does not know whether Gloria is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jeanette can now know that Gloria can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Jeanette","Manuel","Paul"],"index":3253,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phyllis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Lawrence can now know that Phyllis can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Phyllis","Samantha","Lawrence","Joseph"],"index":11608,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9903140664,"difficulty":0.0096859336}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"William can now know that Antoinette can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Ann","Antoinette","Mark"],"index":17223,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980902076,"difficulty":0.0019097924}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marvin does not know whether Michelle is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Michelle can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marvin","Michelle","John"],"index":62237,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997059226,"difficulty":0.002940774}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonna knows whether or not nobody's forehead is muddy. It is publicly announced that Clifford's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Clifford can now know that Jonna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jonna","James","Clifford"],"index":37283,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9892783761,"difficulty":0.0107216239}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peggy's card is shown to Jimmy. Peggy's card is shown to Donald. Sandra's card is shown to Sandra. Donald's card is shown to Peggy. Sandra's card is shown to Peggy. It is publicly announced that someone picked a red card. It is publicly announced that Sandra does not know whether Donald picked a red card. It is publicly announced that Jimmy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Sandra can now know whether Donald can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jimmy","Donald","Sandra","Peggy"],"index":40777,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9957980514,"difficulty":0.0042019486}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Francis can now know that Ryan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angel","Francis","Ryan","Howard"],"index":40048,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9530142546,"difficulty":0.0469857454}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"David can now know that Richard can know that Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Kyle","Richard","Jeffrey"],"index":31184,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966508746,"difficulty":0.0033491254}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. Eva's card is shown to Eva. Gabrielle's card is shown to Eva. Cindy's card is shown to Gabrielle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cindy can now know whether Eva can know that Gabrielle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cindy","Eva","Gabrielle"],"index":33975,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8330398798,"difficulty":1.8330398798}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diana is not thirsty. It is publicly announced that Diana does not know whether Deborah is thirsty. It is publicly announced that Keith does not know whether Angela is thirsty. It is publicly announced that Keith does not know whether Angela is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Deborah can now know that Keith can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Deborah","Diana","Angela"],"index":20071,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9195070863,"difficulty":1.9195070863}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Keith is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"George can now know whether John can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Keith","John","George"],"index":35605,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995117188,"difficulty":0.0004882812}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Stacy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stacy","Richard","Frank","Martin"],"index":63616,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985371828,"difficulty":0.0014628172}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bill's card is shown to Charles. Bill's card is shown to Bill. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Bill does not know whether Charles picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Bill can now know whether Charles can know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Bill"],"index":16200,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.992102325,"difficulty":0.007897675}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph does not know whether or not everyone's forehead is muddy. It is publicly announced that Ralph does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ralph can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ralph","Giovanna"],"index":26934,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9773953557,"difficulty":0.0226046443}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Ashleigh. Larry's card is shown to Renea. Vickie's card is shown to Renea. Renea's card is shown to Vickie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know that Renea can know whether Renea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Ashleigh","Renea","Vickie"],"index":35120,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8503804803,"difficulty":1.8503804803}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy knows whether Randy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Crista can now know whether Crista's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Victor","Frank","Randy","Crista"],"index":55441,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.98826015,"difficulty":1.98826015}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Thomas can now know that Mable can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Mable","Thomas","Mary"],"index":14986,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995439649,"difficulty":0.0004560351}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Iluminada knows whether Cheri's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Cheri can now know whether Shirley can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Iluminada","Cheri","Shirley"],"index":44693,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997420907,"difficulty":0.0002579093}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"John can now know that Marcus can know whether Joel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joel","Marcus","John"],"index":24295,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9682612419,"difficulty":0.0317387581}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Shirley can now know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Anna","Shirley","Richard"],"index":47596,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969371557,"difficulty":0.0030628443}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Danielle. Danielle's card is shown to Steven. Steven's card is shown to Nathan. It is publicly announced that someone picked a red card. It is publicly announced that Nathan does not know whether Nathan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nathan can now know whether Danielle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danielle","Steven","Nathan"],"index":14827,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6722883582,"difficulty":0.3277116418}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Brenda is thirsty. It is publicly announced that Toni knows whether or not everyone is thirsty. It is publicly announced that Toni knows whether Toni is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Toni","Kenneth","Daniel","Brenda"],"index":34739,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997773767,"difficulty":0.0002226233}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gilbert's card is shown to Gloria. Gloria's card is shown to Gilbert. Gilbert's card is shown to Gilbert. Gilbert's card is shown to Jennifer. Jennifer's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gilbert can now know that Jennifer can know whether Gloria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Gilbert","Jennifer"],"index":46575,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6892079711,"difficulty":0.3107920289}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maud knows whether someone is thirsty. It is publicly announced that Charles does not know whether Maud is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Maud can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Larry","Maud","Herman"],"index":36846,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997716546,"difficulty":0.0002283454}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Will can now know whether Norma can know whether Norma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Will","Norma"],"index":10211,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9859123826,"difficulty":0.0140876174}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Agnes's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Edna can now know that Edna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edna","Agnes","James"],"index":54383,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9893641472,"difficulty":0.0106358528}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Mattie. Jill's card is shown to Mattie. Eugene's card is shown to Mattie. Eugene's card is shown to Jill. Jill's card is shown to Eugene. Eugene's card is shown to Eugene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mattie can now know whether Mattie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Mattie","Jill","Eugene"],"index":3473,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9585621953,"difficulty":1.9585621953}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Maribel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 1 ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 1 ] 0","hypothesis":"Maribel can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maribel","Robert","Audrey"],"index":8186,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996293783,"difficulty":0.0003706217}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leah's card is shown to Gilberto. Leah's card is shown to Leah. It is publicly announced that someone picked a red card. It is publicly announced that Leah does not know whether or not everyone picked a red card. It is publicly announced that Gilberto does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Gilberto can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gilberto","Leah"],"index":59650,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.945972085,"difficulty":1.945972085}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillian knows whether Carrie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Carrie can now know whether Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andrew","Lillian","Avery","Carrie"],"index":4545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997388721,"difficulty":0.0002611279}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marguerite knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Dorothy can now know that Richard can know that Marguerite's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","Stacy","Richard","Marguerite"],"index":66657,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984509945,"difficulty":0.0015490055}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barry knows whether Barry is thirsty. It is publicly announced that Lynda knows whether Lynda is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lynda can now know that Barry can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barry","Lynda"],"index":27089,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997847676,"difficulty":0.0002152324}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shawn's card is shown to Steve. Tristan's card is shown to Steve. Steve's card is shown to Shawn. Shawn's card is shown to Shawn. Tristan's card is shown to Shawn. Shawn's card is shown to Jarrod. Tristan's card is shown to Jarrod. It is publicly announced that someone picked a red card. It is publicly announced that Jarrod knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Steve can now know that Jarrod can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steve","Shawn","Jarrod","Tristan"],"index":49242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985584617,"difficulty":0.0014415383}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eric can now know that Tracy can know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tracy","Paul","Eric","Wesley"],"index":18311,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985722303,"difficulty":0.0014277697}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Curt is not thirsty. It is publicly announced that Andre does not know whether Clyde is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Clyde can now know that Andre can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andre","Clyde","Curt","Jennie"],"index":59861,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983727932,"difficulty":0.0016272068}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Don's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Charles can now know that Pedro's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Pedro","Mary","Don"],"index":27156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9765269756,"difficulty":0.0234730244}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Bernice can now know whether Irma can know that Irma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eva","Bernice","Irma"],"index":32069,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7011162639,"difficulty":0.2988837361}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Ty's card is shown to Christopher. Christopher's card is shown to Ty. It is publicly announced that someone picked a red card. It is publicly announced that Ty knows whether or not everyone picked a red card. It is publicly announced that Christopher knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Ty can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Ty"],"index":47444,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958533049,"difficulty":0.0041466951}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martin's card is shown to Theresa. Theresa's card is shown to Elaine. Elaine's card is shown to Elaine. Theresa's card is shown to Martin. Elaine's card is shown to Martin. Martin's card is shown to Martin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elaine can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Theresa","Elaine","Martin"],"index":53726,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985167384,"difficulty":0.0014832616}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Audrey knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Brooke can now know that Brooke's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Audrey","Brooke"],"index":35377,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7864510417,"difficulty":0.2135489583}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Marvin. Renda's card is shown to Marvin. Renda's card is shown to Renda. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pamela can now know whether Renda can know whether Renda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marvin","Renda","Pamela"],"index":20453,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9914668798,"difficulty":0.0085331202}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly knows whether Kelly's forehead is muddy. It is publicly announced that Jacqueline knows whether Jacqueline's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kelly can now know whether James can know whether Jacqueline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Henry","Jacqueline","Kelly","James"],"index":45958,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997295737,"difficulty":0.0002704263}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peggy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Christopher can now know that Peggy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Peggy","Laura","Christopher"],"index":8113,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984093308,"difficulty":0.0015906692}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loretta does not know whether Loretta's forehead is muddy. It is publicly announced that Elizabeth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Albert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elizabeth","Albert","Loretta"],"index":8620,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9416033626,"difficulty":0.0583966374}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evan's card is shown to Terrence. James's card is shown to Gerald. Evan's card is shown to Evan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terrence can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Terrence","Gerald","James","Evan"],"index":40720,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771893,"difficulty":0.000228107}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matt does not know whether Dennis is thirsty. It is publicly announced that Samuel does not know whether or not everyone is thirsty. It is publicly announced that Samuel does not know whether Dennis is thirsty. It is publicly announced that Dennis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Evan can now know that Samuel can know that Samuel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Evan","Dennis","Matt","Samuel"],"index":13238,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9894285798,"difficulty":0.0105714202}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Pamela. Pamela's card is shown to Pamela. Terry's card is shown to Pamela. Anthony's card is shown to Terry. Pamela's card is shown to Stacy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pamela can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Pamela","Terry","Stacy"],"index":51229,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983483553,"difficulty":0.0016516447}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel knows whether Daniel is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Daniel can now know that Sean is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vivian","Sean","Daniel"],"index":32703,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981803894,"difficulty":0.0018196106}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Johnie is thirsty. It is publicly announced that Shawn does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shawn","Johnie","David"],"index":31951,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7704837322,"difficulty":0.2295162678}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Phillip's forehead is muddy. It is publicly announced that Phillip does not know whether or not everyone's forehead is muddy. It is publicly announced that Joseph knows whether Matt's forehead is muddy. It is publicly announced that Joseph knows whether Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Phillip can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Matt","Matthew","Phillip"],"index":62597,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997805059,"difficulty":0.002194941}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Helen. James's card is shown to James. James's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"John can now know that James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","James","John"],"index":10238,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theresa does not know whether James is thirsty. It is publicly announced that John does not know whether Amy is thirsty. It is publicly announced that Theresa knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know whether Amy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Theresa","Amy","John"],"index":22148,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996911287,"difficulty":0.0003088713}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mollie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mollie can now know that Janine can know that Janine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Mollie","Janine"],"index":56037,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998336792,"difficulty":0.001663208}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"John can now know whether William can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","James","Charles","William"],"index":21242,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9949060678,"difficulty":0.0050939322}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Quinton knows whether someone is thirsty. It is publicly announced that Daniel does not know whether Quinton is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Quinton can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Quinton","Orlando","Daniel"],"index":31352,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997726083,"difficulty":0.0002273917}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Mark's card is shown to Jessica. It is publicly announced that someone picked a red card. It is publicly announced that Willie does not know whether or not everyone picked a red card. It is publicly announced that Willie does not know whether or not everyone picked a red card. It is publicly announced that Willie knows whether Mark picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Willie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Willie","Jessica"],"index":61118,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9479308724,"difficulty":1.9479308724}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Manuel. David's card is shown to Manuel. David's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Manuel can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Manuel","Richard","David"],"index":8395,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983065128,"difficulty":0.0016934872}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Megan is thirsty. It is publicly announced that William does not know whether Joan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Megan can now know whether William can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Megan","William","Joan"],"index":35246,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997100234,"difficulty":0.0002899766}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Kendra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jose can now know that Beth can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kendra","Beth","Jose"],"index":9384,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996281862,"difficulty":0.0003718138}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loraine does not know whether Loraine's forehead is muddy. It is publicly announced that Carrie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Terri can now know that Loraine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carrie","Loraine","Terri"],"index":47343,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8359686136,"difficulty":0.1640313864}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to David. Amanda's card is shown to Ann. Margaret's card is shown to Ann. David's card is shown to Amanda. Margaret's card is shown to Amanda. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know whether Amanda can know that Amanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Ann","Amanda","Margaret"],"index":10348,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7412679195,"difficulty":0.2587320805}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcia does not know whether or not everyone is thirsty. It is publicly announced that Mary does not know whether Scott is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mary can now know whether Marcia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Marcia","Scott"],"index":47159,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6763210893,"difficulty":1.6763210893}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Theresa can now know whether John can know whether Theresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephen","Theresa","John"],"index":44354,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999658823,"difficulty":0.000341177}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Larry can now know that Billie can know that Larry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Theresa","Gerald","Billie","Larry"],"index":35119,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.7620027065,"difficulty":0.2379972935}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Maria can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Willian","James"],"index":34360,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9918867946,"difficulty":0.0081132054}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Freda does not know whether Freda's forehead is muddy. It is publicly announced that Jill does not know whether Jill's forehead is muddy. It is publicly announced that Freda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jill can now know whether Donald can know whether Jason's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jill","Jason","Freda","Donald"],"index":2147,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992601275,"difficulty":0.0007398725}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mellisa can now know that Mellisa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Karen","Mellisa","Cheryl"],"index":62555,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976630211,"difficulty":0.0023369789}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond does not know whether Russell is thirsty. It is publicly announced that Raymond is thirsty. It is publicly announced that Russell is thirsty. It is publicly announced that Russell is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] Agentb knows that (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Russell can now know that Raymond can know whether Russell is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Russell"],"index":38455,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.967890501,"difficulty":0.032109499}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Isabelle's card is shown to Danny. It is publicly announced that someone picked a red card. It is publicly announced that Danny knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Danny can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Danny","Isabelle"],"index":1498,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983522892,"difficulty":0.0016477108}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Thomas can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Damaris","Thomas"],"index":46867,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth's forehead is muddy. It is publicly announced that Julia does not know whether Julia's forehead is muddy. It is publicly announced that Karen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Karen can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Karen","Julia"],"index":33095,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9368474483,"difficulty":0.0631525517}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Daniel can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bill","Doris","Daniel"],"index":55418,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985436201,"difficulty":0.0014563799}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether or not everyone's forehead is muddy. It is publicly announced that Dennis knows whether Laverne's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Dennis can now know whether Laverne can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laverne","Dennis","Jill"],"index":40500,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996139407,"difficulty":0.0003860593}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adrian knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Dot can now know that Dot's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dot","Eric","Adrian","Randy"],"index":809,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980481863,"difficulty":0.0019518137}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ruth can now know that Bruce can know that Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bruce","Ruth","William","Kevin"],"index":64644,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984209538,"difficulty":0.0015790462}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian knows whether Brian is thirsty. It is publicly announced that Addie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Brian can now know whether Addie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Addie","Anna"],"index":67271,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996944666,"difficulty":0.0003055334}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Taren can now know whether Rickey can know whether Sherrie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Taren","Rickey","Sherrie","Iris"],"index":27706,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994603992,"difficulty":0.0005396008}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether or not everyone is thirsty. It is publicly announced that Elizabeth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Elizabeth can now know whether Verna can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Verna","Elizabeth"],"index":13006,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen does not know whether William is thirsty. It is publicly announced that Rick does not know whether Karen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Rudy can now know whether Rick can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Rudy","William","Rick"],"index":16298,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Avis can now know that Janet can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janet","Avis","Carla","Joan"],"index":47825,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996249676,"difficulty":0.0003750324}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy. It is publicly announced that Maurice knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"David can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Maurice"],"index":9876,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982764721,"difficulty":0.0017235279}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Carole can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barry","Donna","Carole","Gregory"],"index":24184,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997333884,"difficulty":0.0002666116}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Neal can now know whether Bobby can know whether Bobby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bobby","Kevin","Neal","Kimberly"],"index":29743,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996349812,"difficulty":0.0003650188}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Blanca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Blanca","David","Vincent"],"index":31434,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997401834,"difficulty":0.0002598166}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Iva","Lawrence"],"index":14734,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997820258,"difficulty":0.0002179742}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Kandi knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know that Lewis can know that Kandi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Lewis","Denny","Kandi"],"index":45640,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9705378413,"difficulty":0.0294621587}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Robyn can now know that John can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Toni","John","Robyn","Victor"],"index":52926,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996863604,"difficulty":0.0003136396}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deanne is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Deanne can now know whether Steve can know that Natalie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steve","Deanne","William","Natalie"],"index":14297,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.98117733,"difficulty":0.01882267}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Doris can now know that Tanya can know that Tanya's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tanya","Doris","Katharine"],"index":39598,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9730550051,"difficulty":0.0269449949}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ricky's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Abel can now know that Clifford can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ricky","Abel","Clifford"],"index":51120,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984277487,"difficulty":0.0015722513}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dustin's card is shown to Dustin. Dustin's card is shown to Ricky. It is publicly announced that someone picked a red card. It is publicly announced that Dustin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dustin can now know whether Ricky can know whether Dustin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dustin","Ricky","Michael"],"index":41550,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981160164,"difficulty":0.0018839836}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margeret knows whether Margeret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentb knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Tracey can now know that Margeret can know that Mildred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Tracey","Kathleen","Margeret"],"index":15067,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983189702,"difficulty":0.0016810298}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jane's card is shown to Jane. Lauri's card is shown to Lauri. Christina's card is shown to Christina. Jane's card is shown to Angelo. Christina's card is shown to Angelo. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Angelo can now know that Christina can know that Angelo picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jane","Lauri","Christina","Angelo"],"index":14413,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978708029,"difficulty":0.0021291971}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Eddie can now know that Robert can know whether Annette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annette","Robert","Eddie","James"],"index":19442,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Denise can now know that Beth can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beth","Michele","Denise"],"index":14226,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997687936,"difficulty":0.0002312064}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffery knows whether Jeffery's forehead is muddy. It is publicly announced that Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Mark can now know that Jeffery can know that Deborah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffery","Carol","Deborah","Mark"],"index":48253,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9767333269,"difficulty":1.9767333269}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Olga's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Olga can now know whether Goldie can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olga","Susie","David","Goldie"],"index":28552,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995474219,"difficulty":0.0004525781}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Linda can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debra","Linda","William"],"index":61043,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983578324,"difficulty":0.0016421676}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis's forehead is muddy. It is publicly announced that Rose does not know whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rose can now know whether Dennis can know that Rose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rose","Michael","Dennis"],"index":59428,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6334543824,"difficulty":1.6334543824}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Woodrow can now know whether Dexter can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Dexter","Woodrow"],"index":17246,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997563958,"difficulty":0.0002436042}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether Susan's forehead is muddy. It is publicly announced that Rolland knows whether Rolland's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Rolland can now know that Evan can know that Amanda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amanda","Evan","Rolland","Susan"],"index":54346,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964935184,"difficulty":0.0035064816}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Alice's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Mary can now know whether Bernard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alice","Fred","Bernard","Mary"],"index":44365,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994770885,"difficulty":0.0005229115}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Karen can now know that Mandy can know whether Karen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Karen","Mandy"],"index":38636,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5853699446,"difficulty":1.5853699446}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Mark's card is shown to Ashley. Harry's card is shown to Ashley. Ashley's card is shown to Harry. Mark's card is shown to Bella. Harry's card is shown to Bella. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bella can now know that Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Ashley","Harry","Bella"],"index":67309,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978193045,"difficulty":0.0021806955}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy. It is publicly announced that Dena does not know whether Dena's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mary can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Bettie","Dena"],"index":29171,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kerry can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Emory","Nancy","Amber","Kerry"],"index":39589,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985333681,"difficulty":0.0014666319}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Branden's card is shown to Miguel. Miguel's card is shown to Branden. Miguel's card is shown to Juanita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Miguel can now know whether Juanita can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Miguel","Branden","Juanita"],"index":56593,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9253015518,"difficulty":0.0746984482}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Crystal does not know whether Jay is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Crystal can now know whether Jay can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jay","Crystal"],"index":42031,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997040629,"difficulty":0.0002959371}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather does not know whether Jason is thirsty. It is publicly announced that Jason is thirsty. It is publicly announced that Jason knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Rose can now know whether Jason can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Heather","Jason","Rose"],"index":60285,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurie knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"James can now know whether Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Mary","Barbara","Laurie"],"index":22066,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9252573252,"difficulty":0.0747426748}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey does not know whether Jeffrey's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Brett does not know whether Brett's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jeffrey can now know whether Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Brett","David","Stephen"],"index":34431,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7820318937,"difficulty":0.2179681063}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander knows whether Alan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Alan can now know that Alexander can know whether Alan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alexander","Alan"],"index":55835,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997406602,"difficulty":0.0002593398}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Robert can now know that Mark can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Mark","Thomas"],"index":11560,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983812571,"difficulty":0.0016187429}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Robert can now know that Virginia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cedric","Michael","Virginia","Robert"],"index":21375,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9857403636,"difficulty":0.0142596364}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Norman knows whether Norman's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Norman can now know that Carmen can know whether Norman's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Norman","Carmen"],"index":16305,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995536208,"difficulty":0.0004463792}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Katina can now know whether Lauren can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lauren","Katina","Linda","Mary"],"index":30139,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997174144,"difficulty":0.0002825856}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Miles does not know whether Catherine is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Miles can now know that Rodney can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Miles","Catherine","Rodney"],"index":2252,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997091889,"difficulty":0.0002908111}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Carlyn is thirsty. It is publicly announced that Carlyn does not know whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] Agentd knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"David can now know that Barbara can know that Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Amy","Carlyn","David"],"index":47524,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9720535278,"difficulty":0.0279464722}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zoe's card is shown to Zoe. Sara's card is shown to Zoe. Timothy's card is shown to Sara. Zoe's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Timothy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know that Zoe can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Zoe","Sara","Timothy"],"index":22788,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Willodean. David's card is shown to Virgie. Willodean's card is shown to Virgie. Virgie's card is shown to Virgie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Willodean can now know that David can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Willodean","Virgie"],"index":53296,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7134512067,"difficulty":0.2865487933}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Louis can now know whether Amanda can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Justine","Amanda","Charles"],"index":47034,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997156262,"difficulty":0.0002843738}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Jonathan can now know that Jody can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jody","Jonathan"],"index":22684,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984227419,"difficulty":0.0015772581}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marion knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"John can now know whether Dorothy can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Pasquale","John","Marion"],"index":11548,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980931878,"difficulty":0.0019068122}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Judith. Diane's card is shown to Diane. Donna's card is shown to Diane. Judith's card is shown to Donna. Donna's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Judith can now know that Donna can know that Judith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Judith","Diane","Donna"],"index":48410,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973968267,"difficulty":0.0026031733}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Marvin can now know whether Harold can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marvin","Harold"],"index":8452,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.910033226,"difficulty":0.089966774}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Wanda. Robert's card is shown to Wanda. William's card is shown to Robert. Wanda's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"William can now know that Robert can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wanda","Robert","William"],"index":65046,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997842908,"difficulty":0.0002157092}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Brandon can now know whether Eva can know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eva","Jennifer","Enrique","Brandon"],"index":29498,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.997471869,"difficulty":0.002528131}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobby's card is shown to Herbert. Herbert's card is shown to Melinda. Herbert's card is shown to Bobby. Melinda's card is shown to Bobby. Bobby's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Herbert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Bobby can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Herbert","Melinda","Bobby","Richard"],"index":30077,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963328838,"difficulty":0.0036671162}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrea knows whether Alvin's forehead is muddy. It is publicly announced that Alvin knows whether Alvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dale can now know that Joey can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joey","Alvin","Andrea","Dale"],"index":67135,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984875917,"difficulty":0.0015124083}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that Ashley knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Ashley can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ashley","Robert"],"index":38809,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996995926,"difficulty":0.0003004074}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether Emma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Melinda can now know that Wanda can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wanda","Melinda","Angela","Emma"],"index":23048,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9887151122,"difficulty":0.0112848878}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catherine is thirsty. It is publicly announced that Patrick does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brian can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Catherine","Brian"],"index":64791,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dani knows whether Dani's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Dani can now know whether Flossie can know whether Belinda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Flossie","Dani","Belinda"],"index":27219,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999722302,"difficulty":0.000277698}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Jim can now know that Melvin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melvin","Jim","Charles","Patricia"],"index":58589,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997651279,"difficulty":0.002348721}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanine knows whether or not everyone's forehead is muddy. It is publicly announced that Jeanine knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"David can now know that Jeanine can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Jeanine","Emma"],"index":50177,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Travis can now know that Tiffany's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Travis","Tiffany","Francis"],"index":29256,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984900951,"difficulty":0.0015099049}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Norman can now know that Norman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Norman","Annemarie"],"index":40333,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981886744,"difficulty":0.0018113256}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mildred's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Robert can now know that Eric can know that Evelyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Robert","Evelyn","Mildred"],"index":43827,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966957569,"difficulty":0.0033042431}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Michael's card is shown to Charles. Charles's card is shown to Michael. Michael's card is shown to Michael. Sarah's card is shown to Michael. Sarah's card is shown to Kelly. Charles's card is shown to Sarah. Kelly's card is shown to Sarah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know that Michael can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Michael","Kelly","Sarah"],"index":52713,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971982241,"difficulty":0.0028017759}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Irma's card is shown to Theresa. James's card is shown to Angel. Irma's card is shown to Angel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Irma can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Irma","Theresa","Angel"],"index":16880,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chester does not know whether Chester's forehead is muddy. It is publicly announced that Deborah does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Chester can now know that Tanya can know that Deborah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tanya","Debby","Deborah","Chester"],"index":53418,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6392167211,"difficulty":0.3607832789}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"James can now know whether Stephen can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stephen","James"],"index":4257,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Arnold. Daniel's card is shown to Daniel. Jerry's card is shown to Daniel. Arnold's card is shown to Jerry. Daniel's card is shown to Jerry. Jerry's card is shown to Jerry. Daniel's card is shown to Rickey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Arnold can now know that Rickey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arnold","Daniel","Jerry","Rickey"],"index":61147,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9740575552,"difficulty":0.0259424448}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Kelly. Lori's card is shown to Kelly. Lori's card is shown to Maria. Kelly's card is shown to Lori. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kelly","Maria","Lori"],"index":13725,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983525276,"difficulty":0.0016474724}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terry's card is shown to Terry. Richard's card is shown to Terry. Shannon's card is shown to Richard. Terry's card is shown to Shannon. Richard's card is shown to Shannon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shannon can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terry","Richard","Shannon"],"index":19343,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983242154,"difficulty":0.0016757846}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michele knows whether Gretchen's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Michele can now know that Gretchen can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gretchen","Michele"],"index":61023,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997317195,"difficulty":0.0002682805}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma's forehead is muddy. It is publicly announced that Thelma knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Louise can now know that Wayne can know that Thelma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thelma","Louise","Wayne","Andrew"],"index":13808,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.8767191172,"difficulty":1.8767191172}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cora's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Cora can now know whether Clint can know whether Clint's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cora","Emma","Clint"],"index":23126,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996235371,"difficulty":0.0003764629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Isabella can now know whether Sharon can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Isabella","Robert","Derek","Sharon"],"index":56730,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9219297171,"difficulty":0.0780702829}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur does not know whether or not everyone's forehead is muddy. It is publicly announced that Arthur knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Arthur can now know that Arthur's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Arthur","Barbara"],"index":20768,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5570684671,"difficulty":1.5570684671}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marvin knows whether Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Andrea can now know that Marvin can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patrick","Andrea","Donald","Marvin"],"index":38264,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984605312,"difficulty":0.0015394688}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry does not know whether or not everyone's forehead is muddy. It is publicly announced that Harry does not know whether Harry's forehead is muddy. It is publicly announced that Harry does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Shauna can now know whether Harry can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Harry","Shauna"],"index":41455,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.984837532,"difficulty":0.015162468}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clifford's card is shown to Clifford. Ruth's card is shown to Clifford. Joshua's card is shown to Wanda. Clifford's card is shown to Ruth. Wanda's card is shown to Joshua. Ruth's card is shown to Joshua. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clifford can now know whether Ruth can know whether Joshua picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clifford","Wanda","Ruth","Joshua"],"index":39233,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983112812,"difficulty":0.0016887188}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ebony's card is shown to Ebony. Sylvia's card is shown to Sylvia. Sylvia's card is shown to Bradley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bradley can now know whether Ebony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ebony","Sylvia","Bradley"],"index":19820,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6340808868,"difficulty":1.6340808868}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josie does not know whether Paul is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Paul can now know whether Josie can know that Josie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paul","Josie","Eva"],"index":5255,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9290123582,"difficulty":1.9290123582}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joe's card is shown to Joe. Dennis's card is shown to Beth. Beth's card is shown to Dennis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joe can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joe","Beth","Dennis"],"index":11484,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985253215,"difficulty":0.0014746785}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy does not know whether or not everyone's forehead is muddy. It is publicly announced that Timothy does not know whether Timothy's forehead is muddy. It is publicly announced that Timothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Timothy can now know whether Mark can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Timothy","Mark"],"index":17415,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jerry can now know whether Sandy can know that Sandy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Lois","Jerry","Sandy"],"index":64171,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5944961905,"difficulty":0.4055038095}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phyllis's card is shown to Tom. Paul's card is shown to Tom. Phyllis's card is shown to Phyllis. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Paul does not know whether Tom picked a red card. It is publicly announced that Phyllis knows whether Phyllis picked a red card. It is publicly announced that Phyllis does not know whether or not everyone picked a red card. It is publicly announced that Paul knows whether Phyllis picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Phyllis can now know that Phyllis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tom","Phyllis","Paul"],"index":39165,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7454686165,"difficulty":0.2545313835}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Jonathan. Santo's card is shown to Santo. Anton's card is shown to Santo. Santo's card is shown to Anton. Santo's card is shown to Gene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Santo can now know whether Gene can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonathan","Santo","Anton","Gene"],"index":22015,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9934409261,"difficulty":0.0065590739}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy knows whether Maria's forehead is muddy. It is publicly announced that Patrick's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Patrick can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Patrick","Tracy","Maria"],"index":19888,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997566342,"difficulty":0.0002433658}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brad's card is shown to Brad. Cody's card is shown to Tanya. It is publicly announced that someone picked a red card. It is publicly announced that Cody does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brad can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cody","Brad","Tanya"],"index":65210,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980583787,"difficulty":0.0019416213}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Julia's forehead is muddy. It is publicly announced that Julia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Julia can now know that Geneva's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Geneva","James","Julia"],"index":62996,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5937924981,"difficulty":0.4062075019}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know whether Bernice can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Bernice","Eva","Monica"],"index":4648,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kirk knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Wendy can now know that Kirk can know that Kirk is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juan","Kirk","Wendy","Jennifer"],"index":33203,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9594205022,"difficulty":1.9594205022}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Della does not know whether Michele is thirsty. It is publicly announced that Al does not know whether Della is thirsty. It is publicly announced that Al knows whether or not nobody is thirsty. It is publicly announced that Michele does not know whether Donald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Donald can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michele","Al","Donald","Della"],"index":4814,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9917286038,"difficulty":0.0082713962}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frederick's card is shown to Frederick. Frederick's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Frederick does not know whether John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"John can now know that Frederick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Frederick","John"],"index":20151,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9933251739,"difficulty":1.9933251739}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether Ted's forehead is muddy. It is publicly announced that Bertha's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentd knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Adam can now know that Jason can know whether Ted's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bertha","Jason","Ted","Adam"],"index":7363,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997492433,"difficulty":0.0002507567}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathy's card is shown to Kathy. Donna's card is shown to Kathy. Kathy's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Donna does not know whether Donna picked a red card. It is publicly announced that Kathy knows whether Donna picked a red card. It is publicly announced that Kathy knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Kathy can now know whether Donna can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathy","Donna"],"index":39200,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995476604,"difficulty":0.0004523396}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Michael can now know that Melvin can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jacqueline","Melvin","Michael"],"index":26348,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980060458,"difficulty":0.0019939542}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Gene can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gene","Dorothy","Barbara"],"index":17940,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether Suzanne is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Suzanne can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","John","Suzanne"],"index":65575,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953846335,"difficulty":0.0046153665}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacie does not know whether Ronald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Stacie can now know whether Kurt can know that Kurt is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kurt","Stacie","Ronald","Waltraud"],"index":64049,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5582732558,"difficulty":0.4417267442}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know that Celeste can know whether Douglas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Celeste","Douglas","Eric","Jessie"],"index":1636,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992332458,"difficulty":0.0007667542}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Nancy can now know whether Candy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Candy"],"index":58680,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9963040352,"difficulty":0.0036959648}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eugene knows whether Eugene is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Eugene can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Eugene","Betty"],"index":23495,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kent's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Alice can now know that Kent can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kent","Kimberly","Alice"],"index":10345,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984337687,"difficulty":0.0015662313}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dwayne does not know whether Larry is thirsty. It is publicly announced that Larry does not know whether Dwayne is thirsty. It is publicly announced that Thurman does not know whether or not everyone is thirsty. It is publicly announced that Larry does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Thurman can now know whether Dwayne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Dwayne","Thurman"],"index":32816,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.907617569,"difficulty":1.907617569}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Amanda can now know whether Kevin can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Amanda","Kevin","Oliver"],"index":41208,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9955865145,"difficulty":0.0044134855}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antionette knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Tonya can now know that Antionette can know whether Annette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Antionette","Tonya","Patricia","Annette"],"index":46865,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985352755,"difficulty":0.0014647245}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Winifred's card is shown to Pamela. Pamela's card is shown to Winifred. Winifred's card is shown to Winifred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Winifred can now know that Pamela can know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pamela","Winifred"],"index":54104,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997168839,"difficulty":0.002831161}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandy does not know whether Chris is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Chris can now know that Brandy can know whether Brandy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Chris","Brandy"],"index":30332,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988434315,"difficulty":0.0011565685}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nina's card is shown to Roger. Roger's card is shown to Nina. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Nina knows whether or not nobody picked a red card. It is publicly announced that Roger knows whether Nina picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Roger can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roger","Nina"],"index":24480,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997186065,"difficulty":0.0002813935}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glory knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Scott can now know whether Jennifer can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","David","Jennifer","Glory"],"index":44802,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997680783,"difficulty":0.0002319217}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Roscoe. Marie's card is shown to Roscoe. Marie's card is shown to Kevin. Kevin's card is shown to Marie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kevin can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roscoe","Kevin","Marie"],"index":8736,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942066669,"difficulty":0.0057933331}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Jennie can now know whether Jennifer can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennie","Thomas","Jennifer"],"index":4169,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997132421,"difficulty":0.0002867579}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Douglas can now know that Norman can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Douglas","Norman","Amber"],"index":14562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983605742,"difficulty":0.0016394258}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julio's card is shown to Nancy. Jamika's card is shown to Nancy. Nancy's card is shown to Julio. Julio's card is shown to Julio. Nancy's card is shown to Jamika. Jamika's card is shown to Jamika. It is publicly announced that someone picked a red card. It is publicly announced that Jamika knows whether Julio picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Nancy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Julio","Jamika"],"index":32799,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998595655,"difficulty":0.001404345}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Todd does not know whether Neely is thirsty. It is publicly announced that Neely does not know whether Todd is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jeffrey can now know that Neely is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Neely","Jeffrey","Todd"],"index":3961,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9928446412,"difficulty":0.0071553588}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bessie can now know that Bessie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bessie","Michael","Rachel","Kathleen"],"index":50007,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983338714,"difficulty":0.0016661286}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wm knows whether or not everyone's forehead is muddy. It is publicly announced that Roberto does not know whether Roberto's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Roberto can now know whether Julia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anna","Julia","Roberto","Wm"],"index":27403,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryon's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Carolyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agenta knows that (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Bryon can now know that Carolyn can know that Megan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bryon","Rita","Megan","Carolyn"],"index":59187,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9366859198,"difficulty":0.0633140802}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Dawn. Scott's card is shown to Scott. Daniel's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Dawn can now know that Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dawn","Scott","Daniel"],"index":49677,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951020479,"difficulty":0.0048979521}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie does not know whether Willie's forehead is muddy. It is publicly announced that Willie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Willie can now know whether Karin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Willie","Karin"],"index":14902,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986171722,"difficulty":0.0013828278}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"William can now know that Del can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","James","Mildred","Del"],"index":44558,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997344613,"difficulty":0.0002655387}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janice can now know whether Adriene can know that Janice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janice","Randall","Adriene","Russell"],"index":32729,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9880973101,"difficulty":0.0119026899}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Daniel's forehead is muddy. It is publicly announced that Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Daniel can now know that Joe can know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daniel","Joe"],"index":35583,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8696460724,"difficulty":0.1303539276}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy does not know whether or not everyone's forehead is muddy. It is publicly announced that Max knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Randy can now know whether Lynette can know that Randy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Max","Nancy","Lynette","Randy"],"index":21281,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6783302426,"difficulty":1.6783302426}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know that Kecia can know that Sam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Kecia","Valerie","Sam"],"index":46000,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986774325,"difficulty":0.0013225675}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Janet. Janet's card is shown to Sally. Sally's card is shown to Sally. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Timothy can now know that Crystal picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Janet","Crystal","Sally"],"index":22709,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983514547,"difficulty":0.0016485453}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether Jennifer's forehead is muddy. It is publicly announced that Marian knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Allison can now know that Marian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marian","Allison","Betty","Jennifer"],"index":48360,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8879828453,"difficulty":0.1120171547}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Raymond. Raymond's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Raymond knows whether someone picked a red card. It is publicly announced that Deborah knows whether Deborah picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Raymond can now know whether Deborah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Raymond","Deborah"],"index":48546,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6987192631,"difficulty":1.6987192631}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dean's card is shown to Dean. Carroll's card is shown to Dean. Barbara's card is shown to Dean. Dean's card is shown to Brenda. Carroll's card is shown to Brenda. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brenda can now know that Dean can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dean","Brenda","Carroll","Barbara"],"index":53217,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997166991,"difficulty":0.0002833009}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to John. John's card is shown to Marlene. Willie's card is shown to Willie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Marlene can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Marlene","Willie","Doris"],"index":56801,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984537363,"difficulty":0.0015462637}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mason's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Mason can now know whether Mason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Danny","Anita","Christopher","Mason"],"index":65904,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996676445,"difficulty":0.0003323555}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know whether Chad can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chad","Tiffany","Courtney","Michelle"],"index":33397,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997143149,"difficulty":0.0002856851}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Sandra can now know that Robert can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sandra","Jason","Robert"],"index":11185,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7202054262,"difficulty":1.7202054262}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Norma's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Robert can now know that Norma can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rachel","Robert","Norma"],"index":67505,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997656941,"difficulty":0.0002343059}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether John's forehead is muddy. It is publicly announced that Herman knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Herman can now know that John can know that Herman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Herman","John","Paul"],"index":24275,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978078008,"difficulty":0.0021921992}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Charles's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Jonathan can now know that Charles can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Thomas","Charles","Jonathan"],"index":19248,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984417558,"difficulty":0.0015582442}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter does not know whether Peter's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Peter can now know whether Judy can know whether Peter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Peter","Tina","Judy"],"index":57879,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999309063,"difficulty":0.000690937}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Marguerite can now know whether Beverly can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beverly","Marguerite","Donna"],"index":17677,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997814298,"difficulty":0.0002185702}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Milton. Ronnie's card is shown to Ronnie. Patricia's card is shown to Ronnie. Milton's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Milton does not know whether Milton picked a red card. It is publicly announced that Ronnie picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Ronnie can now know that Milton can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Milton","Ronnie","Patricia"],"index":55440,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985826015,"difficulty":0.0014173985}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bennie's card is shown to Bennie. Benita's card is shown to Bennie. Bennie's card is shown to Benita. Benita's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Benita does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Bennie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bennie","Benita","Cynthia"],"index":37289,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Pat. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether Pat picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Pat can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Pat","Larry"],"index":53706,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debbie does not know whether Debbie's forehead is muddy. It is publicly announced that Magdalena does not know whether Magdalena's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Debbie can now know whether Andy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Magdalena","Michael","Andy","Debbie"],"index":23188,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7792478204,"difficulty":0.2207521796}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter knows whether Tracy's forehead is muddy. It is publicly announced that Tracy knows whether Walter's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Tracy can now know that Walter can know whether Tracy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tracy","Walter"],"index":62221,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999748528,"difficulty":0.000251472}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laverne's card is shown to Laverne. Laverne's card is shown to Lucas. Lucas's card is shown to Lucas. It is publicly announced that someone picked a red card. It is publicly announced that Laverne knows whether or not nobody picked a red card. It is publicly announced that Laverne knows whether Lucas picked a red card. It is publicly announced that Lucas knows whether or not nobody picked a red card. It is publicly announced that Lucas knows whether Lucas picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lucas can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Laverne","Lucas"],"index":21873,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6809573174,"difficulty":1.6809573174}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Edward can now know whether Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edward","Kelly","Patrick"],"index":9900,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9980902076,"difficulty":0.0019097924}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olivia's card is shown to James. James's card is shown to Olivia. James's card is shown to Miguel. Olivia's card is shown to Miguel. It is publicly announced that someone picked a red card. It is publicly announced that Miguel does not know whether Miguel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Olivia can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Olivia","Miguel"],"index":24591,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771893,"difficulty":0.000228107}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Rosemarie can now know that Shirley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Shirley","Rosemarie"],"index":58478,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9838650823,"difficulty":0.0161349177}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mabel knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Timothy can now know that Mabel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mabel","Thelma","Cristina","Timothy"],"index":66234,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8697053194,"difficulty":0.1302946806}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Linda. Eugene's card is shown to Jennifer. Jennifer's card is shown to Angelina. Linda's card is shown to Eugene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Jennifer","Angelina","Eugene"],"index":29364,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9797410965,"difficulty":1.9797410965}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deja's forehead is not muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Deja can now know whether Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Deja","Jasmine"],"index":48585,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997220635,"difficulty":0.0002779365}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Jerry. Kimberly's card is shown to Jerry. Kimberly's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] (Agenta knows whether (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Jerry can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jerry","Kimberly"],"index":47877,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jose can now know whether Linda can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Yvonne","Linda","David","Jose"],"index":18597,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997143149,"difficulty":0.0002856851}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leila does not know whether Stella is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Maria is not thirsty. It is publicly announced that Stella knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Maria can now know whether Leila is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leila","Maria","Stella","Jeanne"],"index":58425,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8923486471,"difficulty":0.1076513529}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Irwin. Irwin's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Lawrence knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Lawrence can now know whether Irwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Irwin","Lawrence"],"index":64272,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.674826622,"difficulty":0.325173378}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly does not know whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Kimberly can now know whether Timothy can know whether Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Kimberly","Judi"],"index":11016,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999108851,"difficulty":0.000891149}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Donna can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Otis","Jennifer","Michael","Donna"],"index":25827,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983458519,"difficulty":0.0016541481}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tonda does not know whether Tonda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Allan can now know that Darlene can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Allan","Darlene","Tonda","Gary"],"index":17401,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985135198,"difficulty":0.0014864802}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lillie can now know that Theresa can know that Lori's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lillie","Lori","Theresa","Jennifer"],"index":45061,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986079335,"difficulty":0.0013920665}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Keri does not know whether John is thirsty. It is publicly announced that Denise does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Denise can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Keri","Denise","Kelvin"],"index":19965,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983568788,"difficulty":0.0016431212}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Alicia can now know whether Mark can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Vilma","Mark","Alicia"],"index":20070,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9645496011,"difficulty":0.0354503989}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Shirley can now know whether Shirley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","Virginia","Shawn","Joseph"],"index":55806,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943574071,"difficulty":0.0056425929}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard knows whether Howard's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Howard can now know whether Howard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Aaron","Howard","Gregory"],"index":45608,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994981289,"difficulty":0.0005018711}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesus's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Juan can now know that Jesus can know that Jesus's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juan","Otis","Jesus"],"index":21091,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.952919364,"difficulty":0.047080636}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to William. Andrea's card is shown to Andrea. Andrea's card is shown to Curtis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Curtis can now know whether William can know that Andrea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Andrea","Curtis"],"index":39115,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9733960032,"difficulty":0.0266039968}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Emma can now know that Maria can know that Emmitt's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Suzanne","Emma","Emmitt","Maria"],"index":33381,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5472379923,"difficulty":0.4527620077}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether Jean is thirsty. It is publicly announced that Douglas does not know whether Jean is thirsty. It is publicly announced that Douglas does not know whether Jean is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jean can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Jean","Douglas"],"index":62283,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984974861,"difficulty":0.0015025139}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald does not know whether or not everyone's forehead is muddy. It is publicly announced that Ronald's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Sallie can now know that Brian can know that Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Helen","Ronald","Sallie"],"index":55455,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8429002166,"difficulty":1.8429002166}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antonia knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Patricia can now know that Gloria can know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Antonia","Gloria"],"index":12356,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958018661,"difficulty":0.0041981339}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda does not know whether Charles is thirsty. It is publicly announced that Amanda does not know whether or not everyone is thirsty. It is publicly announced that Aimee is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Charles can now know whether Amanda can know whether Amanda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Amanda","Aimee"],"index":59365,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982404709,"difficulty":0.0017595291}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvia's forehead is muddy. It is publicly announced that Donald's forehead is muddy. It is publicly announced that Cynthia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Harry can now know whether Sylvia can know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvia","Donald","Harry","Cynthia"],"index":9045,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.996103406,"difficulty":0.003896594}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susan can now know that Arthur can know that Arthur's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anita","Arthur","Susan","Scott"],"index":6858,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985803366,"difficulty":0.0014196634}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyle knows whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Kyle can now know whether Frances can know whether Kyle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kyle","Frances"],"index":23866,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996869564,"difficulty":0.0003130436}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Joshua can now know whether Naomi can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joshua","Naomi","Kristie"],"index":60290,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997181296,"difficulty":0.0002818704}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Jessica can now know whether Mable can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Mable","Jay","Michael"],"index":19281,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997050166,"difficulty":0.0002949834}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Marvin can now know that Marvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Luke","Cheryl","Marvin"],"index":25114,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952986836,"difficulty":0.0047013164}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Edwin can now know whether Shirley can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Myrtle","Virgil","Shirley","Edwin"],"index":13441,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995373487,"difficulty":0.0004626513}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wendy's card is shown to Jared. Michael's card is shown to Wendy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Wendy can now know that Yun picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jared","Wendy","Yun","Michael"],"index":41788,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9950535893,"difficulty":0.0049464107}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Barbara can now know whether Rita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Barbara","Rita"],"index":742,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9952138662,"difficulty":0.0047861338}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandi does not know whether Kathy is thirsty. It is publicly announced that Brandi does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kathy can now know that Linda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brandi","Linda","Kathy"],"index":17585,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9155768752,"difficulty":0.0844231248}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Cesar can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Cesar","Amy"],"index":24147,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9938230515,"difficulty":0.0061769485}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Angelo. Ronald's card is shown to Ronald. Juanita's card is shown to Ronald. Mary's card is shown to Ronald. Ronald's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Angelo does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Ronald can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angelo","Ronald","Juanita","Mary"],"index":29790,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953130484,"difficulty":0.0046869516}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Deanna can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Luis","James","Christopher","Deanna"],"index":2570,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9712235332,"difficulty":0.0287764668}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jennifer can now know that Annie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Annie","Jennifer"],"index":7071,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984324574,"difficulty":0.0015675426}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacey knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Stacey can now know that Richard can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stacey","Richard"],"index":6621,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955001473,"difficulty":0.0044998527}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diego's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Diego can now know whether Rudolph can know that Rudolph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rudolph","Robert","Diego"],"index":28380,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8991459012,"difficulty":1.8991459012}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Stella can now know that Alexander can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stella","Alexander","Sherman","Thelma"],"index":5559,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997618794,"difficulty":0.0002381206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen knows whether Stephen is thirsty. It is publicly announced that Bobby does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Stephen can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jordan","Stephen","Luis","Bobby"],"index":40248,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982231259,"difficulty":0.0017768741}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Heather is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Timothy can now know whether Joseph can know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Alice","Heather","Joseph"],"index":46137,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986184835,"difficulty":0.0013815165}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marlana does not know whether or not everyone is thirsty. It is publicly announced that Marlana knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jose can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jose","Marlana"],"index":29336,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9956943989,"difficulty":0.0043056011}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa does not know whether Teresa's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Kent can now know that Kent's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kent","James","Teresa","Anne"],"index":9953,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9925058484,"difficulty":0.0074941516}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emily does not know whether or not everyone is thirsty. It is publicly announced that Raymond does not know whether John is thirsty. It is publicly announced that Emily does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Emily can now know that Raymond can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Emily","John","Raymond"],"index":10247,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981020093,"difficulty":0.0018979907}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Ellen. Randall's card is shown to Randall. Ellen's card is shown to Janice. Randall's card is shown to Janice. Kevin's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ellen can now know that Randall picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ellen","Randall","Kevin","Janice"],"index":45529,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979711175,"difficulty":0.0020288825}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elinor's forehead is not muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Linda can now know that Elinor can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Elinor","Michael"],"index":53266,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.858019948,"difficulty":1.858019948}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mohammed's card is shown to Linda. Sabrina's card is shown to Linda. Linda's card is shown to Mohammed. Sabrina's card is shown to Mohammed. Mohammed's card is shown to Donald. Sabrina's card is shown to Donald. Linda's card is shown to Sabrina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Mohammed","Donald","Sabrina"],"index":32187,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978821874,"difficulty":0.0021178126}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Rebecca can now know that James can know that Cheryl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rebecca","James","Cheryl","Brian"],"index":51379,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8348380327,"difficulty":0.1651619673}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Margaret can now know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diana","Joshua","Allison","Margaret"],"index":25067,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977546334,"difficulty":0.0022453666}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randolph's card is shown to Randolph. Josephine's card is shown to Josephine. Larry's card is shown to Josephine. Josephine's card is shown to Larry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know whether Randolph can know that Larry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Randolph","Josephine","Larry"],"index":20079,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6568216085,"difficulty":0.3431783915}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lyla does not know whether Maria is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Lyla can now know whether Maria can know that Stephen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lyla","Stephen","Eddie","Maria"],"index":3149,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9965311885,"difficulty":0.0034688115}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Richard. Richard's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Stephen can now know that Richard can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Stephen"],"index":19295,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997026324,"difficulty":0.0002973676}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to David. Daniel's card is shown to David. David's card is shown to Sharon. Sharon's card is shown to Sharon. Lisa's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Lisa can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Lisa","Sharon","Daniel"],"index":4582,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997707009,"difficulty":0.0002292991}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Gertrude knows whether or not everyone is thirsty. It is publicly announced that Freda knows whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] Agenta knows that (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Gertrude can now know that Thomas can know whether Freda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gertrude","Thomas","George","Freda"],"index":43964,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9323608279,"difficulty":0.0676391721}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Forrest's card is shown to Samantha. Samantha's card is shown to Samantha. John's card is shown to Samantha. Samantha's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Forrest can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Forrest","Samantha","John"],"index":7407,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983577132,"difficulty":0.0016422868}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Lorraine can now know that Andrew can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tom","Andrew","Lorraine"],"index":32779,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980250597,"difficulty":0.0019749403}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bertha knows whether or not nobody's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Bertha","Daniel"],"index":33451,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998021841,"difficulty":0.001978159}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darnell is thirsty. It is publicly announced that Darnell does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Darnell can now know that Margaret can know that Darnell is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Darnell","Margaret"],"index":66588,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5418152213,"difficulty":0.4581847787}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tonia knows whether Teresa's forehead is muddy. It is publicly announced that Melinda knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"David can now know whether Tonia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tonia","David","Melinda","Teresa"],"index":36405,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983814955,"difficulty":0.0016185045}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dora's card is shown to Jack. Dora's card is shown to Dora. Jack's card is shown to Lauren. Dora's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Lauren picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Dora can now know that Christopher can know that Lauren picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jack","Dora","Lauren","Christopher"],"index":64694,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9734340906,"difficulty":0.0265659094}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Michael can now know that Allen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","John","Allen","Edward"],"index":51287,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8932376504,"difficulty":0.1067623496}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Judith can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bryan","Judith","Louis"],"index":55766,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982506633,"difficulty":0.0017493367}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis does not know whether or not everyone's forehead is muddy. It is publicly announced that Francis does not know whether Francis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Carol can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","George","Kevin","Francis"],"index":53373,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978074431,"difficulty":0.0021925569}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leah knows whether or not nobody's forehead is muddy. It is publicly announced that Leah knows whether Leah's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Leah can now know that Stella can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leah","Stella"],"index":54698,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997527003,"difficulty":0.0002472997}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Kevin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] 0","hypothesis":"Gerald can now know whether Evelyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerald","Kevin","Doris","Evelyn"],"index":52630,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9895823002,"difficulty":0.0104176998}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Debra can now know that Debra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brinda","Debra","Amanda"],"index":44055,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9914566875,"difficulty":0.0085433125}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether Garth is thirsty. It is publicly announced that Mark does not know whether James is thirsty. It is publicly announced that Mark is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] 0","hypothesis":"Garth can now know that Mark can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Garth","James"],"index":37262,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9948123693,"difficulty":0.0051876307}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gina's card is shown to Gina. Louis's card is shown to Louis. James's card is shown to Louis. Gina's card is shown to James. Gina's card is shown to Concepcion. Louis's card is shown to Concepcion. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gina","Louis","James","Concepcion"],"index":43678,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998380661,"difficulty":0.001619339}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Mike can now know that Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kristin","Matthew","Mike","David"],"index":56383,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9974313378,"difficulty":0.0025686622}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Crystal does not know whether Oma is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Crystal can now know that Dean can know that Oma is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Crystal","Dean","Oma"],"index":30708,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978220463,"difficulty":0.0021779537}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carolyn knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Carolyn can now know whether Eric can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Eric","Quintin","Joan"],"index":53310,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997053742,"difficulty":0.0002946258}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Patrick can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Patrick","William","Bessie"],"index":36623,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984431863,"difficulty":0.0015568137}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leah's card is shown to Leah. Leah's card is shown to Arturo. It is publicly announced that someone picked a red card. It is publicly announced that Arturo knows whether Arturo picked a red card. It is publicly announced that Arturo knows whether or not nobody picked a red card. It is publicly announced that Leah picked a black card. It is publicly announced that Arturo knows whether Leah picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Leah can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Leah","Arturo"],"index":25561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Billy knows whether or not nobody is thirsty. It is publicly announced that Billy does not know whether Jayson is thirsty. It is publicly announced that Lillie knows whether or not everyone is thirsty. It is publicly announced that Jayson knows whether Jayson is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lillie can now know whether Lillie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Billy","Lillie","Jayson"],"index":45655,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983307719,"difficulty":0.0016692281}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Gloria. Gloria's card is shown to Emilee. George's card is shown to Emilee. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Gloria does not know whether Emilee picked a red card. It is publicly announced that George does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Emilee can now know whether George can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gloria","Emilee","George"],"index":23542,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994107485,"difficulty":0.0005892515}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Suzanne. Alan's card is shown to Ervin. Suzanne's card is shown to Harold. Harold's card is shown to Harold. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Suzanne can now know whether Ervin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Suzanne","Ervin","Harold","Alan"],"index":55626,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9445678592,"difficulty":0.0554321408}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmen's card is shown to Carmen. Natasha's card is shown to Carmen. Adam's card is shown to Adam. Carmen's card is shown to Natasha. It is publicly announced that someone picked a red card. It is publicly announced that Adam does not know whether Carmen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Natasha can now know that Carmen can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carmen","Adam","Natasha"],"index":58072,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Maria. Robert's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know that Robert can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Robert","William"],"index":44550,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9901233315,"difficulty":0.0098766685}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Carmen can now know that Bryan can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Carmen","Rena","Bryan"],"index":1930,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997807145,"difficulty":0.0002192855}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Patricia can now know whether Charles can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Patricia"],"index":33987,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997107387,"difficulty":0.0002892613}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wesley's card is shown to Brad. Brad's card is shown to Wesley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brad can now know whether Jared can know whether Wesley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brad","Jared","Wesley"],"index":62832,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990280867,"difficulty":0.0009719133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lillian does not know whether or not everyone is thirsty. It is publicly announced that Matthew does not know whether Leo is thirsty. It is publicly announced that Matthew does not know whether Leo is thirsty. It is publicly announced that Matthew does not know whether Charlie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Charlie can now know whether Lillian can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charlie","Matthew","Lillian","Leo"],"index":20035,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997735858,"difficulty":0.002264142}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frederick's card is shown to Norman. Norman's card is shown to Frederick. It is publicly announced that someone picked a red card. It is publicly announced that Norman does not know whether or not everyone picked a red card. It is publicly announced that Frederick picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Pauline can now know whether Pauline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","Norman","Joyce","Frederick"],"index":241,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5281592607,"difficulty":0.4718407393}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kasey's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Manuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Robert can now know that Manuel can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Manuel","Kasey","Robert"],"index":25370,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984633923,"difficulty":0.0015366077}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Barbara can now know that Joseph can know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nena","Traci","Barbara","Joseph"],"index":36608,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9958586097,"difficulty":0.0041413903}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tameka is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] 0","hypothesis":"Tameka can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tameka","Joe"],"index":57946,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997447133,"difficulty":0.0002552867}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norma's card is shown to Norma. Clayton's card is shown to Norma. Alishia's card is shown to Norma. Virginia's card is shown to Norma. Clayton's card is shown to Clayton. Norma's card is shown to Alishia. Norma's card is shown to Virginia. Alishia's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Alishia does not know whether Alishia picked a red card. It is publicly announced that Norma knows whether Alishia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Clayton can now know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norma","Clayton","Alishia","Virginia"],"index":39543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8699272871,"difficulty":0.1300727129}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glenn's card is shown to Glenn. Glenn's card is shown to Gloria. Gloria's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Glenn can now know that Gloria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Glenn","Gloria"],"index":47554,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996750474,"difficulty":0.003249526}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Robert is thirsty. It is publicly announced that William does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] Agentd knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mary can now know whether William can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","William","Robert","Mary"],"index":42299,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9951729178,"difficulty":0.0048270822}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Blanca. Sherrie's card is shown to Blanca. Duane's card is shown to Sherrie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Blanca can now know whether Duane can know that Duane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Blanca","Duane","Sherrie"],"index":11286,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9412952065,"difficulty":0.0587047935}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dean can now know whether Joann can know whether Billy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joann","Billy","John","Dean"],"index":13888,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991752505,"difficulty":0.0008247495}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy. It is publicly announced that Stephen knows whether Torie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"James can now know that Stephen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Torie","Tamra","James","Stephen"],"index":54276,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977916479,"difficulty":0.0022083521}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hermina's card is shown to Hermina. Barbara's card is shown to Hermina. Marjorie's card is shown to Hermina. Hermina's card is shown to Barbara. Barbara's card is shown to Barbara. Marjorie's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Hermina knows whether Hermina picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Marjorie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hermina","Barbara","Marjorie"],"index":16028,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997213483,"difficulty":0.0002786517}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice knows whether someone is thirsty. It is publicly announced that Janice knows whether Janice is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Janice can now know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carolyn","Robert","Janice"],"index":9766,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954605699,"difficulty":0.0045394301}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ken does not know whether Mary is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Mary can now know that Ken can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ken","Mary"],"index":16505,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7440280318,"difficulty":1.7440280318}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Holly. Don's card is shown to Don. Dean's card is shown to Don. Dean's card is shown to Gregory. Holly's card is shown to Dean. Don's card is shown to Dean. Gregory's card is shown to Dean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Dean can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Holly","Don","Gregory","Dean"],"index":21133,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983243346,"difficulty":0.0016756654}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denise's card is shown to Denise. Theodore's card is shown to Denise. Brian's card is shown to Denise. Theodore's card is shown to James. James's card is shown to Theodore. Theodore's card is shown to Theodore. Denise's card is shown to Brian. James's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:2,3 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:2,3 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Theodore can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Denise","James","Theodore","Brian"],"index":2855,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6042077541,"difficulty":1.6042077541}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Barbara can now know that Brian can know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Jennifer","Louis","Barbara"],"index":10439,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996231794,"difficulty":0.0003768206}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Truman's card is shown to Truman. Justin's card is shown to Truman. William's card is shown to William. Justin's card is shown to Justin. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether Truman picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Justin can now know whether William can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Truman","William","Justin"],"index":66097,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997088313,"difficulty":0.0002911687}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Risa does not know whether or not everyone's forehead is muddy. It is publicly announced that Risa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Risa can now know whether Rosaura can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosaura","Emily","Risa","April"],"index":26570,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995599389,"difficulty":0.0004400611}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ila knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Richard can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ila","Richard","Ana"],"index":51651,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997424483,"difficulty":0.0002575517}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. Calvin's card is shown to Calvin. It is publicly announced that someone picked a red card. It is publicly announced that Andrea knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Andrea can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andrea","Calvin"],"index":61277,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981948733,"difficulty":0.0018051267}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy does not know whether or not everyone's forehead is muddy. It is publicly announced that Karl knows whether someone's forehead is muddy. It is publicly announced that Wendy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jake can now know whether Crystal can know whether Wendy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Crystal","Wendy","Karl","Jake"],"index":55320,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993207455,"difficulty":0.0006792545}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Rex. Rex's card is shown to Rex. Myrtle's card is shown to Rex. Steven's card is shown to Myrtle. Rex's card is shown to Melanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Myrtle can now know whether Steven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Rex","Myrtle","Melanie"],"index":19404,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6544733047,"difficulty":1.6544733047}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that Gary can know whether Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Michael","Gary"],"index":49037,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9038003087,"difficulty":0.0961996913}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether Jacqueline's forehead is muddy. It is publicly announced that Dominga knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Dominga can now know that Jacqueline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Benjamin","Jacqueline","Dominga"],"index":19450,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973504543,"difficulty":0.0026495457}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Lindsay. Sam's card is shown to Sam. Sam's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Lindsay picked a red card. It is publicly announced that Lindsay knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Sam can now know that Matthew can know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lindsay","Sam","Matthew"],"index":33177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9368979931,"difficulty":0.0631020069}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosie does not know whether Johnny is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Rosie can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Johnny","Rosie"],"index":61573,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942031503,"difficulty":0.0057968497}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Adrian can now know whether Ericka's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Evelyn","Ericka","Adrian"],"index":4706,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997351766,"difficulty":0.0002648234}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jim is thirsty. It is publicly announced that Jim knows whether Jim is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Charles can now know that Carlos can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Carlos","Jim"],"index":61915,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6487398148,"difficulty":1.6487398148}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gertrude's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Steve can now know that Steve's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steve","Gertrude","Robert","Kim"],"index":62146,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9790261984,"difficulty":0.0209738016}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mayra knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mayra can now know that Mayra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Troy","Mayra","Ralph"],"index":23892,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.886179626,"difficulty":0.113820374}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arlene knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Arlene can now know whether Louise is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arlene","Louise","Rosa"],"index":53275,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997649014,"difficulty":0.002350986}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexandra knows whether Debrah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Debrah can now know that Esmeralda can know that Kyle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Esmeralda","Kyle","Debrah","Alexandra"],"index":12099,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984179735,"difficulty":0.0015820265}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jade knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jade can now know that Jade's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jana","Jade","Janet","Allene"],"index":2527,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8345791698,"difficulty":0.1654208302}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether Karina's forehead is muddy. It is publicly announced that Anna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Anna can now know that Jack's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","Anna","Debra","Karina"],"index":22378,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9950200319,"difficulty":0.0049799681}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Gerald. Tamara's card is shown to Gerald. Roman's card is shown to Juan. Tamara's card is shown to Juan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gerald","Juan","Roman","Tamara"],"index":38510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983541965,"difficulty":0.0016458035}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Willie knows whether Kay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kay","David","Leila","Willie"],"index":51791,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997109592,"difficulty":0.002890408}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Helen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] 0","hypothesis":"Debbie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debbie","Helen","Jeff","Donald"],"index":30289,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996917367,"difficulty":0.003082633}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether Tia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Tia can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Robert","Dean","Tia"],"index":50674,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985833168,"difficulty":0.0014166832}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Abraham. Abraham's card is shown to Darrell. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Darrell can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Abraham","Darrell","Donna"],"index":65738,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997563958,"difficulty":0.0002436042}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawanda's card is shown to Beth. Lucille's card is shown to Beth. Lucille's card is shown to Lucille. It is publicly announced that someone picked a red card. It is publicly announced that Lawanda does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lawanda can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lawanda","Beth","Lucille"],"index":6839,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980034232,"difficulty":0.0019965768}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Carol can now know that Conrad can know whether Conrad is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Conrad","Jason","James"],"index":65318,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976918697,"difficulty":0.0023081303}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether or not nobody's forehead is muddy. It is publicly announced that Frank knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Frank can now know whether Richard can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Emma","Richard","Frank"],"index":5084,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8055922389,"difficulty":1.8055922389}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Troy can now know whether Audrey can know whether Audrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Nicole","Audrey","Troy"],"index":20996,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8268566728,"difficulty":0.1731433272}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel's forehead is not muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"James can now know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Daniel","Jennifer"],"index":46328,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995957017,"difficulty":0.0004042983}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy does not know whether or not everyone's forehead is muddy. It is publicly announced that Ida knows whether Tammy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Tammy can now know that John can know whether Tammy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ida","Jackie","John","Tammy"],"index":2595,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994543195,"difficulty":0.0005456805}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Claire's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Alejandro can now know that Alexander can know that Claire's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Claire","Leon","Alejandro","Alexander"],"index":28015,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9751433134,"difficulty":0.0248566866}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"John can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Mary","Manuel","Jeanette"],"index":12203,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995180368,"difficulty":0.0004819632}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Betty can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Betty","Donald","Dorothy"],"index":59585,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983546138,"difficulty":0.0016453862}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy. It is publicly announced that George does not know whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Carol can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Carol","George","Glen"],"index":34713,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9849457741,"difficulty":0.0150542259}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peggie's card is shown to Whitney. Richard's card is shown to Whitney. Peggie's card is shown to Peggie. Whitney's card is shown to Chester. Richard's card is shown to Chester. It is publicly announced that someone picked a red card. It is publicly announced that Whitney does not know whether or not everyone picked a red card. It is publicly announced that Richard does not know whether Chester picked a red card. It is publicly announced that Richard does not know whether Chester picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Whitney can now know whether Peggie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Whitney","Peggie","Richard","Chester"],"index":30898,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9476546049,"difficulty":0.0523453951}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Craig is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that Craig does not know whether Annette is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Marcia can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Annette","Marcia","Craig","James"],"index":20849,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997754693,"difficulty":0.0002245307}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jim can now know that Ruth can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jonathan","Calvin","Ruth","Jim"],"index":5462,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983512163,"difficulty":0.0016487837}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know whether Barb can know whether Dale's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dale","Barb","Karen","Melvin"],"index":51331,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995011091,"difficulty":0.0004988909}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sue does not know whether Terry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Rosemary can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rosemary","Sue","Rocio","Terry"],"index":19939,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997656941,"difficulty":0.0002343059}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether or not everyone's forehead is muddy. It is publicly announced that Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Ruth can now know whether Greg's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ruth","Greg","Jessica","Joshua"],"index":56558,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997243285,"difficulty":0.0002756715}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isaura's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Isaura can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Isaura","Hilda","Jason"],"index":22822,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985234141,"difficulty":0.0014765859}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Derek knows whether Ruth is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ruth can now know whether Derek can know whether Ruth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Derek","Ruth"],"index":47842,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990043044,"difficulty":0.0009956956}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jennifer can now know that John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Peter","John","Jennifer"],"index":53094,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983714223,"difficulty":0.0016285777}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that John knows whether Stacy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Stacy can now know that Christopher can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Stacy","Christopher","Heather"],"index":21323,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9931194782,"difficulty":0.0068805218}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Walter knows whether or not everyone is thirsty. It is publicly announced that Mary is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(2) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"Aurora can now know that Walter can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Aurora","Mary","Walter","Eric"],"index":65178,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984941483,"difficulty":0.0015058517}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jerry can now know that Karen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Jerry","Michael","Charles"],"index":3395,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975220561,"difficulty":0.0024779439}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jeffrey can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dwayne","Barbara","Ray","Jeffrey"],"index":67479,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983275533,"difficulty":0.0016724467}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dean's card is shown to Dean. Steven's card is shown to Dean. Dean's card is shown to Steven. It is publicly announced that someone picked a red card. It is publicly announced that Steven knows whether Steven picked a red card. It is publicly announced that Steven picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! 2 ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! 2 ] 0","hypothesis":"Steven can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dean","Steven"],"index":495,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997245669,"difficulty":0.0002754331}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack knows whether Jack's forehead is muddy. It is publicly announced that Deloris's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Deloris can now know whether Jack can know whether Deloris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Jack","Deloris"],"index":34355,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996826649,"difficulty":0.0003173351}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Mark can now know whether Nicholas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nicholas","Joan","Mark"],"index":10545,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999551475,"difficulty":0.000448525}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman knows whether someone's forehead is muddy. It is publicly announced that Linda knows whether someone's forehead is muddy. It is publicly announced that Raymond knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Raymond can now know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Walter","Norman","Linda"],"index":49167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970699549,"difficulty":0.0029300451}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jimmy can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Jimmy","Joan","Donna"],"index":66103,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9941332936,"difficulty":0.0058667064}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Florence's card is shown to Florence. Ruth's card is shown to Florence. Kimberlee's card is shown to Florence. Florence's card is shown to Judy. Judy's card is shown to Judy. Kimberlee's card is shown to Judy. Florence's card is shown to Kimberlee. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Judy can now know whether Judy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Florence","Ruth","Judy","Kimberlee"],"index":40387,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9039846659,"difficulty":1.9039846659}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Julie. Jerome's card is shown to Jerome. Harvey's card is shown to Jerome. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that Jerome picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julie","Jerome","Harvey"],"index":47791,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982783794,"difficulty":0.0017216206}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Lynda can now know whether Crystal can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leslie","Crystal","Lynda","Thomas"],"index":20047,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997822642,"difficulty":0.0002177358}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter knows whether or not nobody's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agenta knows that (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Walter can now know that David can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Walter","David"],"index":28350,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9905943871,"difficulty":1.9905943871}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Louise's card is shown to Kathleen. Adrienne's card is shown to Louise. Louise's card is shown to Adrienne. It is publicly announced that someone picked a red card. It is publicly announced that Adrienne does not know whether Adrienne picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Adrienne can now know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Louise","Adrienne"],"index":17201,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959321618,"difficulty":0.0040678382}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose knows whether someone's forehead is muddy. It is publicly announced that Earl knows whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Earl can now know that Rose's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Earl","Rose"],"index":6410,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970796704,"difficulty":0.0029203296}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelby knows whether Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Janet can now know whether Anthony can know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janet","Mark","Shelby","Anthony"],"index":9684,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9615434408,"difficulty":0.0384565592}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delbert's card is shown to Melda. Melda's card is shown to Delbert. Delbert's card is shown to Delbert. James's card is shown to Delbert. Melda's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Melda can now know whether Delbert can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melda","Delbert","James"],"index":52006,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982958436,"difficulty":0.0017041564}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lourdes's card is shown to Patricia. Lourdes's card is shown to Lourdes. It is publicly announced that someone picked a red card. It is publicly announced that Lourdes does not know whether or not everyone picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Lourdes can now know that Patricia can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Lourdes"],"index":32733,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8827950358,"difficulty":0.1172049642}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick knows whether or not everyone's forehead is muddy. It is publicly announced that Frederick's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Arlene can now know that Lenora's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frederick","Lenora","Arlene"],"index":52979,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9307463169,"difficulty":0.0692536831}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanetta does not know whether or not everyone's forehead is muddy. It is publicly announced that Melvin knows whether or not everyone's forehead is muddy. It is publicly announced that Wanetta does not know whether Wanetta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"April can now know that Carol can know that Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["April","Melvin","Carol","Wanetta"],"index":42229,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6683409214,"difficulty":1.6683409214}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Sharon does not know whether Jessica is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know that Jessica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kurt","Sharon","Jessica"],"index":48856,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9020987153,"difficulty":0.0979012847}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helene does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether Helene's forehead is muddy. It is publicly announced that Helene does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Helene can now know that Robert can know whether Helene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Helene","Robert"],"index":41908,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994537234,"difficulty":0.0005462766}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luke knows whether Lloyd's forehead is muddy. It is publicly announced that Emanuel knows whether Lloyd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Emanuel can now know that Luke can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emanuel","Luke","Lloyd","Marcia"],"index":36889,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9679526687,"difficulty":0.0320473313}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miranda's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristen does not know whether Kristen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Miranda can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kristen","Miranda"],"index":36448,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8607794046,"difficulty":1.8607794046}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Debbie is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Debbie can now know whether Michael can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Debbie","Michael","William"],"index":27306,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997825027,"difficulty":0.0002174973}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christy's card is shown to Christy. Ivan's card is shown to Christy. Donald's card is shown to Ivan. Ivan's card is shown to William. William's card is shown to Donald. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Ivan does not know whether William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"William can now know that Ivan can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christy","Ivan","William","Donald"],"index":62302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925552011,"difficulty":0.0074447989}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Rickey can now know that Janet can know that Gertrude's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Gertrude","Rickey","Charles"],"index":37314,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8064357042,"difficulty":0.1935642958}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Jenice can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jenice","James"],"index":59944,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Eugene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Paul can now know that Eugene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eugene","Paul","Daniel","Magdalena"],"index":59794,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980487823,"difficulty":0.0019512177}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. Stephen's card is shown to Jessica. Stephen's card is shown to Stephen. Tim's card is shown to Stephen. Jessica's card is shown to Tim. Stephen's card is shown to Tim. It is publicly announced that someone picked a red card. It is publicly announced that Tim knows whether Stephen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Stephen can now know that Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessica","Stephen","Tim"],"index":57723,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995888412,"difficulty":0.004111588}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn does not know whether Evelyn's forehead is muddy. It is publicly announced that Evelyn's forehead is muddy. It is publicly announced that Roxanne's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agentd knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Rochelle can now know that Rochelle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","David","Roxanne","Rochelle"],"index":65222,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6133787036,"difficulty":0.3866212964}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Shirley. Renee's card is shown to Shirley. Jean's card is shown to Renee. Renee's card is shown to Kathleen. Kathleen's card is shown to Jean. Jean's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Renee does not know whether Kathleen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentd knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jean can now know that Kathleen can know whether Renee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Renee","Kathleen","Jean"],"index":4950,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9052764773,"difficulty":1.9052764773}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirlee's card is shown to Shirlee. Shirlee's card is shown to Marla. It is publicly announced that someone picked a red card. It is publicly announced that Shirlee does not know whether Marla picked a red card. It is publicly announced that Shirlee does not know whether Marla picked a red card. It is publicly announced that Marla does not know whether Marla picked a red card. It is publicly announced that Marla picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! 2 ] (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! 2 ] 0","hypothesis":"Shirlee can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shirlee","Marla"],"index":44905,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9976796508,"difficulty":1.9976796508}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Harold. Harold's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Sara can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sara","Gloria","Harold"],"index":46145,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997196794,"difficulty":0.0002803206}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that June does not know whether June's forehead is muddy. It is publicly announced that Carolyn does not know whether Carolyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"June can now know whether Catherine can know that June's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carolyn","Catherine","June"],"index":21841,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5020034313,"difficulty":1.5020034313}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jane can now know that Michael can know whether Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Jane","Steven"],"index":25467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996283054,"difficulty":0.0003716946}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Jennifer can now know that Robin can know whether Reyna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Robin","Donna","Reyna"],"index":5738,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997215867,"difficulty":0.0002784133}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ashley can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Regina","Ashley","Jose"],"index":32581,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986076951,"difficulty":0.0013923049}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Raymond. Elizabeth's card is shown to Raymond. Darrell's card is shown to Darrell. Raymond's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Raymond does not know whether Raymond picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Raymond can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Darrell","Elizabeth"],"index":35568,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957695007,"difficulty":0.0042304993}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Arthur. Emanuel's card is shown to Arthur. Emanuel's card is shown to Glen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Arthur can now know that Arthur picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arthur","Emanuel","Glen"],"index":3594,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961531758,"difficulty":0.0038468242}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Carrie does not know whether Lori is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Carrie can now know that Paul is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","George","Lori","Carrie"],"index":61333,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970044494,"difficulty":0.0029955506}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheri's card is shown to Matthew. Merrill's card is shown to Merrill. Merrill's card is shown to Alicia. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Merrill can now know whether Merrill picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sheri","Matthew","Merrill","Alicia"],"index":28589,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9903241396,"difficulty":0.0096758604}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Catherine. Karen's card is shown to Karen. Karen's card is shown to Courtney. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Catherine","Karen","Courtney"],"index":32177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974797368,"difficulty":0.0025202632}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to Richard. Marian's card is shown to Marian. Jesus's card is shown to Marian. Jesus's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Jesus does not know whether Marian picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jesus can now know that Richard can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Marian","Jesus"],"index":34996,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6259359121,"difficulty":0.3740640879}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julia knows whether Julia is thirsty. It is publicly announced that Marlene does not know whether or not everyone is thirsty. It is publicly announced that Loretta does not know whether or not everyone is thirsty. It is publicly announced that Lenna does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Julia can now know whether Lenna can know whether Marlene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lenna","Marlene","Loretta","Julia"],"index":19595,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986796975,"difficulty":0.0013203025}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeff knows whether or not everyone is thirsty. It is publicly announced that Michael is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Jeff can now know whether Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Jeff","Richard"],"index":48988,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8499279618,"difficulty":0.1500720382}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antoinette is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Bill can now know that Janene can know that Janene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antoinette","Steven","Janene","Bill"],"index":7256,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.984798491,"difficulty":0.015201509}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lee's card is shown to Lee. George's card is shown to Lee. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that George knows whether George picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"George can now know whether Lee can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lee","George"],"index":40346,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Katherine can now know that Frances can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["April","Frances","Katherine"],"index":34866,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996355772,"difficulty":0.0003644228}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Ryan. Johnathan's card is shown to Johnathan. Ryan's card is shown to Steven. Johnathan's card is shown to Tammy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tammy can now know whether Johnathan can know whether Ryan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ryan","Johnathan","Steven","Tammy"],"index":44375,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998290956,"difficulty":0.001709044}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether Adelaide's forehead is muddy. It is publicly announced that Rebecca knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Karen can now know whether Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Frederick","Adelaide","Rebecca"],"index":19800,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995698333,"difficulty":0.0004301667}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Bonnie can now know whether Maria can know whether Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bonnie","Maria","Hector","Dorothy"],"index":35362,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990181923,"difficulty":0.0009818077}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy knows whether Victor is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Victor can now know whether Nancy can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Victor","Nancy"],"index":66890,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993023872,"difficulty":0.0006976128}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Olga does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Olga can now know whether Brittney can know that Olga is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Olga","Brittney","Dawn"],"index":53774,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9940244555,"difficulty":0.0059755445}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander's forehead is not muddy. It is publicly announced that Regina's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Regina can now know that Iris can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Regina","Alexander","Iris"],"index":22990,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996328354,"difficulty":0.0003671646}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Frances. Paz's card is shown to Paz. It is publicly announced that someone picked a red card. It is publicly announced that Frances picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Frances can now know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frances","Gregory","Paz"],"index":67404,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8582607508,"difficulty":0.1417392492}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dorothy can now know that Dan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","Dan","Dorothy"],"index":55092,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9876155257,"difficulty":0.0123844743}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Virginia. Roger's card is shown to Virginia. Roger's card is shown to John. Roger's card is shown to Roger. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Roger can now know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Virginia","John","Roger"],"index":43201,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9893653393,"difficulty":0.0106346607}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Charlie can now know whether Suzanne can know that Suzanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Suzanne","Charlie","James"],"index":65258,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996495247,"difficulty":0.0003504753}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tanya's card is shown to Tanya. Tanya's card is shown to Jesse. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] (Agentb knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Jesse can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tanya","Jesse"],"index":39495,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997678399,"difficulty":0.0002321601}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jenifer knows whether or not nobody's forehead is muddy. It is publicly announced that Philip's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Jenifer can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Philip","Jenifer"],"index":42483,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984089732,"difficulty":0.0015910268}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Jenifer. Jenifer's card is shown to Jenifer. William's card is shown to Jerry. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Charles can now know that Jenifer can know whether Jenifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Charles","Jenifer","Jerry"],"index":30968,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.878796041,"difficulty":0.121203959}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emilie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Ramona can now know whether Donald can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darren","Ramona","Emilie","Donald"],"index":36484,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997825027,"difficulty":0.0002174973}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jimmy","Charles","John"],"index":28766,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984747767,"difficulty":0.0015252233}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Dorothy. Mary's card is shown to Mary. Arthur's card is shown to Mary. Dorothy's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Arthur picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Theresa","Mary","Arthur"],"index":24852,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9715989828,"difficulty":1.9715989828}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Timothy. Timothy's card is shown to Theresa. Theresa's card is shown to Theresa. It is publicly announced that someone picked a red card. It is publicly announced that Theresa picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Timothy can now know that Theresa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Timothy","Theresa"],"index":13397,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984966516,"difficulty":0.0015033484}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lenard does not know whether Lillian is thirsty. It is publicly announced that Hannah does not know whether Lenard is thirsty. It is publicly announced that Lillian does not know whether Kent is thirsty. It is publicly announced that Kent does not know whether Hannah is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Kent can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hannah","Lenard","Kent","Lillian"],"index":12395,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984914064,"difficulty":0.0015085936}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grover's card is shown to Carolyn. Adam's card is shown to Adam. Carolyn's card is shown to Maria. Carolyn's card is shown to Grover. Adam's card is shown to Grover. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Grover can now know that Carolyn can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Adam","Maria","Grover"],"index":49404,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984487295,"difficulty":0.0015512705}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jimmy can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alyson","Brent","Jimmy"],"index":1145,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983307719,"difficulty":0.0016692281}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emily does not know whether Mitchell is thirsty. It is publicly announced that James does not know whether Mitchell is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"James can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mitchell","Victor","Emily","James"],"index":14796,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986314178,"difficulty":0.0013685822}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roxy knows whether Eloy's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Roxy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marilyn","Robert","Roxy","Eloy"],"index":16412,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986674786,"difficulty":0.0013325214}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Richard can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Lucina"],"index":55964,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985517859,"difficulty":0.0014482141}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Virginia. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that Virginia does not know whether or not everyone picked a red card. It is publicly announced that Katherine knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Katherine can now know that Virginia can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Virginia","Katherine"],"index":32868,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7228581905,"difficulty":1.7228581905}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that James does not know whether Bertha is thirsty. It is publicly announced that James does not know whether Bertha is thirsty. It is publicly announced that Bertha knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Bertha can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Robert","Bertha"],"index":205,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997312427,"difficulty":0.0002687573}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brendan knows whether or not everyone's forehead is muddy. It is publicly announced that Brendan does not know whether Brendan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Elizabeth can now know whether Brendan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josephine","Brendan","Elizabeth","Teresa"],"index":65479,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994743466,"difficulty":0.0005256534}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myrtle's card is shown to Myrtle. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Myrtle does not know whether Dorothy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Myrtle can now know whether Dorothy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Myrtle","Dorothy"],"index":62698,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9949076772,"difficulty":1.9949076772}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernice does not know whether Jana is thirsty. It is publicly announced that Howard does not know whether Bernice is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jana can now know whether Howard can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jana","Howard","Bernice"],"index":37198,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979051352,"difficulty":0.0020948648}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antonio's forehead is muddy. It is publicly announced that Antonio knows whether or not nobody's forehead is muddy. It is publicly announced that Carlos does not know whether Carlos's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Antonio can now know whether Carlos can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carlos","John","Antonio"],"index":45928,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9951817393,"difficulty":0.0048182607}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Megan. Samantha's card is shown to Samantha. Maria's card is shown to Samantha. Maria's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Megan can now know whether Maria can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Megan","Samantha","Maria"],"index":59502,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995675683,"difficulty":0.0004324317}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Constance's card is shown to Priscilla. James's card is shown to Constance. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Constance can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Priscilla","Constance"],"index":42237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997814298,"difficulty":0.0002185702}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna does not know whether or not everyone is thirsty. It is publicly announced that Arturo knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Donna can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Karla","Arturo","John"],"index":490,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6011347771,"difficulty":0.3988652229}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Gary can now know that John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sara","Gary","John"],"index":37453,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961404204,"difficulty":0.0038595796}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Johanna can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Armando","Johanna","Linda"],"index":54934,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997578263,"difficulty":0.0002421737}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine's forehead is not muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Karen can now know that Richard can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Catherine","Richard"],"index":41190,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9338896871,"difficulty":0.0661103129}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl does not know whether or not everyone's forehead is muddy. It is publicly announced that Carl does not know whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Linda can now know that Carl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carl","Linda"],"index":43440,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9448992014,"difficulty":1.9448992014}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jewell's card is shown to Gary. William's card is shown to William. Jewell's card is shown to Guy. Jewell's card is shown to Jewell. It is publicly announced that someone picked a red card. It is publicly announced that Guy does not know whether Guy picked a red card. It is publicly announced that William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] 0","hypothesis":"Jewell can now know whether Gary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","William","Guy","Jewell"],"index":60372,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8053713441,"difficulty":0.1946286559}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Steven can now know whether Dawn can know that Gladys's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Gladys","Dawn"],"index":32712,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996944666,"difficulty":0.0003055334}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myrtle's card is shown to Myrtle. Ester's card is shown to Myrtle. Myrtle's card is shown to Ester. Ester's card is shown to Ester. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Ester can now know that Myrtle can know whether Ester picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Myrtle","Ester"],"index":15056,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7038181424,"difficulty":1.7038181424}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Stephen can now know that Aaron can know that Aaron's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Aaron","William","Stephen"],"index":40215,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969335794,"difficulty":0.0030664206}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Jerry. Chad's card is shown to Jerry. Jerry's card is shown to Herbert. Herbert's card is shown to Herbert. Jerry's card is shown to Chad. Jack's card is shown to Chad. It is publicly announced that someone picked a red card. It is publicly announced that Jerry does not know whether Jack picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Herbert can now know that Jack can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Herbert","Jack","Chad"],"index":44406,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997141957,"difficulty":0.0002858043}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darryl's forehead is not muddy. It is publicly announced that Frank's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Darryl can now know that Frank can know that Sean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harry","Frank","Darryl","Sean"],"index":4536,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9856128097,"difficulty":0.0143871903}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Greg's card is shown to Greg. Derrick's card is shown to Greg. Zoe's card is shown to Zoe. Greg's card is shown to Derrick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Derrick can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Greg","Zoe","Derrick"],"index":58452,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997263551,"difficulty":0.0002736449}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether or not everyone's forehead is muddy. It is publicly announced that Sharon does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Victor can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sharon","Victor"],"index":2839,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976615906,"difficulty":0.0023384094}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Gregory can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gregory","Mark"],"index":22162,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982301593,"difficulty":0.0017698407}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Al's card is shown to Al. Jerry's card is shown to Al. Al's card is shown to Gloria. Gloria's card is shown to Gloria. Jerry's card is shown to Gloria. Al's card is shown to Jerry. Gloria's card is shown to Jerry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gloria can now know whether Jerry can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Al","Gloria","Jerry"],"index":34161,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oscar's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Katherine can now know that Oscar's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Oscar","George","Susan","Katherine"],"index":8733,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.98576051,"difficulty":0.01423949}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that Bonny can know whether Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Bonny","Cheryl"],"index":6606,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9736350775,"difficulty":0.0263649225}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Andrew can now know that Erica can know that Timothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Andrew","Timothy","Erica"],"index":8624,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981605411,"difficulty":0.0018394589}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Martin's forehead is not muddy. It is publicly announced that Lorenzo's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agentb knows that (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Martin can now know that Lorenzo can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lorenzo","Martin"],"index":48569,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977607727,"difficulty":0.0022392273}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan knows whether Amy's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Charles can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amy","Juan","Robert","Charles"],"index":16744,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959836006,"difficulty":0.0040163994}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Stephanie knows whether Lola's forehead is muddy. It is publicly announced that Arthur's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] (Agentd knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Frances can now know whether Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephanie","Arthur","Lola","Frances"],"index":10629,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993732572,"difficulty":0.0006267428}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theodore does not know whether Dennis is thirsty. It is publicly announced that David does not know whether Dennis is thirsty. It is publicly announced that David is not thirsty. It is publicly announced that Theodore is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! ~(3) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! ~(3) ] 0","hypothesis":"Dennis can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Dennis","Theodore"],"index":66338,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9438723326,"difficulty":0.0561276674}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Martin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Martin can now know that John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Oscar","John","Kenneth","Martin"],"index":56382,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983952641,"difficulty":0.0016047359}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Shawn can now know that Bruce can know whether Shawn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shawn","Bruce","John"],"index":37657,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999748528,"difficulty":0.000251472}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Anna can now know that Jason can know whether Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Jason","Anna"],"index":31372,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995988011,"difficulty":0.0004011989}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathryn does not know whether or not everyone is thirsty. It is publicly announced that Kathryn does not know whether Eugene is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kathryn can now know whether Eugene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eugene","Kathryn"],"index":30145,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6511932611,"difficulty":0.3488067389}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laurie","Mary","Eugenio"],"index":26482,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994556427,"difficulty":0.005443573}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lisa can now know that Angela can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Judy","Wayne","Angela"],"index":46780,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984893799,"difficulty":0.0015106201}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Nelson can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nelson","Michael","Jeffery","Luis"],"index":18044,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9717188478,"difficulty":0.0282811522}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy does not know whether Bonnie is thirsty. It is publicly announced that Katie does not know whether Bonnie is thirsty. It is publicly announced that Glen does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Bonnie can now know whether Bonnie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katie","Glen","Bonnie","Amy"],"index":14343,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987350106,"difficulty":0.0012649894}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that June's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Daniel can now know whether June can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","June","Daniel"],"index":40610,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995492101,"difficulty":0.0004507899}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Dona's card is shown to William. Dwayne's card is shown to Dwayne. Dona's card is shown to Dwayne. William's card is shown to Dona. Dwayne's card is shown to Dona. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether someone picked a red card. It is publicly announced that Dona picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dona can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Dwayne","Dona"],"index":16515,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997015595,"difficulty":0.0002984405}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Norman. Richard's card is shown to Phyllis. Richard's card is shown to Richard. Richard's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Phyllis can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norman","Phyllis","Richard","Mark"],"index":20205,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983528852,"difficulty":0.0016471148}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn's forehead is muddy. It is publicly announced that Evelyn knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Albert can now know whether Amber can know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Evelyn","Linda","Albert","Amber"],"index":63346,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997095466,"difficulty":0.0002904534}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether Michaela can know that Michaela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Michaela"],"index":46439,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7258875966,"difficulty":0.2741124034}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rod can now know that Herbert can know that Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Herbert","Rod","Tyler"],"index":36419,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985724688,"difficulty":0.0014275312}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Bonnie can now know that Bonnie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Colin","Barry","Bonnie"],"index":5213,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9964235425,"difficulty":0.0035764575}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daryl knows whether someone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Daryl can now know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Daniel","Daryl"],"index":40631,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998131454,"difficulty":0.001868546}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ella's card is shown to Charles. Charles's card is shown to Ella. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Monica can now know whether Charles can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Monica","Ella"],"index":17662,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9960243702,"difficulty":0.0039756298}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Sarita. Louise's card is shown to Louise. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Louise can now know whether Louise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sarita","Louise"],"index":47946,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9866720438,"difficulty":0.0133279562}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","Breanna"],"index":477,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997655749,"difficulty":0.0002344251}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dawn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Louise can now know that Michele's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lidia","Dawn","Louise","Michele"],"index":54764,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965513945,"difficulty":0.0034486055}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry knows whether Brian's forehead is muddy. It is publicly announced that Jerry knows whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Margaret can now know whether Jerry can know whether Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Edward","Margaret","Jerry"],"index":16264,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997077584,"difficulty":0.0002922416}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eddie is not thirsty. It is publicly announced that Jamie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"Eddie can now know whether Jamie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Tracy","Eddie","Jamie"],"index":11298,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9963343143,"difficulty":0.0036656857}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to David. Florence's card is shown to Florence. Timothy's card is shown to Erica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Florence can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","David","Florence","Erica"],"index":15632,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984540939,"difficulty":0.0015459061}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Robin. Walter's card is shown to Walter. Al's card is shown to Walter. Robin's card is shown to Al. Walter's card is shown to Al. It is publicly announced that someone picked a red card. It is publicly announced that Walter picked a black card. It is publicly announced that Robin knows whether Robin picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Robin can now know that Al picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robin","Walter","Al"],"index":30685,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9346330166,"difficulty":0.0653669834}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Marie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Beverly","Chance","Marie"],"index":60907,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9963417649,"difficulty":0.0036582351}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kandi knows whether Cathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Molly can now know that Kandi can know whether Kandi's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Molly","Brenda","Cathy","Kandi"],"index":24897,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.989574492,"difficulty":0.010425508}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fannie's card is shown to Fannie. Tracey's card is shown to Katherine. Katherine's card is shown to Michael. Fannie's card is shown to Tracey. Katherine's card is shown to Tracey. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Tracey can now know that Fannie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fannie","Katherine","Michael","Tracey"],"index":27285,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8366032243,"difficulty":0.1633967757}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Concetta's card is shown to Concetta. Regina's card is shown to Regina. Karen's card is shown to Nicholas. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Regina can now know that Concetta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Concetta","Regina","Nicholas"],"index":36631,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7961477637,"difficulty":1.7961477637}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andre does not know whether Vicki is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Noreen can now know whether Andre can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Noreen","Andre","Vicki","Elizabeth"],"index":14292,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979336262,"difficulty":0.0020663738}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maricela's card is shown to Troy. Troy's card is shown to Jasmine. Jasmine's card is shown to Jasmine. Maricela's card is shown to Jasmine. Troy's card is shown to Joseph. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Jasmine does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Maricela can now know that Jasmine can know whether Maricela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Troy","Jasmine","Maricela","Joseph"],"index":44847,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6138107181,"difficulty":1.6138107181}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Audrey's card is shown to Audrey. Helen's card is shown to Audrey. Maria's card is shown to Audrey. Helen's card is shown to James. Maria's card is shown to James. Helen's card is shown to Helen. Maria's card is shown to Helen. Audrey's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether or not everyone picked a red card. It is publicly announced that Maria picked a black card. It is publicly announced that Audrey picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Audrey can now know that Helen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Audrey","James","Helen","Maria"],"index":52728,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983735085,"difficulty":0.0016264915}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Mark can now know that Harold's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Harold","Otis"],"index":17884,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984278679,"difficulty":0.0015721321}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. Jill's card is shown to Jennifer. David's card is shown to Lona. Lona's card is shown to Lona. David's card is shown to Jill. Jill's card is shown to Jill. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Lona picked a red card. It is publicly announced that Jill picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] 0","hypothesis":"Jennifer can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Jennifer","Lona","Jill"],"index":62331,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997242093,"difficulty":0.0002757907}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mario does not know whether or not everyone is thirsty. It is publicly announced that Mario knows whether Mario is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Erma can now know that Mario can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Erma","Mario"],"index":28640,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997814298,"difficulty":0.0002185702}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur does not know whether Arthur's forehead is muddy. It is publicly announced that Jose's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Arthur can now know that Jose can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Arthur","Jose","Mark"],"index":6335,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985058308,"difficulty":0.0014941692}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Gail can now know whether Andrea can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrea","Gail","Johnathan"],"index":59716,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99964571,"difficulty":0.00035429}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jacquelyn can now know that James can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Jacquelyn"],"index":11092,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997326732,"difficulty":0.0002673268}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Twila's card is shown to Twila. Rebecca's card is shown to Edward. Twila's card is shown to Edward. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Twila can now know that Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rebecca","Twila","Edward"],"index":5830,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998277545,"difficulty":0.001722455}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Ruth knows whether Bessie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Bessie can now know that Ruth can know whether Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Guy","Bessie"],"index":24481,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994429946,"difficulty":0.0005570054}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether Frank can know whether Nathaniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Nathaniel","Donald","Bertha"],"index":59749,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995005131,"difficulty":0.0004994869}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy. It is publicly announced that Christina's forehead is not muddy. It is publicly announced that John knows whether Christina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"John can now know whether Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christina","John","Marie"],"index":22275,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995058775,"difficulty":0.0004941225}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Manuel can now know that Leora's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Manuel","Merle","Gustavo","Leora"],"index":57437,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9556542635,"difficulty":0.0443457365}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether Abraham is thirsty. It is publicly announced that Steven does not know whether or not everyone is thirsty. It is publicly announced that Ronald is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Steven can now know whether Abraham can know whether Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Abraham","Steven","Ronald"],"index":31069,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978824258,"difficulty":0.0021175742}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Margaret. Jacqueline's card is shown to Margaret. Margaret's card is shown to Clara. It is publicly announced that someone picked a red card. It is publicly announced that Clara knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Clara can now know that Margaret can know that Jacqueline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Clara","Jacqueline"],"index":21054,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977205396,"difficulty":0.0022794604}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Rhea's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"James can now know that Melissa can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","James","Melissa","Rhea"],"index":9196,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984043241,"difficulty":0.0015956759}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Nestor's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Patricia can now know whether Mary can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nestor","Mary","Patricia"],"index":65312,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9807157516,"difficulty":0.0192842484}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that William knows whether Claire's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Evangeline can now know that William can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Claire","Robert","William","Evangeline"],"index":22382,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973633885,"difficulty":0.0026366115}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delores's card is shown to Kathleen. Dana's card is shown to Kathleen. Delores's card is shown to Delores. Kathleen's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen knows whether Delores picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Dana can now know that Delores picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Delores","Dana"],"index":31,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965023994,"difficulty":0.0034976006}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norma's card is shown to Norma. Donna's card is shown to Norma. Donna's card is shown to Donna. Jeremy's card is shown to Donna. Donna's card is shown to Jeremy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeremy can now know that Donna can know that Donna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norma","Donna","Jeremy"],"index":47672,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9911007285,"difficulty":0.0088992715}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Grover does not know whether Jeanne is thirsty. It is publicly announced that Grover does not know whether Cheryl is thirsty. It is publicly announced that Jeanne does not know whether Cheryl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"William can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cheryl","William","Grover","Jeanne"],"index":47119,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997788072,"difficulty":0.0002211928}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Eugene. Eugene's card is shown to Mark. Eugene's card is shown to Debra. Mark's card is shown to Debra. Debra's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Debra can now know whether Eugene can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","Mark","Debra"],"index":30151,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997698665,"difficulty":0.0002301335}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edna's card is shown to Edna. Edna's card is shown to Marisa. Marisa's card is shown to Marisa. Marisa's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Ralph knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Marisa can now know whether Ralph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edna","Marisa","Ralph"],"index":36946,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9095412493,"difficulty":0.0904587507}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Peter. Margaret's card is shown to Peter. Peter's card is shown to Margaret. Margaret's card is shown to Margaret. Joshua's card is shown to Margaret. Margaret's card is shown to Joshua. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Margaret picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Thomas can now know that Peter can know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Peter","Margaret","Joshua"],"index":62483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9283671975,"difficulty":0.0716328025}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Mary can now know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edward","Patricia","Mary"],"index":40735,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995840192,"difficulty":0.0004159808}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Don is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Fredrick can now know that Betty can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Don","Eneida","Fredrick"],"index":325,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984076619,"difficulty":0.0015923381}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ryan does not know whether Jose is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ryan can now know that Jose can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jose","Ryan"],"index":53861,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998378396,"difficulty":0.001621604}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric is thirsty. It is publicly announced that Eric knows whether Eric is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Eric can now know whether Frank can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Frank","Eric"],"index":61019,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997823834,"difficulty":0.0002176166}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mamie is thirsty. It is publicly announced that Edward does not know whether or not everyone is thirsty. It is publicly announced that Mamie does not know whether Lynda is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Edward can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edward","Mamie","Lynda"],"index":60598,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982913136,"difficulty":0.0017086864}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jimmy can now know whether Jimmy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jimmy","Ray","Sandra","Reina"],"index":16495,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9967304468,"difficulty":0.0032695532}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lakita does not know whether or not everyone's forehead is muddy. It is publicly announced that Maxie knows whether someone's forehead is muddy. It is publicly announced that Lakita does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Linda can now know whether Christy can know that Lakita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Lakita","Maxie","Christy"],"index":8431,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.992926538,"difficulty":0.007073462}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earl knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Paul can now know that Gilda can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Earl","Paul","Gilda"],"index":3540,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969003201,"difficulty":0.0030996799}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peggy knows whether Peggy is thirsty. It is publicly announced that Felicia does not know whether Peggy is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that William does not know whether Melissa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Melissa can now know that Melissa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peggy","William","Melissa","Felicia"],"index":12998,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.980327785,"difficulty":0.019672215}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mildred does not know whether Alice is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Alice can now know that Melissa can know whether Benjamin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Benjamin","Mildred","Alice","Melissa"],"index":2019,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982178807,"difficulty":0.0017821193}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Florence can now know that Kristin can know that Frank's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Frank","Florence","Kristin"],"index":29745,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9388269186,"difficulty":0.0611730814}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa's forehead is muddy. It is publicly announced that John knows whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Jimmy can now know that Melissa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jimmy","Gloria","Melissa","John"],"index":42693,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983918071,"difficulty":0.0016081929}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wynona's card is shown to Carol. Jeanna's card is shown to Wynona. Jeanna's card is shown to Andrew. Jeanna's card is shown to Jeanna. It is publicly announced that someone picked a red card. It is publicly announced that Andrew does not know whether Wynona picked a red card. It is publicly announced that Carol knows whether Wynona picked a red card. It is publicly announced that Jeanna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Carol can now know that Wynona can know whether Wynona picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Wynona","Andrew","Jeanna"],"index":34426,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7537146211,"difficulty":1.7537146211}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Jackie is thirsty. It is publicly announced that Richard does not know whether Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jennifer can now know that Jackie can know whether Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Richard","Jackie","Andrew"],"index":59584,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9952998161,"difficulty":0.0047001839}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Roberta. Jennifer's card is shown to Jennifer. Kelly's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Jennifer does not know whether Roberta picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kelly can now know whether Jennifer can know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roberta","Jennifer","Kelly"],"index":39473,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9969283938,"difficulty":0.0030716062}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracy's card is shown to Andrew. Ernestina's card is shown to Antoinette. Antoinette's card is shown to Tracy. Andrew's card is shown to Ernestina. It is publicly announced that someone picked a red card. It is publicly announced that Ernestina does not know whether or not everyone picked a red card. It is publicly announced that Antoinette picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Tracy can now know that Antoinette can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrew","Antoinette","Tracy","Ernestina"],"index":5070,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981979728,"difficulty":0.0018020272}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph is thirsty. It is publicly announced that Randall is not thirsty. It is publicly announced that Julie does not know whether Lynda is thirsty. It is publicly announced that Joseph does not know whether Julie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Joseph can now know that Randall can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Julie","Lynda","Randall"],"index":48452,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984478951,"difficulty":0.0015521049}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lori does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Howard can now know that Richard can know that Howard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Howard","Charles","Richard","Lori"],"index":5753,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980723858,"difficulty":0.0019276142}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corrie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Corrie can now know that Kevin can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Corrie","Thomas","Kevin"],"index":7394,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7476128936,"difficulty":1.7476128936}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew is not thirsty. It is publicly announced that Matthew does not know whether Alice is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Mary can now know that Matthew can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alice","Mary","Matthew"],"index":47186,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9866617322,"difficulty":0.0133382678}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bryan does not know whether Richard is thirsty. It is publicly announced that Kimberly does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kimberly can now know whether Roger is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bryan","Roger","Kimberly","Richard"],"index":13694,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8937392235,"difficulty":0.1062607765}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Charles can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Cherly","Jeffrey"],"index":53133,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Danielle can now know whether Kenneth can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Retha","Danielle","Kenneth"],"index":5523,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996619225,"difficulty":0.0003380775}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois knows whether Lyman's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Gertrude can now know whether Ramona can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lois","Lyman","Ramona","Gertrude"],"index":58340,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997592568,"difficulty":0.0002407432}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Arlene. Michael's card is shown to Arlene. Arlene's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a black card. It is publicly announced that Arlene knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Arlene can now know that Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Arlene","Michael"],"index":48719,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5221546888,"difficulty":1.5221546888}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether Rebecca's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Archie can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebecca","Heather","Archie","Rose"],"index":43705,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983035326,"difficulty":0.0016964674}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katie does not know whether Joyce is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Katie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katie","Joyce","Raymond"],"index":42523,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985948205,"difficulty":0.0014051795}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Robert can now know whether Leanna can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Robert","Leanna","Murray"],"index":62516,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996275902,"difficulty":0.0003724098}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Forrest can now know whether Paul can know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Forrest","Stephanie","Richard"],"index":33816,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996756315,"difficulty":0.0003243685}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Laura can now know whether Christopher can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laura","Christopher","Robert"],"index":32297,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bart knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Bart can now know whether Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brian","Pinkie","Bart","Judy"],"index":16303,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997197986,"difficulty":0.0002802014}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Manuel. Manuel's card is shown to Kathleen. Kathleen's card is shown to Kathleen. Richard's card is shown to Kathleen. Kathleen's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Manuel does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know whether Kathleen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Manuel","Kathleen","Richard"],"index":66743,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994226694,"difficulty":0.0005773306}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Kathleen's card is shown to Bryan. Bryan's card is shown to Bryan. Kathleen's card is shown to Sherry. Bryan's card is shown to Sherry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bryan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathleen","Bryan","Sherry"],"index":43015,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997753501,"difficulty":0.0002246499}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan does not know whether Tracy is thirsty. It is publicly announced that Susan does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brenna can now know that Tracy can know that Susan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Tracy","Brenna"],"index":60077,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6330751181,"difficulty":1.6330751181}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deanna's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Deanna can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eric","Deanna"],"index":29823,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983817339,"difficulty":0.0016182661}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Esther is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Lewis can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Edward","Esther","Lewis"],"index":66433,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983950257,"difficulty":0.0016049743}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Daisy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know that Daisy can know that Daisy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Daisy","Bruce"],"index":22150,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976473451,"difficulty":0.0023526549}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether Mary's forehead is muddy. It is publicly announced that Howard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Gerald can now know that Howard can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Gerald","Howard"],"index":33644,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Marjorie is thirsty. It is publicly announced that Helen does not know whether Marjorie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Marjorie can now know that Joseph can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Helen","Marjorie"],"index":52024,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997840524,"difficulty":0.0002159476}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee does not know whether Lee's forehead is muddy. It is publicly announced that Yvonne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Lee can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lee","Linda","Kathleen","Yvonne"],"index":23127,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997742772,"difficulty":0.0002257228}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha does not know whether Martha's forehead is muddy. It is publicly announced that Martha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Elisha can now know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harold","Elisha","Martha"],"index":2385,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9524665475,"difficulty":1.9524665475}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Kathleen is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Alphonso can now know whether Alphonso is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kathleen","Alphonso"],"index":12620,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989064932,"difficulty":0.0010935068}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Richard. Elaine's card is shown to David. David's card is shown to Elaine. It is publicly announced that someone picked a red card. It is publicly announced that Rachel does not know whether Richard picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card. It is publicly announced that Rachel knows whether someone picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rachel can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","David","Rachel","Elaine"],"index":26086,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985995889,"difficulty":0.0014004111}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laurel does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Laurel can now know that Robert can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Laurel","Robert","Louis"],"index":20098,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983516932,"difficulty":0.0016483068}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Martha can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Martha","Stephen"],"index":46251,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998462677,"difficulty":0.001537323}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tom does not know whether Brian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Tom can now know that Jeffrey can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Eric","Brian","Tom"],"index":12087,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983261228,"difficulty":0.0016738772}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Stella can now know whether Van's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Van","Walter","Stella","Crystal"],"index":56874,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997505546,"difficulty":0.0002494454}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pearl does not know whether Pearl's forehead is muddy. It is publicly announced that Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Lisa can now know whether Pearl can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lisa","Pearl"],"index":37833,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5086480379,"difficulty":0.4913519621}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Matthew's forehead is muddy. It is publicly announced that Ruby knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Nancy can now know that Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruby","Leonardo","Nancy","Matthew"],"index":355,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8640886545,"difficulty":0.1359113455}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether Naomi's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Deborah can now know that Naomi can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Deborah","Naomi","Ralph"],"index":37223,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984192848,"difficulty":0.0015807152}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth does not know whether Roscoe is thirsty. It is publicly announced that Carol does not know whether Kenneth is thirsty. It is publicly announced that Roscoe does not know whether or not everyone is thirsty. It is publicly announced that Ashley does not know whether Kenneth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Kenneth can now know whether Carol can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Carol","Ashley","Roscoe"],"index":60507,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993150234,"difficulty":0.0006849766}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Bryan. Dennis's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Dennis does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Bryan can now know whether Bryan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bryan","Dennis"],"index":36473,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8801625371,"difficulty":1.8801625371}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joe knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Frances can now know whether Debbie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joe","Frances","Debbie"],"index":64476,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997553229,"difficulty":0.0002446771}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfred knows whether Leah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Louise can now know that Leah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leah","Louise","Alfred"],"index":56674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979072809,"difficulty":0.0020927191}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Margaret can now know that Robert can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Margaret","Robert"],"index":44824,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996168613,"difficulty":0.0003831387}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin knows whether Justin's forehead is muddy. It is publicly announced that Gary knows whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Justin can now know whether Gary can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joyce","Justin","Gary"],"index":57079,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999550879,"difficulty":0.000449121}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ramiro does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Ramiro can now know that William can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jared","William","Elmer","Ramiro"],"index":45764,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983573556,"difficulty":0.0016426444}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Vicky can know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vicky","Russell","Patricia"],"index":8000,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997407794,"difficulty":0.0002592206}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kenneth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Kenneth","Wilma"],"index":15613,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983250499,"difficulty":0.0016749501}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know that Amos can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Derrick","Paula","Amos"],"index":49591,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983624816,"difficulty":0.0016375184}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Danielle. Shayne's card is shown to Shayne. It is publicly announced that someone picked a red card. It is publicly announced that Danielle knows whether or not everyone picked a red card. It is publicly announced that Danielle picked a black card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Danielle can now know that April can know that Shayne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Danielle","April","Shayne"],"index":24302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.68873173,"difficulty":0.31126827}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Socorro's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilyn knows whether Gloria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Socorro can now know that Gloria can know that Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Socorro","Marilyn"],"index":22712,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9880820513,"difficulty":0.0119179487}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dean can now know whether Carrie can know whether Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Dean","Ronnie","Carrie"],"index":64913,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997219443,"difficulty":0.0002780557}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether Nancy's forehead is muddy. It is publicly announced that Nancy knows whether Wanda's forehead is muddy. It is publicly announced that Dana's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Wanda can now know whether Dana can know whether Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wanda","Nancy","Dana"],"index":25148,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997219443,"difficulty":0.0002780557}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy. It is publicly announced that Billye knows whether Billye's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dayna can now know that Mary can know whether Billye's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dayna","Billye","Mary","Dave"],"index":52924,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997410178,"difficulty":0.0002589822}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether or not nobody's forehead is muddy. It is publicly announced that Mildred knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Kathleen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elsa","Mildred","Kathleen"],"index":60988,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985473752,"difficulty":0.0014526248}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Fay is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Fay can now know whether Frances can know that Frances is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frances","Fay","Lawrence","Michael"],"index":61191,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6137751937,"difficulty":0.3862248063}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chrissy's card is shown to Julio. Julio's card is shown to Lynn. Chrissy's card is shown to Lynn. It is publicly announced that someone picked a red card. It is publicly announced that Julio does not know whether or not everyone picked a red card. It is publicly announced that Julio does not know whether Julio picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Julio can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julio","Lynn","Chrissy"],"index":25313,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8395824432,"difficulty":1.8395824432}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Gladys can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Raymond","Gladys"],"index":22144,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983392954,"difficulty":0.0016607046}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlotte knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Randall can now know that Charlotte can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charlotte","Cathy","Randall"],"index":36357,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978852868,"difficulty":0.0021147132}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adele's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Diane can now know whether Johnny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Johnny","Diane","Adele","John"],"index":28964,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997408986,"difficulty":0.0002591014}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Patricia can now know that William can know whether Lawrence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Lawrence","Patricia"],"index":24570,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997237325,"difficulty":0.0002762675}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacob knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jacob can now know that Maria can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Jacob","Beatrice"],"index":1731,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984228611,"difficulty":0.0015771389}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmon's card is shown to Jacob. James's card is shown to Jacob. James's card is shown to Carmon. Jacob's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Jacob does not know whether Jacob picked a red card. It is publicly announced that Carmon does not know whether or not everyone picked a red card. It is publicly announced that James picked a red card. It is publicly announced that Carmon does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jacob can now know that James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jacob","Carmon","James"],"index":19044,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972831011,"difficulty":0.0027168989}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allen's card is shown to Allen. Walter's card is shown to Allen. Walter's card is shown to Walter. Tim's card is shown to Tim. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Allen can now know that Walter can know that Walter picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Allen","Walter","Tim"],"index":33334,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953599572,"difficulty":0.0046400428}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kara does not know whether Alan is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bertha","Kara","David","Alan"],"index":24504,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979681373,"difficulty":0.0020318627}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mindy knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Dorothy can now know that Thomas can know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mindy","Thomas","Dorothy","Jayne"],"index":57592,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972631931,"difficulty":0.0027368069}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cara does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Cara can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cara","Willie","Rex"],"index":62348,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958578944,"difficulty":0.0041421056}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Thomas can now know that Steven can know whether Jacob is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Steven","Jacob","Lester"],"index":63624,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9834311604,"difficulty":0.0165688396}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"John can now know whether Peter can know that Allen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","John","Peter","Allen"],"index":41211,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996775389,"difficulty":0.0003224611}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether Walter's forehead is muddy. It is publicly announced that Lewis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Lewis can now know that Walter can know that Walter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Cynthia","Lewis","Peter"],"index":44435,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.879193902,"difficulty":0.120806098}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chad does not know whether or not everyone is thirsty. It is publicly announced that Chad does not know whether Hallie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Hallie can now know whether Chad can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chad","Hallie","John"],"index":26891,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9391005039,"difficulty":0.0608994961}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Charlotte can now know that Sandra can know that Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlotte","Christopher","Brian","Sandra"],"index":60346,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976050854,"difficulty":0.0023949146}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Michelle knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Michelle can now know that Mary can know whether Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michelle","Mary"],"index":32246,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994916916,"difficulty":0.0005083084}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy. It is publicly announced that Juan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Rodney can now know that Juan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Juan","Howard","Rodney","John"],"index":9816,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7678923607,"difficulty":0.2321076393}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether or not everyone is thirsty. It is publicly announced that Ann does not know whether Laura is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Margaret can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Derek","Laura","Margaret","Ann"],"index":63575,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983187914,"difficulty":0.0016812086}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Camille knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Camille can now know whether Constance can know that Constance is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Constance","Camille","Laura"],"index":31562,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9373014569,"difficulty":0.0626985431}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Clarence can now know whether Christina can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christina","Clarence"],"index":3687,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9769222736,"difficulty":0.0230777264}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Kathy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathy","Allen","Dianne"],"index":4365,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981332421,"difficulty":0.0018667579}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Steven can now know that Miguel can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Miguel","Giuseppina","Steven"],"index":25085,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999778688,"difficulty":0.000221312}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melvin does not know whether Melvin's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Melvin can now know whether Salvador can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melvin","James","Salvador"],"index":53132,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9959812164,"difficulty":1.9959812164}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maynard knows whether Dianne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Maynard can now know whether Dianne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kelvin","Maynard","Dianne","Edwardo"],"index":20931,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995393753,"difficulty":0.0004606247}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cliff's card is shown to Mindy. Ricardo's card is shown to Ricardo. Mindy's card is shown to Judith. Cliff's card is shown to Judith. Mindy's card is shown to Cliff. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ricardo can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mindy","Ricardo","Judith","Cliff"],"index":24380,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997242093,"difficulty":0.0002757907}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Leo. Angelica's card is shown to Leo. Leo's card is shown to Ruth. Angelica's card is shown to Ruth. Leo's card is shown to Angelica. Angelica's card is shown to Angelica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leo","John","Ruth","Angelica"],"index":19910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997265935,"difficulty":0.0002734065}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandy knows whether Louise's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Sandy can now know whether Willie can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Louise","Genia","Sandy"],"index":23147,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999746263,"difficulty":0.000253737}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly does not know whether Kenneth is thirsty. It is publicly announced that Clyde does not know whether Kenneth is thirsty. It is publicly announced that Kenneth does not know whether Kelly is thirsty. It is publicly announced that Kelly is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Clyde can now know that Kenneth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clyde","Kenneth","Kelly"],"index":9193,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5883194208,"difficulty":0.4116805792}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Leeann can now know that Leeann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edmond","William","Sarah","Leeann"],"index":13255,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980552197,"difficulty":0.0019447803}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hubert does not know whether Hubert's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Brandon knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Brandon","Ranee","Hubert"],"index":20668,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7617814541,"difficulty":0.2382185459}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Karen. Karen's card is shown to Amy. Douglas's card is shown to Amy. Karen's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Douglas picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Amy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Amy","Douglas"],"index":34144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997233748,"difficulty":0.0002766252}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Scott can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Opal","Scott","Shawn"],"index":46141,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995715022,"difficulty":0.0004284978}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Carl can know whether Glenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","William","Glenda","Janice"],"index":56649,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997426867,"difficulty":0.0002573133}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Eugene can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alfred","Eugene"],"index":39517,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99817276,"difficulty":0.00182724}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mary can now know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gregory","Robert","Billy","Mary"],"index":23616,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993212223,"difficulty":0.0006787777}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacey's card is shown to Stacey. Stacey's card is shown to Adrianne. It is publicly announced that someone picked a red card. It is publicly announced that Stacey does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Stacey can now know that Adrianne can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stacey","Adrianne","Beverly"],"index":65662,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997072816,"difficulty":0.0002927184}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kay's card is shown to Susan. Susan's card is shown to Kay. It is publicly announced that someone picked a red card. It is publicly announced that Kay does not know whether or not everyone picked a red card. It is publicly announced that Kay knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Kay can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Susan","Kay"],"index":13961,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9927099943,"difficulty":0.0072900057}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julio knows whether Julio's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know that John can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julio","Robert","Oma","John"],"index":9111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997550845,"difficulty":0.0002449155}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Miranda's card is shown to Miranda. Ivette's card is shown to Ivette. Leanna's card is shown to Anne. Ivette's card is shown to Leanna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leanna can now know whether Anne can know that Leanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Miranda","Ivette","Anne","Leanna"],"index":25976,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7447493076,"difficulty":1.7447493076}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elmer's card is shown to Elmer. Eugene's card is shown to Callie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elmer can now know that Elmer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elmer","Callie","Clayton","Eugene"],"index":186,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954413176,"difficulty":0.0045586824}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dia does not know whether Randolph is thirsty. It is publicly announced that Randolph does not know whether Dia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Dia can now know that Randolph can know whether Christine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Dia","Randolph","Reginald"],"index":43499,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9873560071,"difficulty":0.0126439929}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alice does not know whether Gloria is thirsty. It is publicly announced that Sara does not know whether Alice is thirsty. It is publicly announced that Sara knows whether or not nobody is thirsty. It is publicly announced that Gloria does not know whether Melvin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Gloria can now know that Gloria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gloria","Sara","Melvin","Alice"],"index":7289,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9265239835,"difficulty":0.0734760165}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sean does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Maryann can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maryann","James","Sean"],"index":26489,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6645216942,"difficulty":0.3354783058}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hannah does not know whether Mark is thirsty. It is publicly announced that Jose does not know whether Hannah is thirsty. It is publicly announced that Mark does not know whether Jose is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jose can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doretha","Jose","Mark","Hannah"],"index":67632,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984525442,"difficulty":0.0015474558}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Manuel can now know that Roy can know whether Manuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tyler","Manuel","Roy","Darryl"],"index":60084,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997435212,"difficulty":0.0002564788}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacob's forehead is muddy. It is publicly announced that Jacob's forehead is muddy. It is publicly announced that Brian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Paul can now know that Jenette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Jenette","Brian","Jacob"],"index":51700,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.6532212496,"difficulty":0.3467787504}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole does not know whether Nicole's forehead is muddy. It is publicly announced that Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Gerald can now know that Nicole can know whether Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nicole","Gerald"],"index":44018,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989923835,"difficulty":0.0010076165}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy knows whether Wendy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Diane can now know that Rafael can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rafael","Diane","Wendy"],"index":23894,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9883232713,"difficulty":1.9883232713}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Georgia knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Georgia can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leonor","Corey","Georgia"],"index":8761,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8693796992,"difficulty":0.1306203008}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is not muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad does not know whether Chad's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jennifer can now know that Chad can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Chad","Jennifer","Barbara"],"index":5645,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978458881,"difficulty":0.0021541119}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal does not know whether Crystal's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Eric can now know that Crystal can know that Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eric","Crystal"],"index":12770,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9952735305,"difficulty":0.0047264695}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clarice is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Michael can now know that Caroline can know whether Caroline is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clarice","Caroline","Michael"],"index":213,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998693645,"difficulty":0.001306355}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deanna's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Wade can now know whether Deanna can know that Deanna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Wade","Deanna"],"index":24954,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997048974,"difficulty":0.0002951026}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elaine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Richard can now know that Brian can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Qiana","Elaine","Richard"],"index":14031,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984822869,"difficulty":0.0015177131}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Shirley can now know whether Doris is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Natasha","William","Shirley","Doris"],"index":10375,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8730056882,"difficulty":0.1269943118}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angie's card is shown to Angie. Angie's card is shown to Debra. Debra's card is shown to Debra. Debra's card is shown to Leon. It is publicly announced that someone picked a red card. It is publicly announced that Leon does not know whether Angie picked a red card. It is publicly announced that Angie does not know whether Leon picked a red card. It is publicly announced that Leon knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Debra can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angie","Debra","Leon"],"index":64284,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986096621,"difficulty":0.0013903379}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"James can now know whether Shirley can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Benita","James"],"index":23249,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Scott. Jack's card is shown to Scott. Scott's card is shown to Alice. Alice's card is shown to Alice. Jack's card is shown to Alice. Alice's card is shown to Peter. Jack's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Peter knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alice can now know that Scott can know that Jack picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Alice","Peter","Jack"],"index":37485,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969929457,"difficulty":0.0030070543}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Carolyn. Jean's card is shown to Catherine. Catherine's card is shown to Paris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jean can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jean","Carolyn","Catherine","Paris"],"index":8156,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997211099,"difficulty":0.0002788901}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Jose can now know that Socorro is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christine","Jose","Socorro","Donald"],"index":51155,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9218337536,"difficulty":0.0781662464}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rita's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know whether Jose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rita","David","Jose","Thelma"],"index":64055,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9744819999,"difficulty":0.0255180001}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Justin can now know whether Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Elizabeth","Debra","Brian"],"index":21802,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978316426,"difficulty":0.0021683574}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Elizabeth can now know that Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Jean","Ryan","Elizabeth"],"index":30056,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9941523671,"difficulty":0.0058476329}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know that Jan can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Nicholas","Jan"],"index":62055,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984208345,"difficulty":0.0015791655}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Philip does not know whether Leah is thirsty. It is publicly announced that David does not know whether Philip is thirsty. It is publicly announced that David knows whether or not nobody is thirsty. It is publicly announced that Leah does not know whether Annette is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] (Agentd knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Philip can now know whether David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leah","David","Annette","Philip"],"index":64495,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9890117645,"difficulty":0.0109882355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danny knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lauren can now know whether Diane can know whether Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danny","Diane","Lauren","Carol"],"index":28800,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994572997,"difficulty":0.0005427003}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lamar knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Lamar can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lamar","Karen","Lillian","Ladonna"],"index":39601,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9953581691,"difficulty":0.0046418309}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jim knows whether Jim is thirsty. It is publicly announced that Jerrod does not know whether Lance is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Lance can now know whether Lance is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jim","Jerrod","Lance"],"index":43553,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997710824,"difficulty":0.002289176}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Arnulfo can know whether Jeff's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Rosalinda","Arnulfo","Jeff"],"index":35784,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997319579,"difficulty":0.0002680421}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dawn does not know whether Robert is thirsty. It is publicly announced that Robert is not thirsty. It is publicly announced that Dawn is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] Agentc knows that (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] 0","hypothesis":"Marcia can now know that Dawn can know that Morgan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Dawn","Marcia","Morgan"],"index":37934,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9368158579,"difficulty":0.0631841421}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margarette's card is shown to John. Margarette's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Margarette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Margarette","James"],"index":11879,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982913136,"difficulty":0.0017086864}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Alice. Alice's card is shown to Lindsy. William's card is shown to Lindsy. Lindsy's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether or not everyone picked a red card. It is publicly announced that William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Lindsy can now know whether Alice can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Donald","Lindsy","William"],"index":52060,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984017015,"difficulty":0.0015982985}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Paul knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Robert can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Timothy","Paul","Robert"],"index":19340,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Wilma can now know that Brian can know that Milton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Milton","Shane","Wilma","Brian"],"index":30861,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9623618722,"difficulty":0.0376381278}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to James. James's card is shown to Victoria. Victoria's card is shown to Victoria. It is publicly announced that someone picked a red card. It is publicly announced that Victoria picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"James can now know that Victoria can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Victoria"],"index":67388,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973976612,"difficulty":0.0026023388}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donnell knows whether Stanley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Neil can now know that Donnell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Neil","Stanley","Jennifer","Donnell"],"index":34706,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983295798,"difficulty":0.0016704202}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amber knows whether Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"George can now know that Jessica's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessica","George","Amber"],"index":45236,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997616291,"difficulty":0.002383709}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anna does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Anna can now know that Catherine can know that Anna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anna","David","George","Catherine"],"index":22506,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955925345,"difficulty":0.0044074655}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Rita's card is shown to Thomas. Rita's card is shown to Rita. Gina's card is shown to Gina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Gina can know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Rita","Gina"],"index":58516,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959563613,"difficulty":0.0040436387}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Joshua can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Joshua","Amanda","Joseph"],"index":52836,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983361363,"difficulty":0.0016638637}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cecil's card is shown to Nellie. Troy's card is shown to Troy. Tracey's card is shown to Troy. Tracey's card is shown to Cecil. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tracey can now know whether Nellie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nellie","Troy","Tracey","Cecil"],"index":5893,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997116923,"difficulty":0.0002883077}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terri does not know whether or not everyone's forehead is muddy. It is publicly announced that Terri does not know whether Terri's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Terri","Richard"],"index":54544,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976581335,"difficulty":0.0023418665}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl knows whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sharon can now know that Edna can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carl","Sharon","Edna"],"index":13178,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984684587,"difficulty":0.0015315413}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether someone's forehead is muddy. It is publicly announced that Lisa does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know whether Leonardo can know that Leonardo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Leonardo","Ashley"],"index":44597,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.787134707,"difficulty":0.212865293}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Claudine's card is shown to Elizabeth. Claudine's card is shown to Helen. Paul's card is shown to Helen. Helen's card is shown to Claudine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Helen","Claudine","Paul"],"index":50878,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983533621,"difficulty":0.0016466379}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Virginia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] 0","hypothesis":"Virginia can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gabriela","Virginia","John","Robert"],"index":8792,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Todd does not know whether Elmer is thirsty. It is publicly announced that Todd does not know whether David is thirsty. It is publicly announced that David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] Agentd knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] 0","hypothesis":"David can now know that Todd can know that Todd is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joline","Elmer","Todd","David"],"index":8009,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9750401974,"difficulty":1.9750401974}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Clarence. Clarence's card is shown to Joanne. It is publicly announced that someone picked a red card. It is publicly announced that Joanne picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Clarence can now know whether Joanne can know whether Clarence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Clarence","Joanne"],"index":32659,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9974395037,"difficulty":0.0025604963}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jannie does not know whether Brandon is thirsty. It is publicly announced that Carrie is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Carrie can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jannie","Carrie","Brandon"],"index":46489,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9678586721,"difficulty":1.9678586721}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doyle does not know whether Maria is thirsty. It is publicly announced that Rosemary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] 0","hypothesis":"Chase can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maria","Rosemary","Chase","Doyle"],"index":8762,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997822642,"difficulty":0.0002177358}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether Tommy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Bryan can now know whether Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shannon","Tommy","Bryan"],"index":22826,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9919386506,"difficulty":0.0080613494}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether Cyril is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Sarah does not know whether Frances is thirsty. It is publicly announced that Frances does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Daniel can now know whether Cyril can know that Sarah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Cyril","Frances","Sarah"],"index":66835,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9885838032,"difficulty":0.0114161968}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joy knows whether Earl's forehead is muddy. It is publicly announced that Mitchell knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Mitchell can now know that Joy can know whether Mitchell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mitchell","Earl","Joy"],"index":1645,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997373223,"difficulty":0.0002626777}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Dennis can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Thomas","Beulah"],"index":47314,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967125654,"difficulty":0.0032874346}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Max can now know whether William can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Charles","Max"],"index":39081,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether Basil's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Raymond can now know that Jena's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jena","Basil","Karin","Raymond"],"index":47473,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983125925,"difficulty":0.0016874075}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Kara. Kara's card is shown to Mary. Mary's card is shown to Ana. It is publicly announced that someone picked a red card. It is publicly announced that Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Inez can now know that Ana picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kara","Mary","Inez","Ana"],"index":62414,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8955286741,"difficulty":0.1044713259}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Marcie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Megan","Oneida","Marcie"],"index":35881,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Claire can now know whether Claire's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","David","Claire","Stacy"],"index":64417,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.982308805,"difficulty":0.017691195}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julio's card is shown to Tara. Tara's card is shown to Glenn. Julio's card is shown to Glenn. Tara's card is shown to Marshall. Tara's card is shown to Julio. Glenn's card is shown to Julio. It is publicly announced that someone picked a red card. It is publicly announced that Glenn picked a black card. It is publicly announced that Julio does not know whether Julio picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentd knows whether 4) ] Agentc knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Marshall can now know whether Glenn can know that Glenn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tara","Glenn","Marshall","Julio"],"index":33922,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9736390114,"difficulty":0.0263609886}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Mary's card is shown to Mary. David's card is shown to Mary. Mary's card is shown to David. Mary's card is shown to Nina. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Mary picked a red card. It is publicly announced that Mary picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Mary","David","Nina"],"index":22688,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8214262724,"difficulty":1.8214262724}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tanya knows whether Tanya's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joseph can now know that Tanya's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Tanya"],"index":1687,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9974421263,"difficulty":1.9974421263}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronnie's card is shown to Roger. Sylvia's card is shown to Roger. Ronnie's card is shown to Cecile. Cecile's card is shown to Cecile. Cecile's card is shown to Sylvia. Sylvia's card is shown to Sylvia. It is publicly announced that someone picked a red card. It is publicly announced that Ronnie does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Cecile can now know that Cecile picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roger","Ronnie","Cecile","Sylvia"],"index":63413,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9860617518,"difficulty":0.0139382482}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Moises's card is shown to Moises. Sylvia's card is shown to Jason. Sylvia's card is shown to James. Moises's card is shown to Sylvia. Sylvia's card is shown to Sylvia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Moises","Jason","James","Sylvia"],"index":55941,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9001586437,"difficulty":0.0998413563}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfred knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nora can now know that Donald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nora","Donald","Martin","Alfred"],"index":63866,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980505705,"difficulty":0.0019494295}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Gwen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Paul can now know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Paul","Gwen"],"index":62787,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9983566403,"difficulty":0.0016433597}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cynthia knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Patrick can now know whether Louis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Louis","Patrick","Criselda","Cynthia"],"index":65057,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976460338,"difficulty":0.0023539662}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffry does not know whether Richard is thirsty. It is publicly announced that Francie knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jeffry can now know whether Francie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffry","Francie","Richard"],"index":36327,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9940021634,"difficulty":0.0059978366}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris's forehead is not muddy. It is publicly announced that Donna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Chris can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Donna","Chris"],"index":32294,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984568357,"difficulty":0.0015431643}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Damon does not know whether Damon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Damon can now know whether Alan can know that Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Damon","Terry","Alan"],"index":51213,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9676679373,"difficulty":0.0323320627}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raul's card is shown to Joseph. Joseph's card is shown to Raul. Raul's card is shown to Raul. Michael's card is shown to Raul. Raul's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Raul can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Raul","Christopher","Michael"],"index":17747,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973842502,"difficulty":0.0026157498}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adrienne's card is shown to Adrienne. Helen's card is shown to Adrienne. Helen's card is shown to Helen. Albert's card is shown to Helen. Albert's card is shown to Albert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Adrienne can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adrienne","Helen","Albert"],"index":5008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983853102,"difficulty":0.0016146898}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Esther's card is shown to Nina. Nina's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Esther picked a black card. It is publicly announced that Nina knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Esther can now know that Nina can know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Esther","Nina","Jennifer"],"index":6885,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5879947543,"difficulty":1.5879947543}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Ramon's forehead is muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Seth can now know that Ramon can know that Ramon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Seth","Thomas","Ramon"],"index":51265,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7795459032,"difficulty":0.2204540968}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elsie knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Pamela can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frank","Elsie","Pamela"],"index":5412,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971795082,"difficulty":0.0028204918}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Robert can now know that Romeo can know that Romeo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Romeo","Robert","Crystal","Brittny"],"index":42944,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985331297,"difficulty":0.0014668703}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether or not nobody's forehead is muddy. It is publicly announced that Kortney's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Marcella can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marcella","Connie","Gary","Kortney"],"index":28228,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997830987,"difficulty":0.0002169013}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tracey can now know whether Regina can know whether Louis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracey","Adam","Louis","Regina"],"index":25416,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997290969,"difficulty":0.0002709031}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether Lucas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Lucas can now know whether Genaro can know that Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Genaro","Carol","Lucas"],"index":15462,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9784497619,"difficulty":0.0215502381}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy does not know whether or not everyone is thirsty. It is publicly announced that Richard knows whether Amy is thirsty. It is publicly announced that Stephanie does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Richard can now know whether Stephanie can know whether Amy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Amy","Stephanie"],"index":17714,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986530542,"difficulty":0.0013469458}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Morgan does not know whether Morgan's forehead is muddy. It is publicly announced that Dennis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Morgan can now know that Dennis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lori","Morgan","Kevin","Dennis"],"index":17322,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944840074,"difficulty":0.0055159926}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evangeline's card is shown to Joanne. John's card is shown to John. Joanne's card is shown to Joel. Joanne's card is shown to Evangeline. John's card is shown to Evangeline. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joanne can now know that Joel can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joanne","John","Joel","Evangeline"],"index":31346,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984586239,"difficulty":0.0015413761}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mary can now know that Therese can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Mary","Therese"],"index":55730,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997146666,"difficulty":0.002853334}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah is thirsty. It is publicly announced that Shawn does not know whether or not everyone is thirsty. It is publicly announced that Shawn does not know whether Joel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Deborah can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ivette","Joel","Deborah","Shawn"],"index":362,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999773562,"difficulty":0.000226438}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lela's forehead is muddy. It is publicly announced that Lela's forehead is muddy. It is publicly announced that Lela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agentd knows whether (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Jamison can now know whether Henry can know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lela","Henry","Kenneth","Jamison"],"index":9632,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993442893,"difficulty":0.0006557107}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mary can now know that Ruth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ruth","Mary"],"index":26303,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984233379,"difficulty":0.0015766621}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Luvenia can now know whether Sam can know whether Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Luvenia","Sharon","Sam","Joe"],"index":47010,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997220635,"difficulty":0.0002779365}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chastity's card is shown to John. Chastity's card is shown to Chastity. Christina's card is shown to Gregory. Christina's card is shown to Christina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Chastity can now know that Chastity picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Chastity","Gregory","Christina"],"index":40150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973632693,"difficulty":0.0026367307}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmen's card is shown to Georgia. Kristine's card is shown to Georgia. Carmen's card is shown to Kristine. Dennis's card is shown to Kristine. Kristine's card is shown to Dennis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristine can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Georgia","Carmen","Kristine","Dennis"],"index":23348,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999776423,"difficulty":0.000223577}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Charles can know whether Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Bernice","Charles"],"index":15973,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975132942,"difficulty":0.0024867058}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether or not everyone's forehead is muddy. It is publicly announced that Gerald does not know whether Gerald's forehead is muddy. It is publicly announced that Kathleen knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kathleen can now know whether Jose can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gerald","Jose","Kathleen"],"index":52871,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Brett's card is shown to Michael. Pete's card is shown to Michael. Brett's card is shown to Brett. Pete's card is shown to Pete. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pete can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Brett","Pete"],"index":29163,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917884469,"difficulty":0.0082115531}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa knows whether someone's forehead is muddy. It is publicly announced that Rosa knows whether Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Susan can now know whether Alicia can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alicia","Alexander","Susan","Rosa"],"index":62364,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995360374,"difficulty":0.0004639626}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy. It is publicly announced that Karole knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Karole can now know whether Richard can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Karole","Richard"],"index":40374,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997537732,"difficulty":0.0002462268}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alma's card is shown to Alma. Alma's card is shown to Marguerite. Marguerite's card is shown to Marguerite. Alyssa's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Alma does not know whether John picked a red card. It is publicly announced that Alyssa picked a red card. It is publicly announced that Marguerite does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Alma can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alma","Marguerite","John","Alyssa"],"index":37006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5529891849,"difficulty":0.4470108151}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anne does not know whether Scott is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Catherine can now know whether Anne can know whether Anne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anne","Scott","Catherine"],"index":25122,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987753034,"difficulty":0.0012246966}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Kevin can now know that Debra can know whether Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Kevin","Thomas","Mark"],"index":62808,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997387528,"difficulty":0.0002612472}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lanie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Lanie can now know that Randy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lorrie","Lanie","Randy","Kathy"],"index":8670,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997801185,"difficulty":0.0002198815}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether or not everyone is thirsty. It is publicly announced that Laura knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Laura can now know whether Thomas can know whether Jason is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","John","Jason","Laura"],"index":44257,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986850619,"difficulty":0.0013149381}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Howard knows whether or not everyone is thirsty. It is publicly announced that Howard knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Howard can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Franklin","Howard"],"index":24126,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957362413,"difficulty":0.0042637587}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elaine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Vickie can now know that Amelia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ben","Elaine","Amelia","Vickie"],"index":12922,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953994155,"difficulty":0.0046005845}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel does not know whether Joel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Peter can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joel","Mary","Peter"],"index":25264,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999743402,"difficulty":0.000256598}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Marie can now know that Daniel can know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Daniel","Marie"],"index":58240,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957293868,"difficulty":0.0042706132}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edison knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Sean can now know that Sean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edison","Sean"],"index":11364,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980706573,"difficulty":0.0019293427}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Leonard. Leonard's card is shown to Corliss. Judith's card is shown to Nancy. Leonard's card is shown to Judith. Corliss's card is shown to Judith. Judith's card is shown to Judith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Corliss can now know that Judith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leonard","Corliss","Nancy","Judith"],"index":61117,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979091287,"difficulty":0.0020908713}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cindy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Andrew can now know that Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cindy","Andrew"],"index":38899,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9344732761,"difficulty":0.0655267239}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kim knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Kathleen can now know that Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathleen","Kim","Robert","Paul"],"index":9332,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998311758,"difficulty":0.001688242}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ernest can now know that Bessie can know that Rose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edna","Rose","Ernest","Bessie"],"index":23357,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983597398,"difficulty":0.0016402602}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wade does not know whether Richard is thirsty. It is publicly announced that Wade knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Grace can now know that Richard can know whether Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Wade","Grace"],"index":9721,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988798499,"difficulty":0.0011201501}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Keith knows whether someone is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Sheila can now know whether David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sheila","Keith","David","Claudia"],"index":58031,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7821776271,"difficulty":0.2178223729}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nannie's card is shown to Nannie. Vickie's card is shown to Nannie. Alison's card is shown to Nannie. Vickie's card is shown to Vickie. Alison's card is shown to Vickie. Vickie's card is shown to Alison. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vickie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nannie","Vickie","Alison"],"index":48260,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983770847,"difficulty":0.0016229153}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Timothy can now know that Denise can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jonathan","Timothy","Denise","Martha"],"index":38827,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983674884,"difficulty":0.0016325116}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leroy's card is shown to Leroy. Leroy's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Carolyn's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Leroy picked a red card. It is publicly announced that Leroy does not know whether Susan picked a red card. It is publicly announced that Susan knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Carolyn can now know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leroy","Carolyn","Susan"],"index":505,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.71732831,"difficulty":0.28267169}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether Andre's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Winston can now know that Ryan can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andre","Winston","Ryan","Jeffrey"],"index":52003,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996993542,"difficulty":0.0003006458}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether someone's forehead is muddy. It is publicly announced that Paul's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"Lynn can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Adam","Paul","Laura","Lynn"],"index":57339,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999736011,"difficulty":0.000263989}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Melva can now know that Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alycia","Fred","Melva","Roberta"],"index":50147,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9964134097,"difficulty":0.0035865903}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lupe's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Lupe can now know that Fred can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lupe","Esther","Marilyn","Fred"],"index":7100,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5503010154,"difficulty":0.4496989846}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julia does not know whether or not everyone is thirsty. It is publicly announced that Rebecca knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Julia can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rebecca","Julia","Richard"],"index":46329,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Christopher can now know whether Tom can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tom","Shirley","Jesse","Christopher"],"index":56756,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997772574,"difficulty":0.0002227426}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marianne knows whether or not everyone's forehead is muddy. It is publicly announced that Michael knows whether Marianne's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Marianne can now know that Michael can know that Marianne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marianne","Michael"],"index":63552,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7090987563,"difficulty":0.2909012437}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lara knows whether Lara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lara can now know that Wanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronnie","Wanda","Lara","Margaret"],"index":9575,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983490705,"difficulty":0.0016509295}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lakisha knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Harry can now know whether Scott can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harry","Lakisha","Scott"],"index":28623,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995955825,"difficulty":0.0004044175}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Veronica's forehead is not muddy. It is publicly announced that Julie knows whether Veronica's forehead is muddy. It is publicly announced that Veronica knows whether Julie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Veronica can now know whether Julie can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julie","John","Veronica"],"index":631,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994469285,"difficulty":0.0005530715}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marjorie can now know that Mary can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Marjorie","Marshall"],"index":42847,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984080195,"difficulty":0.0015919805}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason does not know whether Mario is thirsty. It is publicly announced that Jason knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Arthur can now know whether Jason can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mario","Arthur","Jason"],"index":48956,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996902943,"difficulty":0.0003097057}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marlyn can now know that Nick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diana","Nick","Theresa","Marlyn"],"index":36028,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8218227625,"difficulty":0.1781772375}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronnie does not know whether Ronnie's forehead is muddy. It is publicly announced that Lindsay does not know whether Lindsay's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lindsay can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lindsay","James","Ronnie"],"index":12076,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986857772,"difficulty":0.0013142228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Neil knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Neil can now know that Stacy can know that Stacy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Neil","Gerald","Stacy","Susan"],"index":49528,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9254527092,"difficulty":0.0745472908}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Linda can now know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Megan","Tony","Linda"],"index":44562,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9836493731,"difficulty":0.0163506269}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacey is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stacey","Robert","Donald","John"],"index":52834,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8330053687,"difficulty":0.1669946313}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin knows whether Benjamin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Benjamin can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vicki","Debbie","Benjamin"],"index":61766,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998324573,"difficulty":0.001675427}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy. It is publicly announced that Christopher knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Anthony can now know that Joseph can know whether Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Christopher","Rodney","Anthony"],"index":19388,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997072816,"difficulty":0.0002927184}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mavis's card is shown to Mavis. Tiffaney's card is shown to Tiffaney. Robin's card is shown to Tiffaney. Mavis's card is shown to Nathan. Mavis's card is shown to Robin. Robin's card is shown to Robin. It is publicly announced that someone picked a red card. It is publicly announced that Tiffaney does not know whether Mavis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mavis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mavis","Tiffaney","Nathan","Robin"],"index":30150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985961318,"difficulty":0.0014038682}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mike can now know whether Floy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Floy","Frank","Mike","Jodi"],"index":27040,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996333122,"difficulty":0.0003666878}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Inez does not know whether or not everyone's forehead is muddy. It is publicly announced that Perry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Billie can now know whether Perry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Perry","Billie","Larry","Inez"],"index":14650,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994232655,"difficulty":0.0005767345}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irene is not thirsty. It is publicly announced that Irene is not thirsty. It is publicly announced that Robert does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robert can now know that John can know that Irene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Robert","Sheryl","Irene"],"index":11629,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9611134529,"difficulty":0.0388865471}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Edward. Joe's card is shown to Joe. Carl's card is shown to Joe. Edward's card is shown to Carl. Edward's card is shown to Margaret. Joe's card is shown to Margaret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edward can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","Joe","Carl","Margaret"],"index":31341,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997732043,"difficulty":0.0002267957}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Courtney knows whether someone's forehead is muddy. It is publicly announced that Courtney knows whether or not everyone's forehead is muddy. It is publicly announced that Deborah's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Deborah can now know that Courtney can know that Steve's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Steve","Courtney","Lonnie"],"index":13460,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.963801682,"difficulty":0.036198318}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jack does not know whether or not everyone is thirsty. It is publicly announced that Jack knows whether Jack is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Louise can now know whether Arthur can know that Jack is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louise","Jack","Arthur"],"index":63675,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9936828613,"difficulty":0.0063171387}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] 0","hypothesis":"Albert can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Albert","Monserrate"],"index":30807,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983221889,"difficulty":0.0016778111}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vance knows whether Jodie's forehead is muddy. It is publicly announced that Vance knows whether Jodie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Vance can now know whether Jodie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vance","Jodie"],"index":57902,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997726083,"difficulty":0.0002273917}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eulalia knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentd knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Eulalia can now know that Elizabeth can know whether Deborah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Gregory","Elizabeth","Eulalia"],"index":14784,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999581039,"difficulty":0.000418961}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Dorothy. Dorothy's card is shown to Duane. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether or not everyone picked a red card. It is publicly announced that Duane knows whether Duane picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dorothy can now know whether Duane can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Duane"],"index":37895,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994712472,"difficulty":0.0005287528}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Jerry's forehead is muddy. It is publicly announced that Nettie knows whether Nettie's forehead is muddy. It is publicly announced that Nettie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentc knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Nancy can now know that Beryl can know that Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nettie","Beryl","Nancy","Jerry"],"index":5330,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9243045449,"difficulty":0.0756954551}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Mable. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Mable knows whether or not everyone picked a red card. It is publicly announced that Mable knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Mable can now know whether Joseph can know that Susan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mable","Joseph","Susan"],"index":1505,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9771651626,"difficulty":0.0228348374}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Candice can now know that Katherine can know whether Angela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Candice","Katherine","Angela"],"index":16213,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997276664,"difficulty":0.0002723336}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frederick's card is shown to Frederick. Miguel's card is shown to Miguel. It is publicly announced that someone picked a red card. It is publicly announced that Miguel knows whether Miguel picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Miguel can now know that Frederick can know that Miguel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Frederick","Miguel"],"index":43484,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9810468554,"difficulty":0.0189531446}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Adelaide can now know that Victoria can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Crystal","Victoria","Adelaide"],"index":55222,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978613257,"difficulty":0.0021386743}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brian can now know that Jerry can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brian","Jerry"],"index":180,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999748528,"difficulty":0.000251472}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred knows whether or not nobody's forehead is muddy. It is publicly announced that Fred's forehead is muddy. It is publicly announced that Fred knows whether Fred's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Fred can now know that Bulah can know that Fred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Fred","Bulah"],"index":20,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6640701294,"difficulty":0.3359298706}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Vance. Maria's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know whether Vance can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vance","Maria","Joseph"],"index":26673,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997701049,"difficulty":0.0002298951}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dave's card is shown to Alvin. Alvin's card is shown to Dave. Alvin's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not everyone picked a red card. It is publicly announced that Dave knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alvin","Dave","Robert"],"index":56496,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Andrew can now know that Heather can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Rudolph","Heather","Andrew"],"index":33207,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997755885,"difficulty":0.0002244115}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not nobody's forehead is muddy. It is publicly announced that Albert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Albert can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eddie","Albert","Christopher"],"index":57262,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990389347,"difficulty":0.0009610653}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Florence does not know whether Robert is thirsty. It is publicly announced that Florence is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(3) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Dorothy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Joseph","Florence","Robert"],"index":16689,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997183681,"difficulty":0.0002816319}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse knows whether Jesse is thirsty. It is publicly announced that Thomas does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jesse can now know that William can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jesse","William","Thomas"],"index":35132,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983717799,"difficulty":0.0016282201}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daryl knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Daryl can now know that Christopher can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Margarita","Daryl"],"index":48938,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995245934,"difficulty":0.0004754066}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nelson knows whether someone's forehead is muddy. It is publicly announced that Kyle does not know whether or not everyone's forehead is muddy. It is publicly announced that Nelson knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Kyle can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kyle","Nelson"],"index":52092,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976281524,"difficulty":0.0023718476}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bethany knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Bethany can now know that Melissa can know that Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelly","Bethany","Melissa"],"index":54318,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944164753,"difficulty":0.0055835247}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Ann. Maranda's card is shown to Ann. Ann's card is shown to Eric. Eric's card is shown to Eric. Maranda's card is shown to Maranda. It is publicly announced that someone picked a red card. It is publicly announced that Eric does not know whether Maranda picked a red card. It is publicly announced that Eric picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Eric can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ann","Eric","Maranda"],"index":58854,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997288585,"difficulty":0.0002711415}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory does not know whether Nicki is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] 0","hypothesis":"Gregory can now know whether Nicki can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gregory","Nicki"],"index":66698,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that James is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"James can now know that Christopher can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Christopher","James"],"index":38285,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983440638,"difficulty":0.0016559362}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rose does not know whether Woodrow is thirsty. It is publicly announced that Dustin knows whether someone is thirsty. It is publicly announced that Rose does not know whether or not everyone is thirsty. It is publicly announced that Denise does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Woodrow can now know whether Dustin can know that Denise is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dustin","Rose","Woodrow","Denise"],"index":62595,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9896479249,"difficulty":0.0103520751}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maurice knows whether Melissa's forehead is muddy. It is publicly announced that Melissa knows whether someone's forehead is muddy. It is publicly announced that Melissa's forehead is muddy. It is publicly announced that Maurice does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Melissa can now know whether Maurice can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melissa","Rose","Maurice"],"index":40782,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerry does not know whether Veronica is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Veronica can now know that Veronica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Veronica","Jerry","Hollis"],"index":23079,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9969570637,"difficulty":0.0030429363}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila knows whether or not nobody's forehead is muddy. It is publicly announced that Gregory's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Sheila can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gregory","Sheila"],"index":4158,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997687936,"difficulty":0.0002312064}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that Christine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gayle","David","Christine","Jason"],"index":1345,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986516833,"difficulty":0.0013483167}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Victoria can now know that Dina can know that Dina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dina","Victoria","Eddie","Angie"],"index":50571,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99611485,"difficulty":0.00388515}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jamie's card is shown to Jamie. Wayne's card is shown to Wayne. It is publicly announced that someone picked a red card. It is publicly announced that Jamie knows whether or not nobody picked a red card. It is publicly announced that Jamie does not know whether Wayne picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jamie can now know whether Wayne can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jamie","Wayne"],"index":41330,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99948138,"difficulty":0.00051862}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Harvey can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Harvey","Carl","Ruth"],"index":38482,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984400868,"difficulty":0.0015599132}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barry's card is shown to Ruben. Barry's card is shown to Ray. Ruben's card is shown to Dennis. Dennis's card is shown to Dennis. Barry's card is shown to Dennis. Ray's card is shown to Barry. It is publicly announced that someone picked a red card. It is publicly announced that Ruben picked a red card. It is publicly announced that Ruben knows whether Ruben picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ruben can now know whether Dennis can know that Ruben picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruben","Ray","Dennis","Barry"],"index":5466,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9103255272,"difficulty":0.0896744728}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know whether Patrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Mary","Lisa"],"index":33902,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997375607,"difficulty":0.0002624393}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Alberta can now know whether Ruby can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruby","Anthony","Alberta","Robert"],"index":59429,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9877049923,"difficulty":0.0122950077}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold does not know whether Joshua is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Harold can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Veronica","Joshua","Harold"],"index":5667,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997702241,"difficulty":0.0002297759}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret does not know whether or not everyone's forehead is muddy. It is publicly announced that Todd knows whether or not nobody's forehead is muddy. It is publicly announced that Margaret does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Margaret can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Manual","Margaret","Todd"],"index":66138,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997153878,"difficulty":0.0002846122}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Edward is thirsty. It is publicly announced that Jackie does not know whether William is thirsty. It is publicly announced that Edward knows whether Edward is thirsty. It is publicly announced that Edward knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Daniel can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","William","Jackie","Daniel"],"index":42738,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna does not know whether Donna's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Donna can now know whether Lynda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ann","Donna","Lynda"],"index":32654,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995636344,"difficulty":0.0004363656}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antoinette knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mathew can now know that Antoinette can know that Mathew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cara","Antoinette","Mathew"],"index":51481,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984483719,"difficulty":0.0015516281}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jc does not know whether John is thirsty. It is publicly announced that Lindsey does not know whether John is thirsty. It is publicly announced that Lindsey knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Lindsey can now know whether Jc can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Jc","Lindsey"],"index":66669,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joyce can now know that Simon can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Simon","Michael","Robert","Joyce"],"index":24952,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9804168344,"difficulty":0.0195831656}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Maureen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Thomas can now know that Omar's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Maureen","Omar"],"index":48876,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982147217,"difficulty":0.0017852783}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bertha knows whether Bertha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bertha","Robert","Jennifer","Christopher"],"index":28929,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999736011,"difficulty":0.000263989}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Patricia can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patricia","Meredith"],"index":56689,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997822642,"difficulty":0.0002177358}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Andres knows whether Tonia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Tonia can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andres","Tonia"],"index":54216,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982600808,"difficulty":0.0017399192}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joann does not know whether Billy is thirsty. It is publicly announced that Arnold does not know whether Joann is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joann can now know that Joann is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arnold","Karen","Joann","Billy"],"index":38119,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.562982738,"difficulty":0.437017262}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether Robert is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether Douglas is thirsty. It is publicly announced that Olivia does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Kimberly can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kimberly","Olivia","Douglas","Robert"],"index":66050,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997261167,"difficulty":0.0002738833}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irene is thirsty. It is publicly announced that Terrence knows whether Terrence is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Terrence can now know whether Irene can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Terrence","Irene"],"index":37149,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9283428192,"difficulty":0.0716571808}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alma is not thirsty. It is publicly announced that Beth is not thirsty. It is publicly announced that Alma does not know whether Jeremiah is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Beth can now know that William can know whether Alma is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeremiah","Alma","William","Beth"],"index":25568,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8132963777,"difficulty":1.8132963777}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Evelyn. Martha's card is shown to Martha. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Martha can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Evelyn","Martha"],"index":38801,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997584224,"difficulty":0.0002415776}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Henry does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that William is thirsty. It is publicly announced that William knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Henry can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Henry","William"],"index":31389,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Jody's card is shown to Bonnie. Jody's card is shown to Jody. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darlene can now know whether Bonnie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlene","Valerie","Bonnie","Jody"],"index":8765,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999620676,"difficulty":0.000379324}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Patty can now know that Stephanie can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judith","Stephanie","Patty","Ralph"],"index":57857,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995391369,"difficulty":0.0004608631}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond does not know whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jerry can now know that Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mel","Jerry","Raymond"],"index":56032,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956253767,"difficulty":0.0043746233}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deena does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Deena can now know that Anika can know that Dale is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heriberto","Deena","Anika","Dale"],"index":27917,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.883510232,"difficulty":0.116489768}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Laura. Barbara's card is shown to Cherie. Margaret's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know that Cherie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Cherie","Margaret","Barbara"],"index":11302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983703494,"difficulty":0.0016296506}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Barbara is thirsty. It is publicly announced that David does not know whether Miguel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Robert can now know whether Barbara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Miguel","Barbara","David"],"index":61748,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9946866035,"difficulty":0.0053133965}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Joseph. Joseph's card is shown to Joseph. Ruth's card is shown to Ruth. Sherri's card is shown to Sherri. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arlene","Joseph","Ruth","Sherri"],"index":66283,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983600974,"difficulty":0.0016399026}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Fernando can now know that Terry can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Fernando","Terry"],"index":46536,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather does not know whether Cyndy is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Cyndy can now know that Jean can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cyndy","Heather","Dean","Jean"],"index":45645,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985088706,"difficulty":0.0014911294}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Flora knows whether someone's forehead is muddy. It is publicly announced that Bruce knows whether someone's forehead is muddy. It is publicly announced that Jean knows whether Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Nadine can now know that Jean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jean","Nadine","Flora","Bruce"],"index":51306,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977691174,"difficulty":0.0022308826}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] 0","hypothesis":"Wayne can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Derrick","Wayne"],"index":27528,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983422756,"difficulty":0.0016577244}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josephine's card is shown to Josephine. Christina's card is shown to Josephine. Christina's card is shown to Christina. Josephine's card is shown to Patrick. Patrick's card is shown to Patrick. It is publicly announced that someone picked a red card. It is publicly announced that Christina does not know whether Josephine picked a red card. It is publicly announced that Christina knows whether Christina picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Josephine can now know that Christina can know that Patrick picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Josephine","Christina","Patrick"],"index":45850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9399958849,"difficulty":0.0600041151}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether Marguerite's forehead is muddy. It is publicly announced that Jose knows whether Marguerite's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Sarah can now know that Jose can know that Marguerite's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Sarah","Marguerite","Megan"],"index":2310,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973352551,"difficulty":0.0026647449}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phillip knows whether Donald's forehead is muddy. It is publicly announced that Donald knows whether Tracy's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Donald can now know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracy","Phillip","Donald"],"index":21561,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8647136688,"difficulty":0.1352863312}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theodore is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] 0","hypothesis":"John can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Theodore","John"],"index":50363,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8709042668,"difficulty":1.8709042668}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ivette knows whether Ivette's forehead is muddy. It is publicly announced that Ivette knows whether Ivette's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ella can now know that Susan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marguerite","Ella","Ivette","Susan"],"index":37593,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998455286,"difficulty":0.001544714}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeraldine does not know whether or not everyone's forehead is muddy. It is publicly announced that Jeraldine does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jeraldine can now know that Jeraldine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jeraldine","Minnie"],"index":5799,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9400767088,"difficulty":1.9400767088}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold knows whether Harold is thirsty. It is publicly announced that Pat does not know whether Harold is thirsty. It is publicly announced that Blanche does not know whether Donald is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Pat can now know that Harold can know that Harold is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harold","Donald","Pat","Blanche"],"index":64282,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7598777413,"difficulty":0.2401222587}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Lenora's card is shown to Lenora. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Nada picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Nada can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nada","Kenneth","Lenora"],"index":21493,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9854194522,"difficulty":0.0145805478}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether or not nobody's forehead is muddy. It is publicly announced that Dorothy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Maria can now know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Maria","Sherrie","Dorothy"],"index":45002,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7408249974,"difficulty":1.7408249974}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Barbara. Jean's card is shown to Elliot. Barbara's card is shown to Patricia. Patricia's card is shown to Jean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Elliot can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Elliot","Patricia","Jean"],"index":40732,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983599782,"difficulty":0.0016400218}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Steven can now know that Phyllis can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samantha","Steven","Larry","Phyllis"],"index":4646,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9950388074,"difficulty":0.0049611926}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bill knows whether someone is thirsty. It is publicly announced that Eddie does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Robert can now know whether Bill is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bill","Eddie","Robert"],"index":50532,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9936885238,"difficulty":0.0063114762}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pam's card is shown to Pam. Pam's card is shown to Betsy. It is publicly announced that someone picked a red card. It is publicly announced that Pam does not know whether Betsy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Pam can now know whether Betsy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pam","Betsy"],"index":10218,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9957662821,"difficulty":0.0042337179}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy is thirsty. It is publicly announced that Wayne is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 1 ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 1 ] 0","hypothesis":"Nellie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wayne","Joan","Nellie","Nancy"],"index":61878,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983028173,"difficulty":0.0016971827}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jana can now know that Jana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erin","Jana","Rolando","Jeffrey"],"index":23148,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984951019,"difficulty":0.0015048981}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert knows whether Richie is thirsty. It is publicly announced that Robert knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Robert can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richie","Robert"],"index":63094,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983092546,"difficulty":0.0016907454}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Johnna knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Johnna can now know whether Joe is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joe","Donna","Johnna"],"index":7637,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997089982,"difficulty":0.002910018}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Kathaleen knows whether Kathaleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kathaleen can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathaleen","James","Sarah","Nicole"],"index":25035,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968661666,"difficulty":0.0031338334}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tom does not know whether Tom's forehead is muddy. It is publicly announced that Tom knows whether or not nobody's forehead is muddy. It is publicly announced that Tom does not know whether Tom's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Anthony can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tom","Anthony"],"index":12789,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984124899,"difficulty":0.0015875101}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Christeen can now know whether Ronald can know that Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darryl","Christeen","Ronald"],"index":50862,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9688943624,"difficulty":0.0311056376}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandon is thirsty. It is publicly announced that Agnes is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(1) ] 0","hypothesis":"Brandon can now know whether Agnes can know that Brandon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Agnes","Brandon","Ann","Mabel"],"index":40569,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9897477627,"difficulty":0.0102522373}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Louis can now know that Louis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eric","Louis"],"index":25130,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976820946,"difficulty":0.0023179054}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether Donald is thirsty. It is publicly announced that Reginald does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Nancy can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Nicholas","Reginald","Donald"],"index":39554,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971364737,"difficulty":0.0028635263}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harriet's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"William can now know that Mary can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Mary","Harriet","William"],"index":57083,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999776423,"difficulty":0.000223577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerardo does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Martha can now know that Raymond can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gerardo","Raymond","Valerie","Martha"],"index":36535,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9854887128,"difficulty":0.0145112872}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric's forehead is muddy. It is publicly announced that Eric knows whether someone's forehead is muddy. It is publicly announced that Elmer's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Eric can now know whether Elmer can know whether Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elmer","Eric"],"index":48960,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997078776,"difficulty":0.0002921224}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Karie. Kim's card is shown to Kim. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kim can now know that Karie can know that Kim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karie","Kim","Carolyn"],"index":17495,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975121021,"difficulty":0.0024878979}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anne knows whether Anne is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Richard can now know whether Anne can know whether Anne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Anne"],"index":25434,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975793958,"difficulty":0.0024206042}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah does not know whether Cory is thirsty. It is publicly announced that Lisa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] 0","hypothesis":"Lisa can now know that Deborah can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cory","Lisa","Deborah"],"index":61436,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997839332,"difficulty":0.0002160668}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darlene does not know whether Darlene's forehead is muddy. It is publicly announced that Audrey does not know whether Audrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Audrey can now know that Darline can know whether Darlene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Audrey","Darline","Floyd","Darlene"],"index":20164,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986795783,"difficulty":0.0013204217}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Christian can now know that Christine can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christian","Christine"],"index":9172,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997569919,"difficulty":0.0002430081}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pauline does not know whether Al is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Al can now know whether Kelly can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pauline","Kelly","Al","Francis"],"index":2099,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997230172,"difficulty":0.0002769828}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derek's card is shown to Derek. Derek's card is shown to Bob. Derek's card is shown to Jeffrey. Bob's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Derek can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Derek","Bob","Jeffrey"],"index":44785,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985200763,"difficulty":0.0014799237}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alyce's card is shown to Lois. Julia's card is shown to Lois. Lois's card is shown to Alyce. Julia's card is shown to Alyce. Jeffrey's card is shown to Alyce. Alyce's card is shown to Julia. Julia's card is shown to Julia. Jeffrey's card is shown to Julia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3,4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3,4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alyce can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lois","Alyce","Julia","Jeffrey"],"index":38213,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997754693,"difficulty":0.0002245307}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Mavis can now know that Kelly can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edgar","Kelly","John","Mavis"],"index":20410,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984032512,"difficulty":0.0015967488}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jim's card is shown to Jim. Richard's card is shown to Jim. David's card is shown to Jim. Richard's card is shown to Richard. Jim's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jim","Richard","David"],"index":11233,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Adan can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ryan","Adan","Sarah"],"index":29830,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9929333925,"difficulty":0.0070666075}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Patricia. Irene's card is shown to Jacob. Beatrice's card is shown to Beatrice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jacob can now know whether Patricia can know that Beatrice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Jacob","Beatrice","Irene"],"index":45861,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9317244887,"difficulty":0.0682755113}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] 0","hypothesis":"Kevin can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Steven","Mary","Jason"],"index":30424,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954923391,"difficulty":0.0045076609}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Leslie can now know whether Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leslie","Richard","Laura"],"index":52844,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997527003,"difficulty":0.0002472997}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gabriel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Barbara can now know whether Shirley can know that Janice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Gabriel","Janice","Shirley"],"index":9697,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9968311191,"difficulty":0.0031688809}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arnold is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"John can now know that Marjorie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marjorie","Arnold","Mary","John"],"index":12246,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9866402745,"difficulty":0.0133597255}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jenifer knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Margaret can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joshua","Margaret","Jenifer","Melody"],"index":6044,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Adam. Adam's card is shown to Fay. Fay's card is shown to Luis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Luis can now know that Fay can know that Adam picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Adam","Fay","Luis"],"index":36727,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979966283,"difficulty":0.0020033717}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randi knows whether or not everyone's forehead is muddy. It is publicly announced that Randi's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Alexander can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Randi","Alexander","Doris"],"index":33502,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9787174463,"difficulty":0.0212825537}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Calvin. Mary's card is shown to Mary. Herman's card is shown to Mary. Calvin's card is shown to Herman. Mary's card is shown to Herman. Herman's card is shown to Herman. It is publicly announced that someone picked a red card. It is publicly announced that Mary picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know whether Calvin can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Calvin","Mary","Herman"],"index":16965,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.996460259,"difficulty":0.003539741}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether Darnell's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Dorothy can now know that Darnell can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dorothy","Darnell"],"index":55458,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984549284,"difficulty":0.0015450716}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alma knows whether someone is thirsty. It is publicly announced that Thomas does not know whether Alma is thirsty. It is publicly announced that Thomas is thirsty. It is publicly announced that Heather does not know whether Alma is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Martina can now know that Heather is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Martina","Thomas","Alma","Heather"],"index":16742,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8866055012,"difficulty":0.1133944988}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. Bryan's card is shown to David. David's card is shown to Bryan. Bryan's card is shown to Bryan. Jeffrey's card is shown to Bryan. Bryan's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bryan can now know that David can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Bryan","Jeffrey"],"index":5833,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997816682,"difficulty":0.0002183318}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Brian. Esther's card is shown to Esther. James's card is shown to Jeffrey. Esther's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know whether James can know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Esther","Jeffrey","James"],"index":39444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986579418,"difficulty":0.0013420582}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Woodrow can now know that David can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Carolyn","David","Woodrow"],"index":57948,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.716512382,"difficulty":1.716512382}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Ross can know that Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","Barbara","Ross"],"index":20564,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985516667,"difficulty":0.0014483333}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas knows whether or not nobody is thirsty. It is publicly announced that Thomas does not know whether Phillip is thirsty. It is publicly announced that Paul knows whether or not everyone is thirsty. It is publicly announced that Phillip knows whether Phillip is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Paul can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Paul","Phillip"],"index":12090,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999725163,"difficulty":0.000274837}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie does not know whether Marjorie's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Barbara can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marjorie","Barbara"],"index":50969,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997244477,"difficulty":0.0002755523}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice does not know whether Edith is thirsty. It is publicly announced that Paris does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Paris can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Edith","Amelia","Paris"],"index":47311,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.995577693,"difficulty":0.004422307}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roseline knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Roseline can now know whether Mark can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roseline","Mark","Michael"],"index":28847,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997408986,"difficulty":0.0002591014}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret knows whether or not nobody is thirsty. It is publicly announced that Margaret is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(2) ] 0","hypothesis":"Margaret can now know that David can know whether Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Margaret"],"index":60248,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9718136787,"difficulty":0.0281863213}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vance knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know whether Vance can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vance","Mark","Lillian"],"index":16643,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996054769,"difficulty":0.0003945231}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marcus","Tanya","Lawrence","David"],"index":50671,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952504635,"difficulty":0.0047495365}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kamala does not know whether Maria is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Kamala does not know whether Johnny is thirsty. It is publicly announced that Annie does not know whether Maria is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Maria can now know whether Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kamala","Annie","Johnny","Maria"],"index":3973,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988760352,"difficulty":0.0011239648}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jesse can now know that Terrell can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anne","Terrell","Jesse"],"index":25184,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter does not know whether Francisco is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Peter can now know that Whitney can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Whitney","Robert","Francisco","Peter"],"index":30357,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9822533727,"difficulty":0.0177466273}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nina's card is shown to Earline. Earline's card is shown to Ryan. Nina's card is shown to Nina. Ryan's card is shown to Natalie. Nina's card is shown to Natalie. Natalie's card is shown to Natalie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Natalie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earline","Ryan","Nina","Natalie"],"index":15600,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985530972,"difficulty":0.0014469028}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Clara can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","James","Clara"],"index":38013,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983437061,"difficulty":0.0016562939}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Kimberly's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn does not know whether Evelyn picked a red card. It is publicly announced that Evelyn does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Evelyn can now know that Evelyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Robert","Mary","Kimberly"],"index":1382,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9635331035,"difficulty":0.0364668965}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Albert. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Albert knows whether or not nobody picked a red card. It is publicly announced that Joseph does not know whether Albert picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Joseph can now know whether Albert can know that Albert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Albert","Joseph"],"index":6435,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8612189293,"difficulty":1.8612189293}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"John can now know that George can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["George","John"],"index":11631,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997629523,"difficulty":0.0002370477}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harry's card is shown to Jami. Sophie's card is shown to Jami. Jami's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Harry does not know whether Harry picked a red card. It is publicly announced that Jami knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jami can now know whether Jami picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jami","Harry","Sophie"],"index":49032,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9955829978,"difficulty":1.9955829978}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Maureen. Maureen's card is shown to Regenia. It is publicly announced that someone picked a red card. It is publicly announced that Regenia knows whether Maureen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Maureen can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maureen","Regenia","Elizabeth"],"index":55204,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966198206,"difficulty":0.0033801794}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irma's card is shown to Gary. George's card is shown to George. Irma's card is shown to Anthony. Irma's card is shown to Irma. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether Anthony picked a red card. It is publicly announced that George picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] 0","hypothesis":"George can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","George","Anthony","Irma"],"index":52674,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8093301058,"difficulty":0.1906698942}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peggy knows whether someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Peggy can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Amado","Peggy","Donald"],"index":3905,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978483915,"difficulty":0.0021516085}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debrah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Debrah can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christopher","Sarah","Debrah"],"index":22138,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997660518,"difficulty":0.0002339482}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonel's forehead is muddy. It is publicly announced that Angelo knows whether or not everyone's forehead is muddy. It is publicly announced that Kent knows whether Leonel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Angelo can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angelo","Kent","Leonel"],"index":37025,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977356195,"difficulty":0.0022643805}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesus knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jesus can now know that Jesus's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jesus","Ronald","Jeffrey"],"index":29579,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.627315402,"difficulty":1.627315402}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josephine's card is shown to Janice. Janice's card is shown to Anne. Janice's card is shown to Josephine. Deloris's card is shown to Josephine. Anne's card is shown to Josephine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deloris can now know whether Josephine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Deloris","Anne","Josephine"],"index":4245,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5705230236,"difficulty":1.5705230236}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Sandra knows whether Geraldine's forehead is muddy. It is publicly announced that Tiffany's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Donald can now know whether Geraldine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sandra","Tiffany","Geraldine","Donald"],"index":122,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994974136,"difficulty":0.0005025864}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille knows whether or not nobody's forehead is muddy. It is publicly announced that Brandon's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Brandon can now know whether Lucille can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brandon","Lucille"],"index":54888,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997519851,"difficulty":0.0002480149}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erin is thirsty. It is publicly announced that Robert does not know whether Jeffrey is thirsty. It is publicly announced that Selina knows whether or not nobody is thirsty. It is publicly announced that Selina is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Jeffrey can now know whether Robert can know that Jeffrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Robert","Selina","Erin"],"index":41573,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9678195715,"difficulty":0.0321804285}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earl knows whether Julia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Earl can now know that Earl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Earl","Charles","Julia"],"index":64566,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980564713,"difficulty":0.0019435287}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Toni's card is shown to Toni. John's card is shown to Toni. Toni's card is shown to Luz. Toni's card is shown to John. Luz's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Toni does not know whether Luz picked a red card. It is publicly announced that Luz knows whether or not everyone picked a red card. It is publicly announced that John knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Luz can now know that John can know whether Luz picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Toni","Luz","John"],"index":14522,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7882193327,"difficulty":0.2117806673}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Quentin can now know that Ramon can know that Ramon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ramon","Quentin"],"index":5952,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9957886338,"difficulty":0.0042113662}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arvilla's card is shown to Jose. Lindsey's card is shown to Jose. Gerald's card is shown to Gerald. Lindsey's card is shown to Gerald. Gerald's card is shown to Arvilla. Lindsey's card is shown to Arvilla. Gerald's card is shown to Lindsey. Lindsey's card is shown to Lindsey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:2,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:2,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Arvilla can now know that Arvilla picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Gerald","Arvilla","Lindsey"],"index":39614,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965205193,"difficulty":0.0034794807}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Doris","Elaine","John","Brenda"],"index":27068,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997503161,"difficulty":0.0002496839}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annice's forehead is not muddy. It is publicly announced that Claudia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Claudia can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brenda","Susan","Annice","Claudia"],"index":60011,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997194409,"difficulty":0.0002805591}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Sterling can now know that Terrance can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sterling","Terrance"],"index":3898,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997190833,"difficulty":0.0002809167}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy. It is publicly announced that Omar's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Omar can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Samuel","Shaun","Omar","Linda"],"index":43185,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997860789,"difficulty":0.0002139211}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that Jaclyn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Susan can now know whether David can know whether Susan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Rebecca","David","Jaclyn"],"index":8948,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997151494,"difficulty":0.0002848506}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether Stanley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Stanley can now know whether Maria can know that Stanley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stanley","Amy","Sarah","Maria"],"index":67562,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9563615918,"difficulty":0.0436384082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether Freddy is thirsty. It is publicly announced that Freddy knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Walter can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anthony","Tiffany","Freddy","Walter"],"index":7726,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997305274,"difficulty":0.0002694726}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Mary. Arthur's card is shown to Mary. Mary's card is shown to Jason. Jason's card is shown to Jason. Betty's card is shown to Jason. Betty's card is shown to Betty. Mary's card is shown to Arthur. Betty's card is shown to Arthur. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Arthur can now know that Betty can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Jason","Betty","Arthur"],"index":7391,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981911778,"difficulty":0.0018088222}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Mary can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Harold","Mary"],"index":34974,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997738004,"difficulty":0.0002261996}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shelley does not know whether Joshua is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Shelley can now know that Joshua can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shelley","Mattie","Joshua"],"index":5182,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.981454134,"difficulty":0.018545866}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Oscar is thirsty. It is publicly announced that Elizabeth is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Joseph can now know that Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Elizabeth","Oscar"],"index":61582,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7169500589,"difficulty":0.2830499411}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Odell does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Odell can now know that Emily can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ann","Emily","Odell"],"index":46224,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997926116,"difficulty":0.002073884}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether or not everyone's forehead is muddy. It is publicly announced that Margaret knows whether or not everyone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Rose can now know whether Kevin can know that Kristi's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Margaret","Kristi","Kevin"],"index":14912,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9969741106,"difficulty":0.0030258894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether Ethel is thirsty. It is publicly announced that Brenda does not know whether Lisa is thirsty. It is publicly announced that Ethel does not know whether Martha is thirsty. It is publicly announced that Martha is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! 4 ] (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! 4 ] 0","hypothesis":"Lisa can now know whether Lisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brenda","Ethel","Lisa","Martha"],"index":35406,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980565906,"difficulty":0.0019434094}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall knows whether Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Brian can now know that Freida can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Brian","Freida","Randall"],"index":18975,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997666478,"difficulty":0.0002333522}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that Philip's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Richard can now know that Vivian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Vivian","Richard","Philip"],"index":63625,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9919769168,"difficulty":0.0080230832}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pam's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"John can now know whether Pam's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Pam"],"index":12021,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995780587,"difficulty":0.0004219413}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Maria can now know that Shana can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Shana","Maria","Michael"],"index":54969,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983581901,"difficulty":0.0016418099}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sidney knows whether Veronica's forehead is muddy. It is publicly announced that Sidney knows whether or not everyone's forehead is muddy. It is publicly announced that Mamie does not know whether Mamie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Mamie can now know that Veronica can know that Mamie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Veronica","Mamie","Sidney"],"index":60473,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.682497561,"difficulty":0.317502439}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Johnny can now know whether Christy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christy","Johnny","Johnathan","Florence"],"index":36391,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997070432,"difficulty":0.0002929568}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Richard. Scott's card is shown to Scott. Scott's card is shown to Joseph. Joseph's card is shown to Joseph. Joseph's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Scott","Joseph","Mary"],"index":23306,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984163046,"difficulty":0.0015836954}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Michelle does not know whether Renee is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Renee can now know that Michelle can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michelle","Renee","Judith"],"index":30963,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984405637,"difficulty":0.0015594363}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelica does not know whether Angelica's forehead is muddy. It is publicly announced that Angelica does not know whether or not everyone's forehead is muddy. It is publicly announced that Jeremiah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] 0","hypothesis":"Angelica can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Angelica","Jim","Jeremiah"],"index":8048,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999720037,"difficulty":0.000279963}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Elizabeth can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rachel","Thomas","Carlos","Elizabeth"],"index":33675,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985305071,"difficulty":0.0014694929}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Nancy can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","John","Nancy","Mary"],"index":38799,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995980859,"difficulty":0.0004019141}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua does not know whether Joshua's forehead is muddy. It is publicly announced that Joshua's forehead is muddy. It is publicly announced that Victoria's forehead is muddy. It is publicly announced that Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Joshua can now know that Bert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Sandra","Victoria","Bert"],"index":54968,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.514490068,"difficulty":1.514490068}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether Mohammad's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mohammad can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Mohammad","Tanya"],"index":5537,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9876044989,"difficulty":0.0123955011}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Alex. Dan's card is shown to Alex. Rose's card is shown to Rose. Alex's card is shown to Dan. Dan's card is shown to Dan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dan can now know whether Dan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alex","Rose","Dan"],"index":8112,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9781211019,"difficulty":0.0218788981}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know whether Christopher can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Margaret","Haywood"],"index":20390,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995556474,"difficulty":0.0004443526}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann does not know whether Amber is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Ann can now know whether Lindsay can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ann","Amber","Lindsay"],"index":58252,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995274544,"difficulty":0.0004725456}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Norma is thirsty. It is publicly announced that Viola does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Linda can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Viola","Linda","Chong","Norma"],"index":21979,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997168183,"difficulty":0.0002831817}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenny knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Kenny can now know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenny","Dorothy","Gregory"],"index":31013,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983326793,"difficulty":0.0016673207}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Branden's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Emily can now know whether Branden can know whether Emily's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cecil","Leah","Branden","Emily"],"index":12864,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9974181652,"difficulty":0.0025818348}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that June knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Mary can now know whether June can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["June","Mary"],"index":65471,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999699235,"difficulty":0.000300765}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Dawn. Stephan's card is shown to Dawn. Dawn's card is shown to Brian. Brian's card is shown to Brian. Stephan's card is shown to Brian. Dawn's card is shown to Stephan. Stephan's card is shown to Stephan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dawn can now know that Stephan can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dawn","Brian","Stephan"],"index":7915,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983265996,"difficulty":0.0016734004}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William is thirsty. It is publicly announced that Jason knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"William can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alex","Eric","Jason","William"],"index":37132,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997346997,"difficulty":0.0002653003}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gabrielle knows whether Gabrielle is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Gabrielle can now know that Scott can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gabrielle","Christopher","Scott"],"index":27428,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997143149,"difficulty":0.0002856851}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Nicole. Earlie's card is shown to Nicole. Roseanne's card is shown to Nicole. Earlie's card is shown to Earlie. Juan's card is shown to Earlie. Roseanne's card is shown to Roseanne. Juan's card is shown to Roseanne. Earlie's card is shown to Juan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juan can now know that Nicole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicole","Earlie","Roseanne","Juan"],"index":29659,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978487492,"difficulty":0.0021512508}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ted's card is shown to James. Eleanor's card is shown to Eleanor. Eleanor's card is shown to Ted. It is publicly announced that someone picked a red card. It is publicly announced that Ted picked a red card. It is publicly announced that Alexis knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Alexis can now know whether James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Eleanor","Alexis","Ted"],"index":18627,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8144222498,"difficulty":0.1855777502}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Gary. Laura's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Gary knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Gary can now know that Laura can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gary","Laura"],"index":66543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983304143,"difficulty":0.0016695857}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Gladys. Gladys's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that Judith does not know whether or not everyone picked a red card. It is publicly announced that Judith knows whether or not nobody picked a red card. It is publicly announced that Gladys picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 1 ] Agentb knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! 1 ] 0","hypothesis":"Judith can now know whether Gladys can know that Judith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gladys","Judith"],"index":14996,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9350215197,"difficulty":1.9350215197}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Guadalupe knows whether Guadalupe is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Guadalupe can now know whether Sandra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Joe","Guadalupe"],"index":14664,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9901042581,"difficulty":0.0098957419}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Oscar can now know whether David can know that Jonathan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Oscar","Shirley","David","Jonathan"],"index":61239,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996683598,"difficulty":0.0003316402}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is not muddy. It is publicly announced that Crystal's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Crystal can now know that Barbara can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Barbara","Mary"],"index":50934,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995936751,"difficulty":0.0004063249}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hillary knows whether Hillary is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Hillary can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Maria","Hillary"],"index":28516,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997250438,"difficulty":0.0002749562}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeannine knows whether Steven's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Steven can now know whether Jeannine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeannine","Steven"],"index":20936,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989896417,"difficulty":0.0010103583}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Barry can now know whether Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Barry","Calvin","Mark"],"index":27401,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997368455,"difficulty":0.0002631545}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Thomas can now know that Ronald can know that Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Teri","Thomas"],"index":58823,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983275533,"difficulty":0.0016724467}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Ronda can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lucille","Ronda","Lloyd","Amanda"],"index":35643,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric is thirsty. It is publicly announced that Ronald is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Ronald can now know that Richard can know whether Eric is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Eric","Ronald"],"index":60228,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6265932918,"difficulty":1.6265932918}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amber knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Julie can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Julie","Amber"],"index":17703,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999522686,"difficulty":0.000477314}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyler's card is shown to Thomas. Thomas's card is shown to Bernice. Thomas's card is shown to Tyler. It is publicly announced that someone picked a red card. It is publicly announced that Thomas knows whether or not everyone picked a red card. It is publicly announced that Loretta does not know whether Bernice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Thomas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Bernice","Loretta","Tyler"],"index":296,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997138381,"difficulty":0.0002861619}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Craig knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Heather can now know whether Heather's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Heather","Craig"],"index":6169,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992592931,"difficulty":0.0007407069}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ebony's card is shown to Ebony. Michelle's card is shown to Ebony. Lorraine's card is shown to Ebony. Lorraine's card is shown to Michelle. Michelle's card is shown to Lorraine. Lorraine's card is shown to Lorraine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ramona can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ramona","Ebony","Michelle","Lorraine"],"index":40636,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9832633734,"difficulty":0.0167366266}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beth's forehead is not muddy. It is publicly announced that Margurite knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Margurite can now know whether Carlos can know whether Margurite's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margurite","Melvin","Beth","Carlos"],"index":26734,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996780157,"difficulty":0.0003219843}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell knows whether Clay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Russell can now know whether Clay can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clay","Sheri","Russell","Emma"],"index":22937,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999687314,"difficulty":0.000312686}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward does not know whether Jennifer is thirsty. It is publicly announced that Edward does not know whether Gladys is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Edward can now know that Gladys is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Jennifer","Edward","Gladys"],"index":34865,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969536066,"difficulty":0.0030463934}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Ronnie is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Ronnie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ronnie can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","David","Ronnie"],"index":30894,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970769882,"difficulty":0.0029230118}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Ruth. Ruth's card is shown to Jesse. Jesse's card is shown to Jesse. Jesse's card is shown to Jeremy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeremy can now know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Jesse","Jeremy","Matilda"],"index":19710,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974761605,"difficulty":0.0025238395}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norma's card is shown to Norma. Kyle's card is shown to Kyle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kyle can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norma","Kyle","Irene","Barb"],"index":56488,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983666539,"difficulty":0.0016333461}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathryn knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Aida can now know that Patricia can know that Kathryn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathryn","Betty","Patricia","Aida"],"index":34674,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8702065349,"difficulty":0.1297934651}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bonnie is thirsty. It is publicly announced that Nicholas knows whether someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Sandra can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nicholas","Bonnie","Sandra"],"index":48703,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997307658,"difficulty":0.0002692342}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Patrice's card is shown to James. Patrice's card is shown to Patrice. It is publicly announced that someone picked a red card. It is publicly announced that Patrice does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Anthony can now know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anthony","James","Patrice"],"index":57104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9862809181,"difficulty":0.0137190819}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arnold does not know whether Jeffery is thirsty. It is publicly announced that Thomas does not know whether John is thirsty. It is publicly announced that Arnold does not know whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Thomas can now know that Jeffery can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","John","Jeffery","Arnold"],"index":53995,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985313416,"difficulty":0.0014686584}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Edith can now know whether Stephanie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Edith","Stephanie","Jeffery"],"index":5856,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997599721,"difficulty":0.0002400279}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that John's forehead is muddy. It is publicly announced that Enedina knows whether or not nobody's forehead is muddy. It is publicly announced that John knows whether Enedina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Bernard can now know whether Bernard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bernard","Enedina","John"],"index":44700,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999245286,"difficulty":0.000754714}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Richard can now know whether Jennifer can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Michael","Brian","Richard"],"index":10568,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996167421,"difficulty":0.0003832579}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Rodney. Charles's card is shown to Evonne. Rodney's card is shown to Charles. Mariano's card is shown to Mariano. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Mariano can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rodney","Evonne","Charles","Mariano"],"index":62883,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9846108556,"difficulty":0.0153891444}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lanny's card is shown to Lanny. Robin's card is shown to Lanny. Robert's card is shown to Lanny. Robert's card is shown to Robin. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Robin does not know whether Robin picked a red card. It is publicly announced that Lanny knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Robert can now know whether Lanny picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lanny","Robin","Robert"],"index":6119,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7439305782,"difficulty":1.7439305782}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Robin's forehead is muddy. It is publicly announced that Robin knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Robin can now know whether John can know that Robin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robin","John"],"index":67353,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8326535225,"difficulty":0.1673464775}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kaila does not know whether Josephine is thirsty. It is publicly announced that Rebecca knows whether Rebecca is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Rebecca can now know that Josephine can know that Josephine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kaila","Josephine","Shanna","Rebecca"],"index":30827,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9791792631,"difficulty":0.0208207369}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is thirsty. It is publicly announced that Jessie knows whether Jessie is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gina can now know whether Gina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessie","James","Gina","Mildred"],"index":48610,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9932749271,"difficulty":0.0067250729}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Wanda knows whether Grace's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Grace can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Miguel","Wanda","Grace","Emma"],"index":28988,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997714162,"difficulty":0.0002285838}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Guillermo knows whether Guillermo is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Katherine can now know that Gabriel can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Guillermo","Gabriel","Katherine","William"],"index":34861,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997652173,"difficulty":0.0002347827}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Brenda knows whether or not nobody's forehead is muddy. It is publicly announced that Carrie knows whether Raquel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Thomas can now know whether Carrie can know whether Brenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Brenda","Raquel","Carrie"],"index":53745,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996892214,"difficulty":0.0003107786}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"David can now know that Mark can know that Mark is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Mark","David","Nancy"],"index":39275,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9320761561,"difficulty":0.0679238439}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cheryl can now know that Jennifer can know whether Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bernice","Jennifer","Cheryl"],"index":40868,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995540977,"difficulty":0.0004459023}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Roger can know that Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Roger","Debra","Paul"],"index":3086,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9903323054,"difficulty":0.0096676946}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vickie knows whether or not nobody's forehead is muddy. It is publicly announced that Daryl's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Virginia can now know whether Daryl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Vickie","Virginia","Daryl"],"index":53916,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997492433,"difficulty":0.0002507567}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Brad can now know that Betty can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sheila","Brad","Betty","Joshua"],"index":29707,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984871149,"difficulty":0.0015128851}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Pauline. Pauline's card is shown to Walter. Patricia's card is shown to Walter. Walter's card is shown to Walter. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pauline can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pauline","Patricia","Walter"],"index":66464,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997716546,"difficulty":0.0002283454}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis does not know whether or not everyone is thirsty. It is publicly announced that Justin knows whether Dennis is thirsty. It is publicly announced that Justin is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Dennis can now know that Justin can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Justin","Dennis"],"index":980,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962303042,"difficulty":0.0037696958}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janie does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mary can now know whether Janie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Janie","Marilyn"],"index":44862,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997113347,"difficulty":0.0002886653}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harriett's card is shown to Delphia. Harriett's card is shown to Alma. Alma's card is shown to Harriett. Harriett's card is shown to Harriett. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alma can now know that Delphia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Delphia","Alma","Harriett"],"index":20096,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981081486,"difficulty":0.0018918514}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy. It is publicly announced that Willie does not know whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mary can now know whether William can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Micheal","Mary","Willie","William"],"index":63916,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6935562491,"difficulty":1.6935562491}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Betty is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Betty can now know that Mary can know that Julie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Julie","Mary"],"index":48791,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981206059,"difficulty":0.0018793941}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Sharon. Rita's card is shown to Sharon. Carl's card is shown to Carl. Rita's card is shown to Carl. Sharon's card is shown to Jerry. Carl's card is shown to Rita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know whether Carl can know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Carl","Jerry","Rita"],"index":38327,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8999449015,"difficulty":0.1000550985}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ray can now know that Dennis can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Dennis","Ray","John"],"index":5513,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995549321,"difficulty":0.0004450679}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rebecca does not know whether Geneva is thirsty. It is publicly announced that Geneva knows whether Geneva is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robert can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rebecca","Robert","Geneva"],"index":66537,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.996989727,"difficulty":0.003010273}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Timothy. Delilah's card is shown to Delilah. Linda's card is shown to Delilah. Delilah's card is shown to Eugene. Timothy's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Delilah picked a black card. It is publicly announced that Delilah does not know whether Timothy picked a red card. It is publicly announced that Delilah knows whether someone picked a red card. It is publicly announced that Delilah does not know whether Timothy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Timothy can now know that Delilah can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Delilah","Eugene","Linda"],"index":36847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997820258,"difficulty":0.0002179742}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wanda does not know whether Donald is thirsty. It is publicly announced that Michael is thirsty. It is publicly announced that Donald knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Donald can now know that Wanda can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wanda","Michael","Donald"],"index":60069,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9684975743,"difficulty":1.9684975743}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tyra knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know whether Tyra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Tyra","Mary","Margaret"],"index":41403,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995107651,"difficulty":0.0004892349}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Bret can now know that Steven can know whether Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Kayla","Bret","Ora"],"index":4592,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996786118,"difficulty":0.0003213882}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Rex. Bradley's card is shown to Ashley. Tamara's card is shown to Ashley. Rex's card is shown to Bradley. Ashley's card is shown to Bradley. Ashley's card is shown to Tamara. Bradley's card is shown to Tamara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bradley can now know that Tamara can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rex","Ashley","Bradley","Tamara"],"index":26521,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997139573,"difficulty":0.0002860427}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackie's forehead is not muddy. It is publicly announced that Jesse knows whether Jackie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jackie can now know that Ashley can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","Jesse","Ashley"],"index":55173,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997294545,"difficulty":0.0002705455}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ida does not know whether Ruth is thirsty. It is publicly announced that Ida does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Ruth can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Ruth","Ida","James"],"index":66638,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99626261,"difficulty":0.00373739}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Virginia. Florence's card is shown to Clarence. Florence's card is shown to Florence. Virginia's card is shown to Renee. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Virginia can now know that Clarence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Clarence","Florence","Renee"],"index":11581,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980917573,"difficulty":0.0019082427}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Tina is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Tina knows whether George is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Tina can now know whether George can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tina","George"],"index":48963,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997772574,"difficulty":0.0002227426}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clyde knows whether Andy's forehead is muddy. It is publicly announced that Clyde's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Andy can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jessie","Andy","Clyde"],"index":42067,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997606874,"difficulty":0.0002393126}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn knows whether Shawn's forehead is muddy. It is publicly announced that Michael knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Shawn","Michael","Amanda"],"index":36585,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971908927,"difficulty":0.0028091073}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teri knows whether or not nobody's forehead is muddy. It is publicly announced that Steven's forehead is muddy. It is publicly announced that Kara does not know whether or not everyone's forehead is muddy. It is publicly announced that Kara's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agentc knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Steven can now know whether Jill's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kara","Teri","Steven","Jill"],"index":28915,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992426634,"difficulty":0.0007573366}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caren's card is shown to Kathryn. Kathryn's card is shown to Bessie. Bessie's card is shown to Bessie. Kathryn's card is shown to Margaret. Bessie's card is shown to Margaret. Kathryn's card is shown to Caren. Caren's card is shown to Caren. It is publicly announced that someone picked a red card. It is publicly announced that Bessie picked a black card. It is publicly announced that Bessie does not know whether Caren picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Bessie can now know that Margaret can know whether Caren picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathryn","Bessie","Margaret","Caren"],"index":30300,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9215990305,"difficulty":1.9215990305}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie does not know whether Willie's forehead is muddy. It is publicly announced that Willie does not know whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Willie can now know that Duane can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Soledad","Willie","Duane"],"index":4431,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8495799303,"difficulty":0.1504200697}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amy","Aurore","William"],"index":10094,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999750793,"difficulty":0.000249207}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Bunny can now know that Larry can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bunny","Larry","Sara","Joann"],"index":35852,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9716288447,"difficulty":0.0283711553}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Robert does not know whether Sandi is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Robert can now know whether Sandi can know whether Sandi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sandi","Robert"],"index":29600,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9967335463,"difficulty":0.0032664537}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jacqueline can now know whether Flavia can know that Flavia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacqueline","Veronica","Flavia","Dennis"],"index":6461,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.648383677,"difficulty":0.351616323}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know that Paula can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Marion","Paula"],"index":40077,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983410835,"difficulty":0.0016589165}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty does not know whether Jose is thirsty. It is publicly announced that Brian does not know whether Jose is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Brian can now know whether Betty can know that Jose is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Brian","Jose"],"index":31818,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9916701317,"difficulty":0.0083298683}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"David can now know whether Dorothy can know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","James","Dorothy"],"index":39796,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5859697461,"difficulty":0.4140302539}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Horacio knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Miguel can now know that Harold can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Horacio","Miguel","Patricia","Harold"],"index":23129,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984710813,"difficulty":0.0015289187}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Krista does not know whether or not everyone's forehead is muddy. It is publicly announced that Krista does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"John can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Krista"],"index":7281,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5209698081,"difficulty":0.4790301919}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Lois. Lois's card is shown to Juliette. Jeffrey's card is shown to Juliette. Jeffrey's card is shown to Frank. Lois's card is shown to Jeffrey. Juliette's card is shown to Jeffrey. Frank's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juliette can now know whether Jeffrey can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lois","Juliette","Frank","Jeffrey"],"index":21544,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997783303,"difficulty":0.0002216697}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori knows whether Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Cora can now know that Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edwin","David","Lori","Cora"],"index":13189,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9972922206,"difficulty":1.9972922206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Effie can now know whether Pedro can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Effie","Tarsha","Pedro","Pauline"],"index":13293,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976254106,"difficulty":0.0023745894}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Edith can now know whether William can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Edith","Mary","Lula"],"index":26262,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roosevelt does not know whether Renaldo is thirsty. It is publicly announced that Leo does not know whether Thea is thirsty. It is publicly announced that Renaldo knows whether Renaldo is thirsty. It is publicly announced that Renaldo knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Roosevelt can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Renaldo","Thea","Leo","Roosevelt"],"index":1598,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5059660077,"difficulty":1.5059660077}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrel knows whether Ralph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Ralph can now know that Deborah can know that Darrel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Deborah","Ralph","Darrel"],"index":50353,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985311031,"difficulty":0.0014688969}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruthie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ruthie can now know that Cassie can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruthie","Edward","Mary","Cassie"],"index":45443,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983438253,"difficulty":0.0016561747}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Joanne can now know that Chris can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Judith","Chris","Joan","Joanne"],"index":33364,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998337388,"difficulty":0.001662612}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Frances can now know that Stacie can know that Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Eric","Stacie","Frances"],"index":55221,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6936942935,"difficulty":0.3063057065}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Henry can now know that Thomas can know that Henry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Thomas","Jared","Ted"],"index":32886,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981001019,"difficulty":0.0018998981}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcus knows whether someone's forehead is muddy. It is publicly announced that Marcus's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] 0","hypothesis":"Alma can now know that Marcus can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marcus","Alma","Natalie"],"index":5300,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6733879447,"difficulty":1.6733879447}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Kathi's forehead is muddy. It is publicly announced that Patricia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Kathi can now know that Patricia can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathi","Patricia","Wilma"],"index":60549,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984503984,"difficulty":0.0015496016}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Octavia's card is shown to Robert. Victor's card is shown to Victor. Robert's card is shown to Octavia. Octavia's card is shown to Octavia. It is publicly announced that someone picked a red card. It is publicly announced that Victor does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Victor","Octavia","Helen"],"index":18440,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Don knows whether Judith is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Judith knows whether Judith is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Judith can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Don","Judith"],"index":56958,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985779524,"difficulty":0.0014220476}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanette's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeanette","Louis","Michael","Elsie"],"index":55178,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9956521392,"difficulty":0.0043478608}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Robert does not know whether Gloria is thirsty. It is publicly announced that Gloria knows whether Gloria is thirsty. It is publicly announced that Gloria knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Robert can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gloria","Robert"],"index":19647,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Veronica knows whether or not everyone is thirsty. It is publicly announced that Veronica knows whether Belinda is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Belinda can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Belinda","Veronica"],"index":32982,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997330308,"difficulty":0.0002669692}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether someone's forehead is muddy. It is publicly announced that Veronica does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Brittany can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Veronica","Brittany","Robert"],"index":764,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9687430859,"difficulty":0.0312569141}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether someone's forehead is muddy. It is publicly announced that Jane knows whether Jane's forehead is muddy. It is publicly announced that Marylou knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Shirley can now know that Jane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jane","Shirley","Marylou"],"index":59631,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9942435622,"difficulty":0.0057564378}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Launa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Richard can now know that Travis can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Travis","Launa","Richard"],"index":27765,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985035658,"difficulty":0.0014964342}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether or not everyone is thirsty. It is publicly announced that Margaret does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"David can now know whether Ruth can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","David","Ruth"],"index":45357,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alex knows whether Phillip's forehead is muddy. It is publicly announced that Alex knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Adam can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Adam","Phillip","Alex"],"index":62575,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997261167,"difficulty":0.0002738833}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monique is thirsty. It is publicly announced that Lucille knows whether Lucille is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether 1) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Monique can now know that Darryl is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lucille","Darryl","Marie","Monique"],"index":25280,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9727905989,"difficulty":0.0272094011}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Denny knows whether Denny is thirsty. It is publicly announced that Mary knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Mary can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Edwin","Denny"],"index":27659,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alice does not know whether Mathew is thirsty. It is publicly announced that Elias is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Elias can now know that Priscilla can know that Alice is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Priscilla","Elias","Alice","Mathew"],"index":47826,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9859284759,"difficulty":0.0140715241}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sue can now know whether Travis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sue","Agnes","Travis","Jed"],"index":10421,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997369647,"difficulty":0.0002630353}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Matthew can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Emily","Liz"],"index":17877,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977255464,"difficulty":0.0022744536}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catalina's card is shown to Robert. Robert's card is shown to Catalina. Catalina's card is shown to Catalina. Catalina's card is shown to Sheila. Sheila's card is shown to Sheila. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Catalina can now know whether Sheila picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Catalina","Sheila"],"index":47218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7283701301,"difficulty":0.2716298699}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ken's card is shown to Ken. Ken's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Ken knows whether or not nobody picked a red card. It is publicly announced that Ken does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ken","Robert","Marcia","John"],"index":13114,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6395909786,"difficulty":0.3604090214}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alvin's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Alvin"],"index":20186,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997773767,"difficulty":0.0002226233}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Gordon can now know that Joyce can know whether Randy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gordon","Joyce","Randy"],"index":8078,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997219443,"difficulty":0.0002780557}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Asia knows whether Thelma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Thelma can now know whether David can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thelma","Asia","Joseph","David"],"index":10774,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6995763779,"difficulty":0.3004236221}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Kathy can now know that Jose can know that Kathy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathy","Frank","Jose"],"index":12980,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9960362315,"difficulty":0.0039637685}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Debbie can now know that Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Yan","Rebecca","Debbie"],"index":17222,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7634779215,"difficulty":0.2365220785}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bret does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Patrick can now know that Bradley can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bret","Bradley","Odell","Patrick"],"index":2609,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9628826976,"difficulty":0.0371173024}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Lindsay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Lindsay can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lindsay","John","Denise","Vicki"],"index":5214,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982628226,"difficulty":0.0017371774}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Teresa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jennifer can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Teresa","Mary"],"index":5120,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982795715,"difficulty":0.0017204285}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joann's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Joann can now know whether Patrick can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patrick","Joann"],"index":33896,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997829795,"difficulty":0.0002170205}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jay does not know whether Brittany is thirsty. It is publicly announced that Ruth does not know whether or not everyone is thirsty. It is publicly announced that Jay does not know whether Carolyn is thirsty. It is publicly announced that Brittany knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jay can now know whether Carolyn can know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brittany","Jay","Ruth","Carolyn"],"index":53007,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9158810973,"difficulty":1.9158810973}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Rene can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sarah","George","Rene","Katherine"],"index":66723,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Elizabeth's forehead is muddy. It is publicly announced that Elizabeth knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Mary can now know that William can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","John","Elizabeth","William"],"index":28789,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995475411,"difficulty":0.0004524589}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antoinette's forehead is muddy. It is publicly announced that Frances does not know whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Frances can now know that Scott can know that Antoinette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frances","Scott","Antoinette"],"index":5508,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6750786304,"difficulty":1.6750786304}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Clarence knows whether someone is thirsty. It is publicly announced that Sue does not know whether Clarence is thirsty. It is publicly announced that Sue knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Laura can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Laura","Sue","Clarence"],"index":34669,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997826219,"difficulty":0.0002173781}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kurtis does not know whether Andrew is thirsty. It is publicly announced that Tiffiny does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Kerri can now know whether Kerri is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tiffiny","Andrew","Kerri","Kurtis"],"index":6692,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9981585145,"difficulty":0.0018414855}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joann knows whether Merrill is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Merrill can now know that Joann can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Merrill","Joann"],"index":23528,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997062087,"difficulty":0.0002937913}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy knows whether Alexander's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Jimmy can now know whether Alexander can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alexander","Jimmy"],"index":5448,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyle knows whether or not everyone's forehead is muddy. It is publicly announced that Kyle's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 1 ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Milton can now know that Kyle can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kyle","Milton"],"index":36924,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997531772,"difficulty":0.0002468228}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nellie's forehead is not muddy. It is publicly announced that Guadalupe knows whether Nellie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Guadalupe can now know whether Kelly can know whether Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nellie","Guadalupe","Kelly"],"index":18619,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5657004118,"difficulty":1.5657004118}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lindsey's card is shown to Matthew. Bernadine's card is shown to Matthew. Lindsey's card is shown to Lindsey. It is publicly announced that someone picked a red card. It is publicly announced that Matthew does not know whether Paige picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Matthew can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Lindsey","Bernadine","Paige"],"index":48203,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9920626283,"difficulty":0.0079373717}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura is thirsty. It is publicly announced that Dale knows whether Dale is thirsty. It is publicly announced that Laura does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Nancy can now know whether Dale is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dale","Laura","Nancy","Michael"],"index":14702,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8196800351,"difficulty":1.8196800351}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Val knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Iris can now know that Milton can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Milton","David","Iris","Val"],"index":14429,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984089732,"difficulty":0.0015910268}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Cynthia can now know that Jake can know whether Della's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jake","Della","Cynthia"],"index":38855,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997436404,"difficulty":0.0002563596}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Richard's card is shown to Douglas. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Douglas can now know whether Richard can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Douglas"],"index":34569,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.996049583,"difficulty":0.003950417}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Marianne's card is shown to Christopher. Marianne's card is shown to Marianne. It is publicly announced that someone picked a red card. It is publicly announced that Marianne knows whether or not nobody picked a red card. It is publicly announced that Marianne does not know whether Christopher picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Christopher can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Marianne"],"index":41379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9890489578,"difficulty":0.0109510422}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacqueline does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Dorothy can now know whether Michael can know whether Jacqueline is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Michael","Homer","Jacqueline"],"index":53374,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988476038,"difficulty":0.0011523962}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Imelda's card is shown to Juan. Marcella's card is shown to Thomas. Thomas's card is shown to Imelda. Marcella's card is shown to Imelda. Juan's card is shown to Marcella. Thomas's card is shown to Marcella. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marcella can now know that Juan can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juan","Thomas","Imelda","Marcella"],"index":11459,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6766174436,"difficulty":1.6766174436}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deidre does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Deidre can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Deidre","Carlton"],"index":21267,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960436821,"difficulty":0.0039563179}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Michael can now know that Carol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jimmy","Charles","Carol","Michael"],"index":50361,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984011054,"difficulty":0.0015988946}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Brenda does not know whether David picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Brenda can now know whether David can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brenda","David"],"index":45662,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994910955,"difficulty":0.0005089045}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anita's card is shown to Carol. Caleb's card is shown to Caleb. John's card is shown to John. John's card is shown to Anita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Caleb can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Caleb","John","Anita"],"index":57628,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christine does not know whether Betty is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Betty can now know whether Richard can know whether Betty is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christine","Isabelle","Betty","Richard"],"index":59883,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988710284,"difficulty":0.0011289716}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stefanie does not know whether Stefanie's forehead is muddy. It is publicly announced that Stefanie does not know whether Stefanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Alexander can now know that Stefanie can know whether Alexander's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Stefanie","Alexander"],"index":57821,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.994595468,"difficulty":0.005404532}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know whether Vincent can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pauline","Calvin","Dorothy","Vincent"],"index":40447,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997705817,"difficulty":0.0002294183}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. William's card is shown to Anthony. Anthony's card is shown to Bennie. Bennie's card is shown to Bennie. Bennie's card is shown to Tracy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bennie can now know that Anthony can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","William","Bennie","Tracy"],"index":65118,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976434112,"difficulty":0.0023565888}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenn knows whether Julie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Donald can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Glenn","Julie"],"index":16908,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998270154,"difficulty":0.001729846}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dean is thirsty. It is publicly announced that Timothy does not know whether Michael is thirsty. It is publicly announced that Timothy does not know whether Annette is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentd knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dean can now know that Michael can know that Timothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Annette","Michael","Dean"],"index":18064,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9627023339,"difficulty":0.0372976661}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Bernard can now know whether Bernard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Delana","Bernard","Theodore"],"index":680,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994654059,"difficulty":0.0005345941}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Courtney does not know whether or not everyone's forehead is muddy. It is publicly announced that Courtney does not know whether or not everyone's forehead is muddy. It is publicly announced that Davina knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Courtney can now know that Davina can know whether Davina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Davina","Courtney"],"index":45708,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7052916288,"difficulty":0.2947083712}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Herbert's card is shown to William. Ruth's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Herbert","Ruth","Dominick"],"index":64669,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9887825847,"difficulty":0.0112174153}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Glenda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Esteban can now know that Glenda can know that Esteban is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Esteban","Glenda","Amy","Jorge"],"index":45691,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.878372848,"difficulty":0.121627152}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda knows whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Linda can now know whether Linda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Victoria","Jodi","Henry"],"index":44388,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982985854,"difficulty":0.0017014146}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ada does not know whether Ada's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Theodore can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Theodore","Ada","Jennifer"],"index":54965,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9844719768,"difficulty":0.0155280232}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marina's card is shown to Gaylene. Marina's card is shown to David. Marina's card is shown to Marina. Herbert's card is shown to Herbert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that Herbert can know whether Herbert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gaylene","David","Marina","Herbert"],"index":32319,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7261019349,"difficulty":1.7261019349}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sylvia can now know whether Constance can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Constance","Charles","Sylvia","Jeffrey"],"index":45003,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996117949,"difficulty":0.0003882051}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hazel's card is shown to Robert. Loretta's card is shown to Hattie. Robert's card is shown to Loretta. Hattie's card is shown to Loretta. Loretta's card is shown to Loretta. Hazel's card is shown to Loretta. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Hattie","Loretta","Hazel"],"index":11881,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8492438197,"difficulty":1.8492438197}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Raymond does not know whether Tamika is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Samuel can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tamika","Raymond","Samuel","Steven"],"index":5757,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.944945693,"difficulty":1.944945693}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether Kimberly's forehead is muddy. It is publicly announced that Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Kimberly can now know that Gregory can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lee","Gregory","Kimberly"],"index":2343,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984765649,"difficulty":0.0015234351}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Allison can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Allison","Jose"],"index":23365,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986275434,"difficulty":0.0013724566}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie knows whether Elsie's forehead is muddy. It is publicly announced that Elsie knows whether Rodney's forehead is muddy. It is publicly announced that Marie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agenta knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Rodney can now know that Elsie can know that Elsie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rodney","Elsie","Marie"],"index":63232,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9868053198,"difficulty":0.0131946802}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward does not know whether Edward's forehead is muddy. It is publicly announced that Donald knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Edward can now know whether Donald can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Edward","Donald"],"index":6329,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9968660474,"difficulty":1.9968660474}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Lena can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Albert","Virginia","Lena"],"index":28225,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985829592,"difficulty":0.0014170408}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Mary. Terry's card is shown to Terry. Terry's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Terry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Timothy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Terry","Timothy"],"index":8167,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997262359,"difficulty":0.0002737641}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rafael does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Emma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Rafael can now know that Rafael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Linda","Emma","Rafael"],"index":36548,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5194132924,"difficulty":0.4805867076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leatha does not know whether Debra is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Leatha can now know whether Debra can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leatha","Lucy","Debra","Beverly"],"index":43349,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997801185,"difficulty":0.0002198815}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alvaro's card is shown to Richard. Richard's card is shown to Karen. Karen's card is shown to Karen. Carla's card is shown to Karen. Alvaro's card is shown to Karen. Karen's card is shown to Carla. Richard's card is shown to Alvaro. It is publicly announced that someone picked a red card. It is publicly announced that Carla does not know whether Richard picked a red card. It is publicly announced that Richard knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Karen can now know whether Alvaro can know that Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Karen","Carla","Alvaro"],"index":13177,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9522621632,"difficulty":0.0477378368}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know that Alicia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Denise","Jose","Douglas","Alicia"],"index":43317,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985799789,"difficulty":0.0014200211}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Richard can now know whether Ola can know that Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Jennifer","Ola","Richard"],"index":54651,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996783733,"difficulty":0.0003216267}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that Edmond's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Matthew can now know whether Edmond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Edmond","Matthew"],"index":6811,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997162223,"difficulty":0.0002837777}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Marilyn. Sarah's card is shown to Marilyn. Marilyn's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Katherine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marilyn","Katherine","Sarah"],"index":23304,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984429479,"difficulty":0.0015570521}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cristina knows whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Nicole can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cristina","Susan","Nicole"],"index":45849,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985217452,"difficulty":0.0014782548}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eduardo's card is shown to Eduardo. Russell's card is shown to Lois. Lois's card is shown to Russell. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Russell can now know whether Lois can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eduardo","Lois","Russell"],"index":55059,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9135151505,"difficulty":0.0864848495}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vivian does not know whether Vivian's forehead is muddy. It is publicly announced that Vivian does not know whether Vivian's forehead is muddy. It is publicly announced that Vivian knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Mark can now know whether Vivian can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mark","Vivian"],"index":25651,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997114539,"difficulty":0.0002885461}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Danielle can now know that James can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","James","Danielle"],"index":47305,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984203577,"difficulty":0.0015796423}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rochelle does not know whether Summer is thirsty. It is publicly announced that Leonardo does not know whether Thomas is thirsty. It is publicly announced that Leonardo does not know whether Summer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Summer can now know that Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leonardo","Summer","Thomas","Rochelle"],"index":9934,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9944682121,"difficulty":0.0055317879}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether Barb's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Barb can now know that Cecil's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barb","Margaret","Ashley","Cecil"],"index":48440,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998288691,"difficulty":0.001711309}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carrie's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether Carrie picked a red card. It is publicly announced that Jeffrey does not know whether Jeffrey picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jeffrey can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jeffrey","Carrie"],"index":53033,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986079335,"difficulty":0.0013920665}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Fritz's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sandra can now know whether Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Douglas","Fritz","Sandra"],"index":62923,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9972417355,"difficulty":0.0027582645}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eugene","John"],"index":59406,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998462677,"difficulty":0.001537323}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mckinley does not know whether Mckinley's forehead is muddy. It is publicly announced that Miriam knows whether or not nobody's forehead is muddy. It is publicly announced that Miriam knows whether Miriam's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Mckinley can now know whether Mckinley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mckinley","Miriam"],"index":21430,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.804680407,"difficulty":1.804680407}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathy's card is shown to Terry. Larry's card is shown to Kathy. Terry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Kathy does not know whether or not everyone picked a red card. It is publicly announced that Kathy knows whether Larry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Larry can now know whether Larry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Terry","Kathy","Larry"],"index":48641,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9877912998,"difficulty":0.0122087002}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Magdalena's card is shown to Elton. Elton's card is shown to Erick. Erick's card is shown to Erick. Magdalena's card is shown to Erick. It is publicly announced that someone picked a red card. It is publicly announced that Magdalena picked a black card. It is publicly announced that Magdalena picked a black card. It is publicly announced that Elton does not know whether Erick picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Elton can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elton","Erick","Magdalena"],"index":32316,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979012012,"difficulty":0.0020987988}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amelia knows whether Amelia's forehead is muddy. It is publicly announced that Amelia knows whether Amelia's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Amelia can now know whether Jack can know whether Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jacqueline","Amy","Amelia","Jack"],"index":25310,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995445609,"difficulty":0.0004554391}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Elizabeth can now know whether Sarah can know that Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sarah","Kimberly","Elizabeth","Marcus"],"index":55904,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994995594,"difficulty":0.0005004406}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Cindy's card is shown to Michael. Alfred's card is shown to Michael. Ralph's card is shown to Michael. Cindy's card is shown to Cindy. Michael's card is shown to Alfred. Michael's card is shown to Ralph. Alfred's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Alfred does not know whether Alfred picked a red card. It is publicly announced that Michael knows whether Alfred picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Alfred can now know that Alfred picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Cindy","Alfred","Ralph"],"index":22782,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9604175687,"difficulty":0.0395824313}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Susan can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathleen","Andres","Susan","Jason"],"index":5972,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99957937,"difficulty":0.00042063}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brett knows whether Sheilah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sarah can now know that Brett can know whether Brett's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brett","Sheilah","Sarah"],"index":13897,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995509982,"difficulty":0.0004490018}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Roberto can now know that Roberto's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Bernice","Jennifer","Roberto"],"index":7038,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981204867,"difficulty":0.0018795133}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Joanne. Joanne's card is shown to Scott. Scott's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Scott knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joanne does not know whether Scott picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Joanne can now know whether Scott can know that Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joanne","Scott"],"index":25170,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9447675347,"difficulty":1.9447675347}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin's forehead is muddy. It is publicly announced that Walter knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Justin can now know whether Harry can know that Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bessie","Harry","Justin","Walter"],"index":53734,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996943474,"difficulty":0.0003056526}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether Marilyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Marilyn can now know that Miriam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marilyn","Brenda","Miriam","Rachel"],"index":26524,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998380661,"difficulty":0.001619339}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Gladys. Gladys's card is shown to Jose. Gladys's card is shown to Gregory. Jose's card is shown to Gregory. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jose can now know that Gladys can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gladys","Jose","Gregory"],"index":14578,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carole's card is shown to Carole. Carole's card is shown to Karen. Karen's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Karen knows whether Karen picked a red card. It is publicly announced that Carole does not know whether Karen picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Carole can now know whether Carole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Carole","Karen"],"index":46585,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9936170578,"difficulty":0.0063829422}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas knows whether someone is thirsty. It is publicly announced that Leah does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Thomas can now know whether Leah can know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Leah"],"index":60279,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982953668,"difficulty":0.0017046332}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jason can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Melissa","James","Jason"],"index":34930,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997437596,"difficulty":0.0002562404}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dina's card is shown to Dina. Robert's card is shown to Dina. Dina's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Robert can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dina","Robert"],"index":18972,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9972533584,"difficulty":0.0027466416}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Floyd's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Floyd can now know whether Floyd's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Floyd","Christie"],"index":31820,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6742212772,"difficulty":1.6742212772}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shiela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Katheryn can now know whether Larry can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Timothy","Katheryn","Shiela"],"index":64040,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997807145,"difficulty":0.0002192855}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin does not know whether Dennis is thirsty. It is publicly announced that Justin does not know whether Avril is thirsty. It is publicly announced that Justin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] 0","hypothesis":"Justin can now know that Dennis can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Justin","Dennis","Avril"],"index":65715,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5694742203,"difficulty":0.4305257797}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Angel can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angel","Carl","Iris","Rosa"],"index":39858,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983055592,"difficulty":0.0016944408}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gayle's forehead is not muddy. It is publicly announced that Gayle knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Gayle can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elise","George","Sondra","Gayle"],"index":17817,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8479378223,"difficulty":1.8479378223}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Elaine can now know whether Brady can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elaine","Robbie","Brady"],"index":4753,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997193217,"difficulty":0.0002806783}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Gregory can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Claire","Ima","Gregory","Adrian"],"index":52481,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999709785,"difficulty":0.000290215}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] 0","hypothesis":"Bobbi can now know whether Mica can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bobbi","Mica"],"index":59199,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gilda can now know that Rhonda can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rhonda","Billie","Gilda","Shawna"],"index":22291,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997528195,"difficulty":0.0002471805}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether Kristy is thirsty. It is publicly announced that George knows whether George is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Kristy can now know whether Anthony can know whether Anthony is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Kristy","Michael","George"],"index":56989,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983302951,"difficulty":0.0016697049}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard knows whether or not nobody is thirsty. It is publicly announced that Francisco does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Francisco can now know whether Donald can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Francisco","Richard"],"index":64530,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977930784,"difficulty":0.0022069216}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lane knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Elvira can now know that Elvira is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lane","Linda","Bambi","Elvira"],"index":26686,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9463844299,"difficulty":0.0536155701}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Manuel can now know that Brian can know that Chad's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Manuel","Chad","Brian","Marlene"],"index":57820,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963738322,"difficulty":0.0036261678}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Silvia's card is shown to Leo. Leo's card is shown to Charles. Silvia's card is shown to Charles. Leo's card is shown to Silvia. It is publicly announced that someone picked a red card. It is publicly announced that Leo does not know whether Leo picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Charles can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leo","Charles","Silvia"],"index":29992,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986311793,"difficulty":0.0013688207}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Florence can now know whether Donna can know that Donna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","Donna","Charles"],"index":5496,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9286661744,"difficulty":0.0713338256}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that Eulalia knows whether Eulalia is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Juan can now know whether Eulalia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Eulalia","Mildred","Juan"],"index":19444,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7235688567,"difficulty":1.7235688567}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Dorothy can now know that John can know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Tracie","John","Dorothy"],"index":43823,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971516728,"difficulty":0.0028483272}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lino knows whether or not everyone's forehead is muddy. It is publicly announced that Rachael knows whether Lino's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Lino can now know whether Rachael can know that Lino's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lino","Rachael"],"index":47117,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995318651,"difficulty":0.0004681349}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Stanley's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Alejandra can now know that Stanley can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alejandra","Stanley"],"index":39399,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985340834,"difficulty":0.0014659166}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharlene's forehead is not muddy. It is publicly announced that Luis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Luis can now know whether Sharlene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eugenia","Sharlene","Luis","Esther"],"index":41044,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995225668,"difficulty":0.0004774332}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Lonnie. Pedro's card is shown to Pedro. Kenneth's card is shown to Pedro. Bert's card is shown to Bert. Lonnie's card is shown to Kenneth. Pedro's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Bert picked a red card. It is publicly announced that Pedro picked a black card. It is publicly announced that Pedro knows whether Kenneth picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Bert can now know that Pedro can know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lonnie","Pedro","Bert","Kenneth"],"index":19071,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7950390577,"difficulty":1.7950390577}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ray's card is shown to Lesley. Lesley's card is shown to Ray. Ray's card is shown to Ray. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Ray can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lesley","Ray"],"index":25688,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997534156,"difficulty":0.0002465844}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Opal knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Opal can now know whether Geri can know whether Geri's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Geri","Cathy","Diane","Opal"],"index":1147,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5949031711,"difficulty":1.5949031711}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly does not know whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kelly can now know whether Linda can know whether Kelly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelly","Mary","Linda"],"index":31578,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9981248975,"difficulty":0.0018751025}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilma's card is shown to Wilma. Steve's card is shown to Wilma. Wilma's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Wilma knows whether Wilma picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Steve can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wilma","Steve"],"index":32645,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9451220036,"difficulty":0.0548779964}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Michelle knows whether Anthony is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Edwin can now know whether Charles can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Anthony","Edwin","Charles"],"index":9655,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973019361,"difficulty":0.0026980639}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know that Riley is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Sarah","Jennifer","Riley"],"index":13930,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985901713,"difficulty":0.0014098287}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy. It is publicly announced that Joyce's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Joseph can now know that Joyce can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emil","Joseph","Joyce"],"index":51183,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Richard. Kevin's card is shown to Kevin. Michael's card is shown to Kevin. Richard's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Kevin can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Kevin","Michael"],"index":36413,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.996776998,"difficulty":0.003223002}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Toby does not know whether or not everyone is thirsty. It is publicly announced that Margaret does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Toby can now know that Patricia can know that Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Toby","Patricia","Margaret"],"index":29073,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.74091506,"difficulty":1.74091506}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clyde's forehead is not muddy. It is publicly announced that Jeff's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Clyde can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Antonio","Jeff","Clyde"],"index":28375,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997783303,"difficulty":0.0002216697}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Keri's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] 0","hypothesis":"Todd can now know that Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Todd","Huey","Keri","Nancy"],"index":47632,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967986345,"difficulty":0.0032013655}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Walter can now know whether Rick can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Walter","Helen","Rick"],"index":33486,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99978441,"difficulty":0.00021559}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Andrew. Andrew's card is shown to Sherry. Helen's card is shown to Sherry. Sherry's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Sherry knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Andrew can now know whether Sherry can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Sherry","Helen"],"index":33937,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999714911,"difficulty":0.000285089}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Earl can now know that Angela can know whether Jackson's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","Jackson","Earl","Mary"],"index":29673,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996102452,"difficulty":0.0003897548}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alex does not know whether Neil is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Carol is thirsty. It is publicly announced that Alex knows whether Carol is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Alex can now know that Carol is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Carol","Alex","Neil"],"index":65638,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9514074326,"difficulty":1.9514074326}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffery's card is shown to Jeffery. Jeffery's card is shown to Ralph. Samantha's card is shown to Ralph. Ralph's card is shown to Samantha. Jeffery's card is shown to Stanley. Samantha's card is shown to Stanley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffery can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffery","Ralph","Samantha","Stanley"],"index":56174,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Antoinette. Rita's card is shown to Antoinette. Antoinette's card is shown to Claudine. Michael's card is shown to Claudine. Michael's card is shown to Michael. Antoinette's card is shown to Rita. Michael's card is shown to Rita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Claudine can now know whether Rita can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Antoinette","Claudine","Michael","Rita"],"index":2447,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Williams knows whether someone's forehead is muddy. It is publicly announced that Williams knows whether someone's forehead is muddy. It is publicly announced that Williams knows whether someone's forehead is muddy. It is publicly announced that Williams knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Faye can now know whether Williams's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Williams","John","Faye"],"index":49588,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997082353,"difficulty":0.0002917647}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Silvia knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Aaron can now know whether Silvia can know whether Penny is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Silvia","Aaron","Penny"],"index":35934,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998788774,"difficulty":0.001211226}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy. It is publicly announced that Ninfa does not know whether Ninfa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rudolph can now know that Rudolph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ninfa","Rudolph","Patricia"],"index":44600,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9931957722,"difficulty":1.9931957722}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth does not know whether Del is thirsty. It is publicly announced that Brain does not know whether Del is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Kathryn can now know whether Del can know whether Ruth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Kathryn","Brain","Del"],"index":57414,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998667717,"difficulty":0.001332283}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joann knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Joann can now know whether Warren can know that Joann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Warren","Joann"],"index":6402,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992120266,"difficulty":0.0007879734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Dorothy can know whether Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Christopher","William","Dorothy"],"index":7933,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6942027807,"difficulty":0.3057972193}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Guadalupe. Guadalupe's card is shown to Katherine. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that Guadalupe knows whether Katherine picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Katherine can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Guadalupe","Katherine"],"index":32108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edith does not know whether or not everyone is thirsty. It is publicly announced that Edith does not know whether or not everyone is thirsty. It is publicly announced that Andrea knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Edith can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Andrea","Edith"],"index":13955,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997225404,"difficulty":0.0002774596}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Margaret can now know that Pauline can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffery","Margaret","Pauline","George"],"index":46678,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999779284,"difficulty":0.000220716}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Ernestine can now know whether Edward is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edward","Ernestine"],"index":13182,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9742621779,"difficulty":0.0257378221}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leroy does not know whether or not everyone is thirsty. It is publicly announced that Leroy does not know whether Kristine is thirsty. It is publicly announced that Marvin knows whether Marvin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kristine can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marvin","Joseph","Kristine","Leroy"],"index":28833,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998414278,"difficulty":0.001585722}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernard knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Michael can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bernard","Michael"],"index":16074,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997163415,"difficulty":0.0002836585}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Noelle can now know whether Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Noelle","David","Ruth","Sharon"],"index":38878,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997358918,"difficulty":0.0002641082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karyn is thirsty. It is publicly announced that Sophie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that Sophie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sophie","Karyn","Theresa","Robert"],"index":3932,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.664493978,"difficulty":0.335506022}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicole is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Joseph can now know whether Nicole can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Nicole","Joseph"],"index":36425,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9964864254,"difficulty":0.0035135746}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Travis's card is shown to Elena. Elena's card is shown to Doris. Doris's card is shown to Doris. Elena's card is shown to Travis. It is publicly announced that someone picked a red card. It is publicly announced that Elena does not know whether Doris picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Doris can now know that Travis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elena","Doris","Travis"],"index":59124,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958586097,"difficulty":0.0041413903}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Doris's card is shown to Michael. Doris's card is shown to Doris. It is publicly announced that someone picked a red card. It is publicly announced that Doris knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Doris can now know that Michael can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Doris"],"index":59558,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Richard can now know that Mary can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Tara","Mary","Laura"],"index":43180,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9950182438,"difficulty":0.0049817562}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Perla's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Perla can now know whether Richard can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Perla","Joseph"],"index":55784,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999761045,"difficulty":0.000238955}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra does not know whether or not everyone is thirsty. It is publicly announced that Gary knows whether Sandra is thirsty. It is publicly announced that Kathleen does not know whether Gary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Sandra can now know whether Gary can know whether Kathleen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Sandra","Kathleen"],"index":40916,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984982014,"difficulty":0.0015017986}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Waldo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Robert can now know that Neva can know that Neva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Waldo","Neva"],"index":24287,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984586239,"difficulty":0.0015413761}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gilbert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Aida can now know that Gilbert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Aida","Glenn","Gilbert","Jamie"],"index":66519,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7566602826,"difficulty":0.2433397174}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Harold. Elsie's card is shown to Elsie. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harold","Elsie","Elizabeth"],"index":29886,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971151352,"difficulty":0.0028848648}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michele's card is shown to Michele. Fernando's card is shown to Fernando. Michele's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Fernando can now know whether Maria can know that Maria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michele","Fernando","Maria"],"index":50180,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7283283472,"difficulty":1.7283283472}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Robert can now know that Carmelo's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Robert","Carmelo","Sonya"],"index":44070,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974303842,"difficulty":0.0025696158}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Genia's card is shown to Genia. Janet's card is shown to Genia. Genia's card is shown to Janet. Rickey's card is shown to Janet. Janet's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rickey can now know that Genia can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Genia","Rickey","Janet"],"index":17253,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Marco. Nelida's card is shown to Nicole. Nicole's card is shown to Nicole. Nelida's card is shown to Philip. Marco's card is shown to Philip. It is publicly announced that someone picked a red card. It is publicly announced that Marco knows whether or not everyone picked a red card. It is publicly announced that Nelida picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Marco can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nelida","Marco","Nicole","Philip"],"index":26060,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997230172,"difficulty":0.0002769828}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard does not know whether Leonard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Leonard can now know that Darrel can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Darrel","Leonard"],"index":31089,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997619987,"difficulty":0.0002380013}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that Beverly knows whether Beverly's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Beverly can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Beverly"],"index":38459,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984213114,"difficulty":0.0015786886}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Melissa can now know whether Keith can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Keith","Melissa","Mary"],"index":62291,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997349381,"difficulty":0.0002650619}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eugene does not know whether Bonnie is thirsty. It is publicly announced that Willie knows whether Willie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Bonnie can now know that Eugene can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eugene","Bonnie","Terry","Willie"],"index":40438,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984090924,"difficulty":0.0015909076}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie does not know whether Connie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Betty can now know that Connie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Robert","Connie"],"index":40638,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9712846875,"difficulty":0.0287153125}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lara does not know whether Minnie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Phyllis can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Phyllis","Lara","Minnie"],"index":21332,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986220598,"difficulty":0.0013779402}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kirk does not know whether Dewayne is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Kirk can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dewayne","Debbie","Marcia","Kirk"],"index":35734,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9959977865,"difficulty":0.0040022135}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Zachary does not know whether Mary is thirsty. It is publicly announced that Anne does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Janelle can now know that Anne can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Janelle","Zachary","Anne"],"index":30976,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998005569,"difficulty":0.001994431}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcella does not know whether Lois is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Lois can now know whether Marcella can know whether Lois is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lois","Marcella"],"index":46482,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998115778,"difficulty":0.001884222}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Mary can now know whether Joyce can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Joyce"],"index":52400,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983660579,"difficulty":0.0016339421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clifton knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Clifton can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Keith","Katherine","Clifton"],"index":64187,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997738004,"difficulty":0.0002261996}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Gary is thirsty. It is publicly announced that Robert does not know whether Anthony is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Anthony can now know that Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Gary","Robert"],"index":66676,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955513477,"difficulty":0.0044486523}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lonnie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Zada can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tony","James","Lonnie","Zada"],"index":67330,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994977653,"difficulty":0.005022347}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Mattie. Mattie's card is shown to April. April's card is shown to April. Mattie's card is shown to Marlene. Marlene's card is shown to Marlene. It is publicly announced that someone picked a red card. It is publicly announced that April knows whether Mattie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"April can now know that Marlene can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mattie","April","Marlene"],"index":12325,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Lorenzo. Matthew's card is shown to Shelly. Shelly's card is shown to James. James's card is shown to James. Lorenzo's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Lorenzo does not know whether Matthew picked a red card. It is publicly announced that Shelly picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Lorenzo can now know whether Lorenzo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorenzo","Shelly","James","Matthew"],"index":12452,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9941097498,"difficulty":1.9941097498}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ora's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ora knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Ora can now know whether Edwin can know whether Dawna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ora","Edwin","Dawna","Kevin"],"index":4843,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999222517,"difficulty":0.000777483}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether someone's forehead is muddy. It is publicly announced that Jason knows whether Jean's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Jean can now know whether Mary can know that Jean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Jean","Mandy","Jason"],"index":21177,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993020296,"difficulty":0.0006979704}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda does not know whether or not everyone is thirsty. It is publicly announced that Amanda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Amanda can now know whether Monica can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sheila","Amanda","Monica"],"index":40373,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997100234,"difficulty":0.0002899766}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn does not know whether John is thirsty. It is publicly announced that James does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Julie can now know that Evelyn can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Julie","Evelyn","John"],"index":13280,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958769083,"difficulty":0.0041230917}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elena knows whether Ray's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kurt can now know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Ray","Elena","Kurt"],"index":37406,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998273015,"difficulty":0.001726985}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Patricia. James's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Robert can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Robert","James"],"index":64836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deana's card is shown to Deana. Tammy's card is shown to Tammy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Deana can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Deana","Tammy"],"index":51666,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Judith can now know that Patricia can know that Judith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Judith","Patricia"],"index":63306,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9945827127,"difficulty":0.0054172873}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Frank can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kevin","Frank"],"index":37611,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982016087,"difficulty":0.0017983913}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ron knows whether or not nobody is thirsty. It is publicly announced that Ron does not know whether Melissa is thirsty. It is publicly announced that Sandra does not know whether or not everyone is thirsty. It is publicly announced that Ron does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Melissa can now know whether Sandra can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melissa","Ron","Sandra"],"index":13468,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997716546,"difficulty":0.0002283454}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffery does not know whether Sharon is thirsty. It is publicly announced that Jeffery does not know whether Wendy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Wendy can now know that Justin can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffery","Wendy","Sharon","Justin"],"index":62659,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9622430801,"difficulty":0.0377569199}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Loretta's card is shown to Loretta. Michelle's card is shown to Loretta. Michelle's card is shown to Michelle. Letha's card is shown to Michelle. Shirley's card is shown to Letha. Letha's card is shown to Letha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Loretta can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Loretta","Michelle","Shirley","Letha"],"index":14114,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997242093,"difficulty":0.0002757907}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tessa knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Sharon can now know whether Ashley is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tessa","Ashley","Sharon"],"index":49502,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973798394,"difficulty":0.0026201606}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Susana can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Susana","Michael"],"index":49737,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996988773,"difficulty":0.0003011227}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Basil does not know whether or not everyone is thirsty. It is publicly announced that Taylor does not know whether Patrick is thirsty. It is publicly announced that Basil does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Patrick can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Basil","Taylor"],"index":49822,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997772574,"difficulty":0.0002227426}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Lewis. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Lewis knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Barbara can now know whether Lewis can know that Lewis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lewis","Barbara"],"index":41985,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6026719809,"difficulty":1.6026719809}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Marilyn. Marilyn's card is shown to Carlos. Carlos's card is shown to Carlos. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marilyn can now know that Betty can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Marilyn","Carlos"],"index":48337,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sam's card is shown to Fred. Sam's card is shown to Sam. Joann's card is shown to Sam. Fred's card is shown to Joann. Sam's card is shown to Joann. Joann's card is shown to Joann. It is publicly announced that someone picked a red card. It is publicly announced that Sam picked a red card. It is publicly announced that Sam does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Fred can now know that Sam can know whether Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Fred","Sam","Joann"],"index":40922,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8397435546,"difficulty":1.8397435546}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Violet's card is shown to Violet. Violet's card is shown to Brenda. Brenda's card is shown to Brett. Helen's card is shown to Brett. Helen's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Brenda knows whether or not nobody picked a red card. It is publicly announced that Brett picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Violet can now know that Brenda can know that Brenda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Violet","Brenda","Brett","Helen"],"index":52040,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9214017987,"difficulty":0.0785982013}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether Lawrence is thirsty. It is publicly announced that Joe does not know whether Lawrence is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robert can now know whether Joe is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Joe","Robert","Eric"],"index":43153,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9621080756,"difficulty":0.0378919244}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jeffrey can now know that Paul can know that Debra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juan","Paul","Debra","Jeffrey"],"index":1012,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9960973859,"difficulty":0.0039026141}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pierre is thirsty. It is publicly announced that Pierre does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Brian can now know that Kimberly can know whether Kimberly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pierre","Kimberly","Brian"],"index":48052,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980751276,"difficulty":0.0019248724}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamie knows whether Tamie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Tamie can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tiffany","Tamie"],"index":5051,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997554421,"difficulty":0.0002445579}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Maureen. Sara's card is shown to Sara. It is publicly announced that someone picked a red card. It is publicly announced that Maureen does not know whether Maureen picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Maureen can now know that Sara can know that Sara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maureen","Sara"],"index":47017,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9870266318,"difficulty":1.9870266318}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharmaine's forehead is not muddy. It is publicly announced that Sharmaine's forehead is not muddy. It is publicly announced that Sharmaine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Darlene can now know whether Pamela can know whether Darlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlene","Sharmaine","Pamela","Barbara"],"index":48092,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996800423,"difficulty":0.0003199577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Anna can now know that Christopher can know that Augusta is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Augusta","Christopher","Anna"],"index":61124,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9772769213,"difficulty":0.0227230787}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether David is thirsty. It is publicly announced that Frances does not know whether or not everyone is thirsty. It is publicly announced that Frances does not know whether David is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"David can now know that Frances can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edith","David","James","Frances"],"index":15570,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8807879686,"difficulty":0.1192120314}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Phyllis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Phyllis","Margarita","Pamela","Tracy"],"index":21067,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982278943,"difficulty":0.0017721057}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene does not know whether Irene's forehead is muddy. It is publicly announced that Irene does not know whether Irene's forehead is muddy. It is publicly announced that Irene's forehead is not muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Irene can now know that Larry can know that Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Larry","Irene","Kenneth"],"index":40563,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9327456355,"difficulty":0.0672543645}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Orlando knows whether Lynn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Leon can now know whether Orlando can know whether Leon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leon","Orlando","Lynn","Joanne"],"index":33099,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982591271,"difficulty":0.0017408729}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Constance. Gregory's card is shown to Constance. Constance's card is shown to Lois. Jean's card is shown to Lois. Lois's card is shown to Jean. Jean's card is shown to Jean. Gregory's card is shown to Jean. Constance's card is shown to Gregory. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know whether Lois can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Constance","Lois","Jean","Gregory"],"index":38739,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997109771,"difficulty":0.0002890229}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to Martha. Barbara's card is shown to Martha. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Martha can now know whether Barbara can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Martha","Barbara"],"index":15515,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997672439,"difficulty":0.0002327561}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Percy is thirsty. It is publicly announced that Percy does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"James can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Jack","Percy","Patricia"],"index":37941,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999776423,"difficulty":0.000223577}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stefanie knows whether or not nobody is thirsty. It is publicly announced that Lynette does not know whether Stefanie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lita can now know that Stefanie can know that Lynette is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lynette","Stefanie","Lita"],"index":22284,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996853292,"difficulty":0.003146708}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norma's card is shown to Brandy. Brandy's card is shown to Norma. Carlton's card is shown to Stacy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carlton can now know that Stacy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carlton","Brandy","Norma","Stacy"],"index":19083,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984742999,"difficulty":0.0015257001}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mildred knows whether or not nobody's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Kevin can now know that Mildred can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kevin","Mildred"],"index":38776,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983172417,"difficulty":0.0016827583}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Kim can now know that Bobby can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marion","Kim","Bobby"],"index":23615,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997606874,"difficulty":0.0002393126}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Benjamin does not know whether Marjorie is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Benjamin can now know whether Marjorie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marjorie","Benjamin","Cynthia","Lawrence"],"index":56392,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9964696169,"difficulty":0.0035303831}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Charles can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Gregory"],"index":14936,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947196245,"difficulty":0.0052803755}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Dorthy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","John","Sheryl","Dorthy"],"index":9484,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986481071,"difficulty":0.0013518929}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacklyn is thirsty. It is publicly announced that Jacklyn knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Mohammad can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jacklyn","Mohammad"],"index":26792,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997401834,"difficulty":0.0002598166}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anna does not know whether Helen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Helen can now know that James can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","James","Anna"],"index":23651,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998329103,"difficulty":0.001670897}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know that Yu can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Devin","Keith","Yu"],"index":10855,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983906746,"difficulty":0.0016093254}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christian knows whether someone's forehead is muddy. It is publicly announced that Steven does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Douglas can now know whether Steven can know whether Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Douglas","Christian"],"index":53596,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8755803704,"difficulty":0.1244196296}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dawn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Jennifer can now know that Carrie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Carrie","Dawn","Norman"],"index":41240,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9754782915,"difficulty":0.0245217085}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheri's card is shown to Sheri. Aaron's card is shown to Andrea. Sheri's card is shown to Andrea. Harry's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Sheri does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Aaron can now know whether Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aaron","Sheri","Andrea","Harry"],"index":16684,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7409079075,"difficulty":1.7409079075}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alice knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Angela can now know whether Daniel can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Daniel","Alice"],"index":22849,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9589884877,"difficulty":0.0410115123}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee knows whether Lee's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that Virginia can know that Virginia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Winnifred","Virginia","Lee","Robert"],"index":25432,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984062314,"difficulty":0.0015937686}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Nancy can now know whether Barbara can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Debra","Nancy","Darrell"],"index":46634,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997519851,"difficulty":0.0002480149}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erwin's card is shown to Erwin. Erwin's card is shown to Richard. Richard's card is shown to Richard. Linda's card is shown to Richard. Erwin's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Erwin","Richard","Linda"],"index":44677,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wendell does not know whether or not everyone is thirsty. It is publicly announced that Wendell does not know whether Marilyn is thirsty. It is publicly announced that Marilyn does not know whether Cora is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Dennis can now know that Cora can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wendell","Marilyn","Dennis","Cora"],"index":3252,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7872424722,"difficulty":0.2127575278}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to June. Linda's card is shown to June. Richard's card is shown to June. Linda's card is shown to Linda. June's card is shown to Richard. Linda's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Linda can now know whether June can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["June","Linda","Richard"],"index":63814,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980254173,"difficulty":0.0019745827}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jess does not know whether or not everyone's forehead is muddy. It is publicly announced that Jess does not know whether Jess's forehead is muddy. It is publicly announced that Betsy's forehead is muddy. It is publicly announced that Betsy knows whether Jess's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Betsy can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jess","Betsy"],"index":14044,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948939085,"difficulty":0.0051060915}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Penny knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Herminia can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Penny","Herminia"],"index":38831,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978734255,"difficulty":0.0021265745}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Salvador's card is shown to Salvador. Salvador's card is shown to Pamela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Salvador can now know that Pamela can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Salvador","Pamela"],"index":64450,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.987896204,"difficulty":0.012103796}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beth knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Joyce can now know that Beth can know whether Doris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joyce","Beth","Doris"],"index":10111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997122884,"difficulty":0.0002877116}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Daniel can now know whether David can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Daniel"],"index":25187,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996900558,"difficulty":0.0003099442}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda is thirsty. It is publicly announced that Rebecca knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Amanda can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anita","Dennis","Rebecca","Amanda"],"index":11833,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985504746,"difficulty":0.0014495254}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clifford can now know whether Eloise can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clifford","Eloise","Ruth"],"index":62134,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997619987,"difficulty":0.0002380013}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal does not know whether Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Malcom can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","George","Malcom","Crystal"],"index":22177,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983762503,"difficulty":0.0016237497}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Tina. Donald's card is shown to Patricia. Tina's card is shown to Donald. Patricia's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether Donald picked a red card. It is publicly announced that Tina knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Tina can now know that Tina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tina","Patricia","Donald"],"index":50811,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9792732,"difficulty":0.0207268}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether Merri's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Guadalupe can now know that Merri's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Guadalupe","Merri"],"index":44044,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973862767,"difficulty":0.0026137233}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joyce can now know that Bruce's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joyce","Bruce","Jeff"],"index":8895,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7222297192,"difficulty":0.2777702808}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marjorie's card is shown to Mirta. Marjorie's card is shown to Marie. Tina's card is shown to Tina. Marie's card is shown to Marjorie. Tina's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Tina does not know whether Marie picked a red card. It is publicly announced that Mirta knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marie can now know whether Marjorie can know whether Marie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mirta","Marie","Tina","Marjorie"],"index":18609,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9969789982,"difficulty":0.0030210018}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Wayne can now know whether Lisa can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Wayne","Robert"],"index":65201,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9972291589,"difficulty":0.0027708411}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether Carol's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carol can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carol","Renee"],"index":4217,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983158112,"difficulty":0.0016841888}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether Margery's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Jessica can now know whether Margery can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Maria","Margery"],"index":14888,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995999932,"difficulty":0.0004000068}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Margaret can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christine","Robert","Margaret"],"index":33291,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983620048,"difficulty":0.0016379952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura knows whether someone is thirsty. It is publicly announced that Elizabeth does not know whether Brian is thirsty. It is publicly announced that Theresa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Laura can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Theresa","Laura","Elizabeth","Brian"],"index":2638,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99851197,"difficulty":0.00148803}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"David can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Gary","Patty","Ralph"],"index":10353,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996759892,"difficulty":0.0003240108}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dora's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Dora can now know whether Mack's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dora","Mack","Thomas"],"index":52112,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997330308,"difficulty":0.0002669692}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ted knows whether Tyrone's forehead is muddy. It is publicly announced that Tyrone's forehead is muddy. It is publicly announced that Fredrick does not know whether Fredrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Tyrone can now know whether Ted can know whether Fredrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fredrick","Patricia","Ted","Tyrone"],"index":61462,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991366267,"difficulty":0.0008633733}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clyde does not know whether Sarah is thirsty. It is publicly announced that Juanita does not know whether Clyde is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sarah can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Fay","Clyde","Sarah"],"index":1623,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997292161,"difficulty":0.0002707839}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vito's card is shown to Vito. Mable's card is shown to Vito. Mable's card is shown to Mable. Vivian's card is shown to Vivian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vivian can now know that Mable can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vito","Mable","Vivian"],"index":63741,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997180104,"difficulty":0.0002819896}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty does not know whether or not everyone's forehead is muddy. It is publicly announced that Betty does not know whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Betty can now know whether Joan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rose","Ronald","Joan","Betty"],"index":6110,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991443157,"difficulty":0.0008556843}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. William's card is shown to William. William's card is shown to Luis. Luis's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Nicholas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Nicholas","William","Luis"],"index":19777,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8349634409,"difficulty":0.1650365591}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leota's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Roosevelt can now know whether Leota can know that Vicky's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bobby","Leota","Vicky","Roosevelt"],"index":38771,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9896798134,"difficulty":0.0103201866}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emily does not know whether Mona is thirsty. It is publicly announced that Laura does not know whether Mona is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Laura can now know whether Emily can know whether Mona is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mona","Emily","Laura"],"index":45400,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985622764,"difficulty":0.0014377236}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Gabriel can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jonathon","Heidi","Gabriel","Barbara"],"index":16038,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983781576,"difficulty":0.0016218424}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lucretia can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ted","Mary","Donna","Lucretia"],"index":47287,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984483719,"difficulty":0.0015516281}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether Benjamin is thirsty. It is publicly announced that Karie does not know whether Mark is thirsty. It is publicly announced that Benjamin is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] (Agentd knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Karie can now know whether Anna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Mark","Benjamin","Karie"],"index":21902,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9799913168,"difficulty":0.0200086832}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Robert. Maurice's card is shown to Jeffrey. Edward's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Robert does not know whether Maurice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Maurice can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Jeffrey","Maurice","Edward"],"index":1265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.991887033,"difficulty":0.008112967}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Jeffrey is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Jeffrey can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Jeffrey"],"index":14200,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is not muddy. It is publicly announced that Lila does not know whether Lila's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lila can now know that Kimberly can know that Lila's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lila","Joseph","Kimberly"],"index":51157,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9808716774,"difficulty":0.0191283226}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karl's card is shown to Karl. Susan's card is shown to Karl. Susan's card is shown to Susan. Karl's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Karl can now know whether Harold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Karl","Susan","Harold"],"index":19930,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6304668784,"difficulty":0.3695331216}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Monica's card is shown to Anthony. Anthony's card is shown to Cheryl. Monica's card is shown to Cheryl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know that Monica can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Monica","Cheryl"],"index":25546,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983248115,"difficulty":0.0016751885}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Jared. Jared's card is shown to Misti. Misti's card is shown to Misti. It is publicly announced that someone picked a red card. It is publicly announced that Jared knows whether Aaron picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Aaron can now know that Jared can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Aaron","Jared","Misti"],"index":45342,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9427565336,"difficulty":1.9427565336}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Percy knows whether Wendy's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Wendy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Timothy can now know whether Wendy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wendy","Percy","Timothy","Alfred"],"index":53844,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996682405,"difficulty":0.0003317595}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen does not know whether or not everyone's forehead is muddy. It is publicly announced that Mark knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentc knows whether (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Albert can now know whether Kathleen can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Henry","Albert","Kathleen"],"index":23238,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997730851,"difficulty":0.0002269149}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nellie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Shannon can now know whether Nellie can know that Nellie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerald","William","Nellie","Shannon"],"index":57152,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996416569,"difficulty":0.0003583431}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Johnnie can now know whether Joshua can know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnnie","Donna","Joshua"],"index":63197,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997162223,"difficulty":0.0002837777}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Natasha knows whether or not nobody is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty. It is publicly announced that Theresa knows whether Theresa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"William can now know whether Theresa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Natasha","William","Theresa"],"index":4857,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.861354351,"difficulty":1.861354351}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ethel knows whether Megan's forehead is muddy. It is publicly announced that Ethel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Megan can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Megan","Ethel"],"index":58136,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5647387505,"difficulty":0.4352612495}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Patricia. Patricia's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card. It is publicly announced that Patricia knows whether Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Patricia can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Michael"],"index":56879,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99967134,"difficulty":0.00032866}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leticia does not know whether Mike is thirsty. It is publicly announced that Jennifer does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Louis can now know that Mike is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leticia","Louis","Jennifer","Mike"],"index":17206,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9412911534,"difficulty":0.0587088466}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether Dominick's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brenda can now know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dominick","Brenda","Thomas"],"index":39480,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998239994,"difficulty":0.001760006}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Andrea. Jared's card is shown to Andrea. Andrea's card is shown to Larry. Larry's card is shown to Larry. Jared's card is shown to Larry. Larry's card is shown to Elizabeth. Jared's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Andrea can now know whether Elizabeth can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrea","Larry","Elizabeth","Jared"],"index":10703,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996334314,"difficulty":0.0003665686}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether Anna can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Neoma","Darrell","Anna"],"index":265,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995741248,"difficulty":0.0004258752}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Joann can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Everett","Josie","Larry","Joann"],"index":43412,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9134776592,"difficulty":0.0865223408}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Douglas can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Douglas","Irene","Martha"],"index":41250,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984978437,"difficulty":0.0015021563}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jan does not know whether Nicole is thirsty. It is publicly announced that Jan does not know whether Meryl is thirsty. It is publicly announced that Nicole knows whether Nicole is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jan can now know that Meryl can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Meryl","Jan","Nicole"],"index":19228,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983260036,"difficulty":0.0016739964}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josefina does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Josefina can now know that Martha can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josefina","Julia","Martha","Joe"],"index":4853,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997768998,"difficulty":0.0002231002}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether David is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"David can now know that Michael can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","David"],"index":60348,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9799302816,"difficulty":0.0200697184}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy. It is publicly announced that Sylvia does not know whether Sylvia's forehead is muddy. It is publicly announced that Sylvia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Roosevelt can now know whether Sylvia can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roosevelt","Linda","Sylvia"],"index":29066,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997045398,"difficulty":0.0002954602}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Matthew can now know that John can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","John","Lucas","James"],"index":67350,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997790456,"difficulty":0.0002209544}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Barbara can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Robert","Margaret","Ralph"],"index":35786,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983843565,"difficulty":0.0016156435}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jay's card is shown to Doris. Jay's card is shown to Martha. Doris's card is shown to Jay. Jay's card is shown to Jay. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Martha can now know whether Martha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doris","Martha","Jay","Lydia"],"index":26577,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.838283062,"difficulty":0.161716938}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marie knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Emily can now know whether Marie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Courtney","Emily","Michael"],"index":13279,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974730611,"difficulty":0.0025269389}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"James can now know that Alexander's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","James","John","Alexander"],"index":51450,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9776479006,"difficulty":0.0223520994}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Paul can now know that Amanda can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amanda","Paul","Craig","Marie"],"index":59109,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984301925,"difficulty":0.0015698075}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Cathleen can now know that Danielle can know that Cathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ezra","Cathleen","Danielle","Nancy"],"index":60392,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981579185,"difficulty":0.0018420815}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dwight does not know whether or not everyone is thirsty. It is publicly announced that Dwight knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Cynthia can now know that Dwight can know that Dwight is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cynthia","Dwight"],"index":2101,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9934734702,"difficulty":0.0065265298}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daisy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Jimmy can now know that Daisy can know that Daisy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Jimmy","Daisy","Edith"],"index":42873,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9761611819,"difficulty":0.0238388181}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lance does not know whether or not everyone is thirsty. It is publicly announced that Audrey knows whether someone is thirsty. It is publicly announced that Helen does not know whether Audrey is thirsty. It is publicly announced that Helen does not know whether Ellen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Helen can now know that Ellen can know whether Audrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Audrey","Ellen","Helen","Lance"],"index":42740,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8797379732,"difficulty":0.1202620268}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dustin does not know whether Dustin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Dustin can now know that Reynaldo can know that Dustin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacqueline","Dustin","Reynaldo","Israel"],"index":35473,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959646463,"difficulty":0.0040353537}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether or not nobody's forehead is muddy. It is publicly announced that Neal knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Gary can now know that Neal can know that Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Neal","Gary"],"index":9968,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7271238565,"difficulty":0.2728761435}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether or not everyone's forehead is muddy. It is publicly announced that Joan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Sandra can now know that Joan can know that Joan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diana","Shirley","Sandra","Joan"],"index":6415,"s-l":"forehead_mirror-0","deberta_pred":1,"deberta_confidence":0.5081920028,"difficulty":1.5081920028}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Lisa. Eric's card is shown to Lisa. James's card is shown to Eric. Latonya's card is shown to Eric. Eric's card is shown to Latonya. It is publicly announced that someone picked a red card. It is publicly announced that Lisa does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Eric","James","Latonya"],"index":39758,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7247262597,"difficulty":1.7247262597}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. Harry's card is shown to Cindy. Cindy's card is shown to Harry. Harry's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Harry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Cindy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cindy","Harry","Dorothy"],"index":48526,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7503051162,"difficulty":1.7503051162}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pamela can now know whether Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Fidel","Bruce","Pamela","Sarah"],"index":36655,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997362494,"difficulty":0.0002637506}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Catherine can now know whether Carolyn can know whether Carolyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Katie","Rebecca","Catherine"],"index":24508,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995319843,"difficulty":0.0004680157}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyler's card is shown to Tyler. Patrick's card is shown to Tyler. Edith's card is shown to Patrick. Edith's card is shown to Edith. Michelle's card is shown to Michelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patrick can now know that Edith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tyler","Patrick","Edith","Michelle"],"index":5691,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982126951,"difficulty":0.0017873049}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Warren does not know whether Katelyn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"James can now know that Alison can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katelyn","Warren","Alison","James"],"index":62137,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997107387,"difficulty":0.0002892613}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know whether Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joni","Adalberto","Robert","Jeffrey"],"index":48069,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9944135547,"difficulty":0.0055864453}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Marian knows whether Lois's forehead is muddy. It is publicly announced that Blanche's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Lois can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marian","Blanche","Lois","Cecil"],"index":36466,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954909682,"difficulty":0.0045090318}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know whether Jose can know whether Jamey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annette","Jose","Jamey","Ruth"],"index":367,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991664886,"difficulty":0.0008335114}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley does not know whether or not everyone's forehead is muddy. It is publicly announced that Kari knows whether or not nobody's forehead is muddy. It is publicly announced that Ashley does not know whether Ashley's forehead is muddy. It is publicly announced that Kari knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Kari can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ashley","Kari"],"index":4518,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9924992919,"difficulty":0.0075007081}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Grover knows whether Grover's forehead is muddy. It is publicly announced that Shirley knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Kimberly can now know that Grover's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kimberly","Grover","Carmella","Shirley"],"index":63103,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974079728,"difficulty":0.0025920272}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eunice does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Dana can now know that Dana's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dana","Eunice","Ronald"],"index":23805,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9946711659,"difficulty":0.0053288341}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"John can now know that Jean can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Jean"],"index":17200,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.989829123,"difficulty":0.010170877}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Cindi can now know whether Thomas can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Thomas","Carter","Cindi"],"index":24835,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999776423,"difficulty":0.000223577}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence does not know whether or not everyone's forehead is muddy. It is publicly announced that Tom knows whether Tom's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Florence can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tom","Florence"],"index":67044,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977293611,"difficulty":0.0022706389}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Faith does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Maria can now know that David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Betsy","Faith","David"],"index":67348,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9635276794,"difficulty":0.0364723206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry does not know whether Ricky is thirsty. It is publicly announced that Ricky does not know whether Darlene is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Darlene can now know that Mary can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlene","Mary","Ricky","Larry"],"index":27622,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999779284,"difficulty":0.000220716}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alanna's card is shown to Alanna. George's card is shown to Alanna. Alanna's card is shown to Jeff. Paul's card is shown to Paul. Alanna's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alanna can now know whether George can know whether Alanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alanna","Jeff","Paul","George"],"index":49576,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980260134,"difficulty":0.0019739866}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristina does not know whether Kristina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Jennie can now know that Jennie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennie","Virgil","Robert","Kristina"],"index":35434,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968888164,"difficulty":0.0031111836}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Donna. Donna's card is shown to Scot. Scot's card is shown to Scot. Dorothy's card is shown to Scot. Donna's card is shown to Dorothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Scot can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Scot","Dorothy"],"index":37332,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984967709,"difficulty":0.0015032291}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adele's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Debra can now know that Susan can know that Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debra","Adele","Susan"],"index":29383,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.927708447,"difficulty":0.072291553}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mariana's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Patrick can now know that Mariana can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nathaniel","Tom","Mariana","Patrick"],"index":60607,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983048439,"difficulty":0.0016951561}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ana knows whether Vincent's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Shirley can now know whether Vincent can know whether Shirley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ana","Shirley","Vincent","Helen"],"index":13240,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9949323535,"difficulty":0.0050676465}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Dina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Elsie can now know that Elsie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elsie","Donald","Dina","James"],"index":43236,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980558157,"difficulty":0.0019441843}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diane is not thirsty. It is publicly announced that Diane does not know whether Brenda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Diane can now know that Joseph can know that Brenda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brenda","Joseph","Diane"],"index":38286,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9798911214,"difficulty":0.0201088786}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rodolfo does not know whether Homer is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Rodolfo can now know that Homer can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Homer","Rodolfo"],"index":17928,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997020364,"difficulty":0.0002979636}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leah does not know whether Jean is thirsty. It is publicly announced that Jean is not thirsty. It is publicly announced that Leah is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know that Leah can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jean","Leah","Michael","Timothy"],"index":24363,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8478262424,"difficulty":0.1521737576}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Charles can now know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Charles"],"index":36354,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9925422668,"difficulty":0.0074577332}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl knows whether Bruce's forehead is muddy. It is publicly announced that Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"Eugene can now know whether Cheryl can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eugene","Sharon","Bruce","Cheryl"],"index":66997,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997500777,"difficulty":0.0002499223}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Marjorie can now know whether Amanda can know that Marjorie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Amelia","Marjorie"],"index":52061,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992465973,"difficulty":0.0007534027}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catherine does not know whether or not everyone is thirsty. It is publicly announced that Catherine does not know whether Leonard is thirsty. It is publicly announced that Leonard knows whether Leonard is thirsty. It is publicly announced that Leonard knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Leonard can now know that Leonard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Leonard","Catherine"],"index":15827,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8757331967,"difficulty":1.8757331967}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yolanda knows whether Vera's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Vera can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Yolanda","Tracy","Vera"],"index":41458,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997650981,"difficulty":0.0002349019}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter does not know whether Peter's forehead is muddy. It is publicly announced that Steven's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] 0","hypothesis":"Kori can now know whether Peter can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Peter","Kori","Steven"],"index":57404,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995500445,"difficulty":0.0004499555}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Julia knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"James can now know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julia","David","Ruth","James"],"index":40866,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994959831,"difficulty":0.0005040169}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Lillie knows whether or not nobody's forehead is muddy. It is publicly announced that Lillie knows whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Lillie can now know whether Laura can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Laura","Lillie"],"index":48011,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9961236119,"difficulty":0.0038763881}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether Alexander can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Alexander","Glenn"],"index":32705,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9888855219,"difficulty":0.0111144781}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anthony","Angelo","Michael"],"index":54400,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997512698,"difficulty":0.0002487302}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Antonio's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"James can now know that Mary can know whether Antonio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Steven","Antonio","James"],"index":7667,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997521043,"difficulty":0.0002478957}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marion's forehead is not muddy. It is publicly announced that Sandra knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Martha can now know that Eva can know that Martha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Martha","Marion","Eva"],"index":31901,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9061966538,"difficulty":0.0938033462}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Dante can now know that Michael can know that Dante's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Dante"],"index":60667,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959822893,"difficulty":0.0040177107}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Christopher's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Christopher can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Matthew"],"index":6564,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998364985,"difficulty":0.001635015}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Catherine. Barbara's card is shown to Carol. Carol's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Catherine picked a red card. It is publicly announced that Catherine does not know whether Carol picked a red card. It is publicly announced that Barbara knows whether Carol picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Catherine can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Catherine","Barbara","Carol"],"index":4423,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997156262,"difficulty":0.0002843738}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Stacy. Ashley's card is shown to Stacy. Charles's card is shown to Charles. Calvin's card is shown to Charles. Stacy's card is shown to Calvin. Charles's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that Stacy does not know whether Calvin picked a red card. It is publicly announced that Charles picked a black card. It is publicly announced that Stacy does not know whether Stacy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Calvin can now know whether Stacy can know that Stacy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stacy","Charles","Calvin","Ashley"],"index":5565,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9435238242,"difficulty":0.0564761758}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loretta knows whether Norman's forehead is muddy. It is publicly announced that Loretta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Nathan can now know that Norman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Talia","Loretta","Norman","Nathan"],"index":50362,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7893745303,"difficulty":0.2106254697}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Holly does not know whether Holly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Jeremy can now know that Darleen can know that Holly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeremy","Darleen","Leora","Holly"],"index":30040,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965912104,"difficulty":0.0034087896}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice knows whether someone's forehead is muddy. It is publicly announced that Louise's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] 0","hypothesis":"Ryan can now know that Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alice","Ryan","Louise","Jeffrey"],"index":54945,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9395654202,"difficulty":0.0604345798}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Ethan. Ethan's card is shown to Ethan. Dana's card is shown to Ethan. Matthew's card is shown to Margaret. Margaret's card is shown to Margaret. Dana's card is shown to Margaret. Matthew's card is shown to Dana. Margaret's card is shown to Dana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ethan can now know that Matthew can know that Ethan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Matthew","Ethan","Margaret","Dana"],"index":60864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962905645,"difficulty":0.0037094355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen's forehead is not muddy. It is publicly announced that Kathleen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Melissa can now know that Manuel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Manuel","James","Kathleen"],"index":17445,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9913471341,"difficulty":0.0086528659}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether someone's forehead is muddy. It is publicly announced that Willie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Karen can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Alex","Jay","Willie"],"index":12397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977632761,"difficulty":0.0022367239}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Damien knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Graciela knows whether Graciela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Damien can now know that Graciela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Graciela","Joe","Damien","Aaron"],"index":11971,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9950044751,"difficulty":0.0049955249}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mildred is thirsty. It is publicly announced that Mildred does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mildred can now know that Mary can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Mildred"],"index":34890,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987150431,"difficulty":0.0012849569}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Virginia can now know that Michael can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Virginia","Michael","John","Bridgett"],"index":32901,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981581569,"difficulty":0.0018418431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Beverly can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverly","James","Robert","Arthur"],"index":61237,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5731829405,"difficulty":0.4268170595}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Matthew. Elsie's card is shown to Matthew. Elsie's card is shown to Elsie. It is publicly announced that someone picked a red card. It is publicly announced that Elsie knows whether or not nobody picked a red card. It is publicly announced that Elsie does not know whether Matthew picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Elsie can now know that Elsie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Matthew","Elsie"],"index":48854,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8452242613,"difficulty":1.8452242613}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Rafael can now know that William can know whether Gracie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gracie","William","Sharon","Rafael"],"index":14726,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997319579,"difficulty":0.0002680421}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Jennifer's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that Ana knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know whether Ana can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ana","Jennifer","Lucy","David"],"index":2699,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7387684584,"difficulty":0.2612315416}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glen knows whether Glen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lester can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Glen","Jamie","Lester","Jerry"],"index":16675,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986230135,"difficulty":0.0013769865}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is not thirsty. It is publicly announced that Cathy does not know whether Kay is thirsty. It is publicly announced that Kay does not know whether Cathy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 2) ] Agenta knows whether (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"James can now know whether Melvin can know that Kay is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Cathy","Melvin","Kay"],"index":30641,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9920864701,"difficulty":0.0079135299}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rufus's card is shown to Florence. Victor's card is shown to Florence. Juliette's card is shown to Juliette. Rufus's card is shown to Victor. Florence's card is shown to Victor. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juliette can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rufus","Florence","Juliette","Victor"],"index":7606,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985185266,"difficulty":0.0014814734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know that Charles can know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","William","Margaret","Charles"],"index":27484,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963418841,"difficulty":0.0036581159}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry does not know whether Barry's forehead is muddy. It is publicly announced that Corina knows whether Corina's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Corina can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Corina","Barry"],"index":50031,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986126423,"difficulty":0.0013873577}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adolfo's card is shown to Dan. Adolfo's card is shown to Mary. Geoffrey's card is shown to Mary. Dan's card is shown to Adolfo. It is publicly announced that someone picked a red card. It is publicly announced that Dan knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Dan can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dan","Mary","Adolfo","Geoffrey"],"index":45444,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9723204374,"difficulty":0.0276795626}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather does not know whether Josefa is thirsty. It is publicly announced that Kelvin is thirsty. It is publicly announced that Josefa is thirsty. It is publicly announced that Kelvin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 1 ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 1 ] 0","hypothesis":"Heather can now know whether Josefa can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelvin","Josefa","Heather"],"index":65250,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992524981,"difficulty":0.0007475019}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether Cherie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Cherie can now know whether Bradley can know that Frances is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frances","Bradley","Cherie"],"index":33627,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.983667016,"difficulty":0.016332984}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jeanne knows whether Jeanne's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jerry can now know that Jeanne can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeanne","Jerry"],"index":43502,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985465407,"difficulty":0.0014534593}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynne's card is shown to Lynne. Lynne's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card. It is publicly announced that Christopher knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Lynne can now know whether Christopher can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lynne","Christopher"],"index":36746,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephany does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Robert can now know that Stephany can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Stephany"],"index":31427,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Carla's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Lonnie can now know that Mark can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carla","Mark","John","Lonnie"],"index":53402,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995802045,"difficulty":0.0004197955}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joshua's card is shown to Phyllis. Sue's card is shown to Sue. Joshua's card is shown to Joshua. Phyllis's card is shown to Jeanie. It is publicly announced that someone picked a red card. It is publicly announced that Phyllis picked a red card. It is publicly announced that Jeanie does not know whether Jeanie picked a red card. It is publicly announced that Sue knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Phyllis can now know that Jeanie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phyllis","Sue","Joshua","Jeanie"],"index":5526,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996980429,"difficulty":0.0003019571}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Robert. Robert's card is shown to Adam. Adam's card is shown to Adam. It is publicly announced that someone picked a red card. It is publicly announced that Adam knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Robert can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Adam"],"index":44746,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Frances. David's card is shown to Frances. David's card is shown to Patricia. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"David can now know that Frances can know that Frances picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frances","Patricia","David"],"index":6988,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6733557582,"difficulty":0.3266442418}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dolores's card is shown to John. John's card is shown to Dolores. Dolores's card is shown to Stefanie. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Dolores knows whether Dolores picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know whether Dolores picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Dolores","Stefanie"],"index":20909,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9934784174,"difficulty":0.0065215826}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janelle's card is shown to Janelle. Berniece's card is shown to Janelle. Janelle's card is shown to Daniel. Janelle's card is shown to Berniece. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Daniel can now know that Berniece picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janelle","Daniel","Berniece"],"index":65368,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981895089,"difficulty":0.0018104911}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oren knows whether Reginald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Reginald","Sharon","William","Oren"],"index":32008,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985082746,"difficulty":0.0014917254}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alfred is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentd knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Carmen can now know whether Alfred can know that Alfred is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfred","Michael","Jill","Carmen"],"index":64123,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9477232099,"difficulty":0.0522767901}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmy's card is shown to Jimmy. Helen's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Jimmy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Helen can now know whether Jimmy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jimmy","Helen"],"index":8151,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996885061,"difficulty":0.0003114939}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terry's card is shown to Angie. Sandy's card is shown to Sandy. Sandy's card is shown to Terry. Angie's card is shown to Gladys. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gladys can now know that Angie can know whether Gladys picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angie","Sandy","Terry","Gladys"],"index":43910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9148259163,"difficulty":0.0851740837}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Amanda can now know that Samantha can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samantha","John","Amy","Amanda"],"index":36030,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997814298,"difficulty":0.0002185702}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pedro knows whether Jeremy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Pedro can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeremy","James","Joshua","Pedro"],"index":56176,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983652234,"difficulty":0.0016347766}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard does not know whether Howard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Erik can now know that Howard can know whether Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Billy","Howard","Erik"],"index":756,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988332391,"difficulty":0.0011667609}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Johanna does not know whether or not everyone is thirsty. It is publicly announced that Barbara does not know whether Augustine is thirsty. It is publicly announced that Johanna does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Johanna can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Augustine","Johanna","Barbara"],"index":7260,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9929558039,"difficulty":0.0070441961}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marshall does not know whether Marshall's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Louise can now know whether William can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marshall","Louise","William"],"index":2981,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.922257483,"difficulty":0.077742517}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Mattie. Tom's card is shown to Tom. It is publicly announced that someone picked a red card. It is publicly announced that Mattie does not know whether Mattie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Tom can now know that Mattie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mattie","Tom"],"index":53370,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985938668,"difficulty":0.0014061332}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Lola can now know whether Justin can know whether Justin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eva","Justin","Lola"],"index":54150,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9961161613,"difficulty":0.0038838387}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jamie's card is shown to Jamie. Eva's card is shown to Jamie. Eva's card is shown to William. Jamie's card is shown to Victor. William's card is shown to Eva. Eva's card is shown to Eva. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether Jamie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"William can now know whether Victor can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jamie","William","Victor","Eva"],"index":26394,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5532009006,"difficulty":1.5532009006}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Frederick's card is shown to Mary. Troy's card is shown to Troy. Troy's card is shown to Frederick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether Troy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Troy","Frederick"],"index":43485,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.569485724,"difficulty":1.569485724}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill knows whether Bill's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Bill can now know that Roman can know whether Olive's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bill","Olive","Roman","John"],"index":33200,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997324347,"difficulty":0.0002675653}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robbie knows whether Jennifer's forehead is muddy. It is publicly announced that Robbie does not know whether or not everyone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy. It is publicly announced that Jennifer knows whether Robbie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jennifer can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robbie","Jennifer"],"index":45146,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9580658674,"difficulty":0.0419341326}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jorge knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Constance can now know that Fred can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Fred","Constance","Nancy","Jorge"],"index":13357,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984644651,"difficulty":0.0015355349}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Allen can now know that Victoria can know that Brittni's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Allen","Brittni","Victoria"],"index":13670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983255267,"difficulty":0.0016744733}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Donna can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Dominic","John","Robert"],"index":62732,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998242259,"difficulty":0.001757741}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Betty can now know whether Martha can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Thomas","Betty","Noel"],"index":20892,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9900628924,"difficulty":0.0099371076}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernardo's card is shown to Lana. Lana's card is shown to Lana. It is publicly announced that someone picked a red card. It is publicly announced that Lana picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Bernardo can now know whether Bernardo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bernardo","Lana"],"index":625,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9852924943,"difficulty":0.0147075057}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether or not everyone is thirsty. It is publicly announced that Vicki knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Vicki can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vicki","Margaret","Thomas"],"index":2376,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981074333,"difficulty":0.0018925667}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Annie can now know that Gerard can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Annie","Gerard"],"index":418,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997475743,"difficulty":0.0002524257}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Omer's forehead is not muddy. It is publicly announced that Wanda does not know whether Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Omer can now know that Wanda can know that Wanda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Allie","Wanda","Omer"],"index":49484,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9743233919,"difficulty":0.0256766081}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Clifford's forehead is muddy. It is publicly announced that Clifford knows whether Jennifer's forehead is muddy. It is publicly announced that Jennifer's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Clifford can now know that Jennifer can know that Clifford's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clifford","Jennifer","William"],"index":12001,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9631358385,"difficulty":0.0368641615}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Damaris knows whether Damaris is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Annie can now know whether Damaris can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Annie","Damaris","Jeffrey"],"index":30089,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997707009,"difficulty":0.0002292991}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eugene does not know whether or not everyone is thirsty. It is publicly announced that Eugene does not know whether Toni is thirsty. It is publicly announced that Kenneth does not know whether Toni is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Kenneth can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kenneth","Toni","Virginia","Eugene"],"index":26538,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Timothy. Valerie's card is shown to Timothy. Timothy's card is shown to Valerie. It is publicly announced that someone picked a red card. It is publicly announced that Valerie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Timothy can now know that Valerie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Timothy","Valerie"],"index":10333,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997001886,"difficulty":0.0002998114}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know that William can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","William"],"index":2069,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984291196,"difficulty":0.0015708804}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia knows whether Bruce's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"James can now know that Bruce can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Bruce","Julia"],"index":22775,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997465014,"difficulty":0.0002534986}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Shirley. Patsy's card is shown to Shirley. Shirley's card is shown to Kimberly. Shirley's card is shown to Patsy. It is publicly announced that someone picked a red card. It is publicly announced that Shirley picked a red card. It is publicly announced that Kimberly knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Shirley knows whether Patsy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Patsy can now know that Shirley can know that Patsy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shirley","Kimberly","Patsy"],"index":52489,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8898383975,"difficulty":0.1101616025}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy. It is publicly announced that Alecia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] 0","hypothesis":"Kenneth can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ralph","Kenneth","Robert","Alecia"],"index":1112,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998627305,"difficulty":0.001372695}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara knows whether or not everyone's forehead is muddy. It is publicly announced that Tamara knows whether Natalie's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Norma can now know whether Tamara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Natalie","Tamara","Norma"],"index":56353,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995903373,"difficulty":0.0004096627}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cruz's card is shown to Cruz. Maria's card is shown to John. Cruz's card is shown to Maria. John's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Cruz can now know whether John can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cruz","John","Maria"],"index":42022,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6670017838,"difficulty":0.3329982162}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwardo's card is shown to George. Michael's card is shown to George. George's card is shown to Edwardo. Edwardo's card is shown to Edwardo. Phillip's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Edwardo","Michael","Phillip"],"index":53976,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984856248,"difficulty":0.0015143752}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Eugenia. Marjorie's card is shown to Helen. Helen's card is shown to David. Helen's card is shown to Marjorie. Marjorie's card is shown to Marjorie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eugenia","Helen","David","Marjorie"],"index":9881,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997246861,"difficulty":0.0002753139}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Charles can now know whether Jeremy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeremy","Eliza","Charles"],"index":26044,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977250695,"difficulty":0.0022749305}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Veronica knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Judy can now know whether Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Veronica","Judy"],"index":39837,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997361302,"difficulty":0.0002638698}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Andrea's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Andrea can now know whether Andrea's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrea","Jennifer","John"],"index":9666,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9875453115,"difficulty":0.0124546885}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Kristine is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Steven can now know that Carrie can know whether Kristine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Kristine","Carrie","Ruben"],"index":20397,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8168779612,"difficulty":0.1831220388}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Royal does not know whether Royal's forehead is muddy. It is publicly announced that Anthony knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Royal can now know that Anthony can know whether Royal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Royal","Anthony"],"index":450,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994319081,"difficulty":0.0005680919}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roberta's card is shown to Gertrude. Angela's card is shown to Gertrude. Gertrude's card is shown to Roberta. Gertrude's card is shown to Gloria. Roberta's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Gertrude does not know whether Gertrude picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gertrude can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gertrude","Roberta","Gloria","Angela"],"index":57608,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997108579,"difficulty":0.0002891421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillie does not know whether Lillie's forehead is muddy. It is publicly announced that Brandon knows whether Brandon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Brandon can now know whether Cheryl can know whether Cheryl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cheryl","Brandon","Lillie"],"index":22915,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5438191295,"difficulty":0.4561808705}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa's forehead is muddy. It is publicly announced that Rosa's forehead is muddy. It is publicly announced that Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Vicki can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vicki","Brian","Rosa","Hilda"],"index":46884,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997236133,"difficulty":0.0002763867}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Clemente. Nona's card is shown to Nona. Carolyn's card is shown to Nona. Clemente's card is shown to Carolyn. Nona's card is shown to Carolyn. It is publicly announced that someone picked a red card. It is publicly announced that Nona does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Clemente can now know whether Nona can know whether Evelyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clemente","Nona","Evelyn","Carolyn"],"index":17867,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997972548,"difficulty":0.002027452}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kevin can now know whether Michael can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Kevin","Michael"],"index":36499,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996601343,"difficulty":0.0003398657}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Arthur can now know that Camelia can know that Kory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Arthur","Kory","Camelia"],"index":41557,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986457229,"difficulty":0.0013542771}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"James can now know that Armand can know whether Armand's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Michael","Armand"],"index":50732,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9889448285,"difficulty":0.0110551715}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Kevin is thirsty. It is publicly announced that Mary is thirsty. It is publicly announced that Kevin is thirsty. It is publicly announced that Kevin is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] Agentb knows whether (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Kevin can now know whether Mary can know that Kevin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Kevin"],"index":41021,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9901582599,"difficulty":0.0098417401}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Steven. Raquel's card is shown to David. Doris's card is shown to Doris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raquel can now know that David can know that Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","David","Raquel","Doris"],"index":11857,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983546138,"difficulty":0.0016453862}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Charles can now know that Adeline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Catherine","Adeline","Charles"],"index":61824,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980618358,"difficulty":0.0019381642}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vivian knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Vivian can now know whether Stephanie can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Vivian","Stephanie"],"index":54053,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994766116,"difficulty":0.0005233884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alexis does not know whether Terence is thirsty. It is publicly announced that Terence does not know whether Lina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Lina can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lina","Terence","Alexis"],"index":20717,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997817874,"difficulty":0.0002182126}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shelley does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether Carl can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Michael","Donna","Shelley"],"index":43824,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alida knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Kathryn can now know that Alida can know whether Kathryn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathryn","Alida"],"index":5529,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999745667,"difficulty":0.000254333}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Natasha's card is shown to Natasha. Natasha's card is shown to Manuel. Manuel's card is shown to Michael. Michael's card is shown to Michael. Natasha's card is shown to Carol. Carol's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Natasha does not know whether or not everyone picked a red card. It is publicly announced that Natasha picked a red card. It is publicly announced that Natasha does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Manuel can now know that Natasha can know whether Manuel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Natasha","Manuel","Michael","Carol"],"index":45394,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8639174104,"difficulty":1.8639174104}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy knows whether Laurie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Laurie can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dorothy","Laurie"],"index":41643,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997730851,"difficulty":0.0002269149}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emma is thirsty. It is publicly announced that Emma knows whether or not nobody is thirsty. It is publicly announced that Emma does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marilyn can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Emma","Mary","Marilyn","Jamie"],"index":13731,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9027217627,"difficulty":1.9027217627}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane does not know whether Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jane can now know that Alan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alan","Donald","Jane","Richard"],"index":66611,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974646568,"difficulty":0.0025353432}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Alyson can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wendy","George","Alyson","Mark"],"index":18036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939012527,"difficulty":0.0060987473}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Beatrice can now know whether Mark can know whether Julia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beatrice","Barbara","Mark","Julia"],"index":15367,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997119308,"difficulty":0.0002880692}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol does not know whether Carol's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Carol can now know that Nicole can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carol","Nicole","Luis"],"index":66233,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958486557,"difficulty":0.0041513443}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Fred can now know whether Elizabeth can know whether Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sarah","Elizabeth","Fred","Nancy"],"index":17161,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997346997,"difficulty":0.0002653003}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Lena's card is shown to Richard. Gussie's card is shown to Richard. Richard's card is shown to Homer. Homer's card is shown to Gussie. Gussie's card is shown to Gussie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Homer can now know whether Lena can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Homer","Lena","Gussie"],"index":44215,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ta can now know whether Tana can know that Tana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tana","Dale","Deborah","Ta"],"index":36368,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9035643935,"difficulty":0.0964356065}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Patrick. Ann's card is shown to Ann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lee can now know that Patrick can know whether Ann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patrick","Lee","Ann"],"index":5904,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5710164309,"difficulty":1.5710164309}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is not thirsty. It is publicly announced that Lucinda knows whether or not everyone is thirsty. It is publicly announced that John knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Susannah can now know whether Stephen can know that Stephen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lucinda","Susannah","John","Stephen"],"index":47080,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7766401768,"difficulty":1.7766401768}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Mary can now know that Linda can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Linda"],"index":45426,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9066487551,"difficulty":0.0933512449}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Octavia does not know whether or not everyone is thirsty. It is publicly announced that Billie knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Billie can now know that Octavia can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Octavia","Teresa","Charles","Billie"],"index":52618,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997107387,"difficulty":0.0002892613}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isabel does not know whether or not everyone is thirsty. It is publicly announced that Isabel does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Isabel can now know that Isabel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ashlee","Richard","Isabel"],"index":11085,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9740021229,"difficulty":0.0259978771}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Veronica's card is shown to Patricia. Patricia's card is shown to Veronica. Veronica's card is shown to Veronica. Stephen's card is shown to Veronica. Patricia's card is shown to Stephen. Stephen's card is shown to Stephen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Veronica can now know whether Stephen can know whether Veronica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Veronica","Stephen"],"index":45290,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979419112,"difficulty":0.0020580888}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Curtis can now know whether Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Curtis","Jacqueline"],"index":4939,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996244907,"difficulty":0.0003755093}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Timothy. Marc's card is shown to Marc. It is publicly announced that someone picked a red card. It is publicly announced that Marc knows whether Marc picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Marc can now know whether Timothy can know that Marc picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Timothy","Marc"],"index":36017,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.85994941,"difficulty":0.14005059}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lora knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know that Charles can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christine","Charles","Julio","Lora"],"index":64528,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995538592,"difficulty":0.0004461408}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Margaret's forehead is muddy. It is publicly announced that Margaret knows whether Shirley's forehead is muddy. It is publicly announced that Charles's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Charles can now know whether Margaret can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Margaret","Charles"],"index":41467,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ryan does not know whether John is thirsty. It is publicly announced that Ryan does not know whether or not everyone is thirsty. It is publicly announced that Ryan does not know whether Michell is thirsty. It is publicly announced that John does not know whether Michell is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Michell can now know whether Nancy can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michell","Nancy","John","Ryan"],"index":16758,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9868985415,"difficulty":0.0131014585}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is thirsty. It is publicly announced that Jessica is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(1) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(1) ] 0","hypothesis":"Priscilla can now know whether Jessie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","James","Jessie","Priscilla"],"index":45353,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997128844,"difficulty":0.0002871156}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether or not everyone's forehead is muddy. It is publicly announced that Elaine does not know whether Elaine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ashley can now know whether Betty can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Betty","Elaine","Ashley"],"index":45235,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995991588,"difficulty":0.0004008412}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernest's card is shown to Ernest. Shannon's card is shown to Ernest. Ernest's card is shown to Shannon. Emily's card is shown to Shannon. Shannon's card is shown to Emily. Ernest's card is shown to Adam. It is publicly announced that someone picked a red card. It is publicly announced that Shannon knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Shannon picked a black card. It is publicly announced that Ernest does not know whether Adam picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 4) ] Agenta knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Ernest can now know that Shannon can know that Ernest picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ernest","Shannon","Emily","Adam"],"index":28215,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8530004025,"difficulty":0.1469995975}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Victor knows whether Philip's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Philip can now know that Elvis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Victor","Elvis","Philip"],"index":44274,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965652823,"difficulty":0.0034347177}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeanna does not know whether or not everyone is thirsty. It is publicly announced that Reyes is thirsty. It is publicly announced that Jeanna does not know whether Marilyn is thirsty. It is publicly announced that Jeanna does not know whether Marilyn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jeanna can now know that Marilyn can know whether Marilyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Reyes","Jeanna","Marilyn"],"index":21102,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987105131,"difficulty":0.0012894869}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bessie knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know that Bessie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bessie","Kenneth","Karol"],"index":28804,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969269633,"difficulty":0.0030730367}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene knows whether Annie's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Annie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Arlene","Annie"],"index":37077,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Susan. Carolyn's card is shown to Carolyn. Susan's card is shown to Sandra. It is publicly announced that someone picked a red card. It is publicly announced that Carolyn does not know whether Sandra picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Sandra can now know that Susan can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Carolyn","Sandra"],"index":35445,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9372344017,"difficulty":0.0627655983}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma knows whether Robert's forehead is muddy. It is publicly announced that Chris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Chris can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Chris","Hannah","Thelma","Robert"],"index":3141,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997723699,"difficulty":0.0002276301}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Mark","Robert"],"index":31525,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982846379,"difficulty":0.0017153621}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bessie knows whether or not everyone is thirsty. It is publicly announced that Elvis knows whether Bessie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Bessie can now know that Elvis can know that Elvis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elvis","Bessie","William"],"index":275,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6638706923,"difficulty":1.6638706923}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jennifer can now know whether Helen can know that Minh's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Minh","Jennifer"],"index":22208,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984423518,"difficulty":0.0015576482}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacey knows whether Stacey is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Charles can now know whether Shiloh can know that Shiloh is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steve","Stacey","Charles","Shiloh"],"index":13179,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.508118093,"difficulty":1.508118093}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jonathan can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jonathan","Stephanie","Barry","Ralph"],"index":17093,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997523427,"difficulty":0.0002476573}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francesca does not know whether Donna is thirsty. It is publicly announced that Troy knows whether Troy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Donna can now know that Francesca is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Troy","Francesca","Elizabeth"],"index":42383,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997355938,"difficulty":0.002644062}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Rene","Vergie"],"index":61094,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940522313,"difficulty":0.0059477687}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Mary can now know whether Dustin can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dustin","Thomas","Mary","Clara"],"index":52880,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996449947,"difficulty":0.0003550053}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Beverly. Rudy's card is shown to James. Steven's card is shown to Steven. James's card is shown to Rudy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know that James can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","James","Steven","Rudy"],"index":19986,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997151494,"difficulty":0.0002848506}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Robert knows whether Timothy's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Timothy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Timothy can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Timothy","Robert"],"index":33231,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9328221083,"difficulty":0.0671778917}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Stanley can now know whether Stanley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Theresa","Stanley","Paul"],"index":46611,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6806694865,"difficulty":0.3193305135}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Melissa can now know whether Cordelia can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cordelia","Melissa"],"index":622,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997403026,"difficulty":0.0002596974}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victor's card is shown to Richard. Albertina's card is shown to Albertina. Viola's card is shown to Albertina. Richard's card is shown to Victor. Victor's card is shown to Victor. Viola's card is shown to Victor. Richard's card is shown to Viola. Viola's card is shown to Viola. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:1,3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:1,3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Victor can now know that Richard can know whether Albertina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Albertina","Victor","Viola"],"index":45149,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5696917772,"difficulty":1.5696917772}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Elizabeth is thirsty. It is publicly announced that George does not know whether Gary is thirsty. It is publicly announced that Elizabeth is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Gary can now know whether Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jennifer","Gary","Elizabeth","George"],"index":57460,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9392187595,"difficulty":1.9392187595}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda does not know whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Brenda can now know that Lori can know whether Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lori","Darrel","William","Brenda"],"index":14651,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.983561933,"difficulty":0.016438067}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Katherine. Robin's card is shown to Robin. Rhonda's card is shown to Rhonda. It is publicly announced that someone picked a red card. It is publicly announced that Robin picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Robin does not know whether Katherine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Katherine can now know that Robin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katherine","Robin","Rhonda"],"index":61990,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6961627007,"difficulty":0.3038372993}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that April is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"John can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["April","Barry","Robert","John"],"index":20046,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984234571,"difficulty":0.0015765429}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peggy knows whether or not nobody's forehead is muddy. It is publicly announced that Peggy knows whether Peggy's forehead is muddy. It is publicly announced that William's forehead is muddy. It is publicly announced that Harry knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"William can now know that Virginia can know that Peggy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Peggy","Harry","Virginia"],"index":48310,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9604406953,"difficulty":0.0395593047}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keith's card is shown to Daisy. Judi's card is shown to Raymond. Daisy's card is shown to Judi. Raymond's card is shown to Judi. Judi's card is shown to Judi. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know that Raymond can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Daisy","Raymond","Judi"],"index":66482,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Floyd can now know that Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Floyd","Roderick","Melissa"],"index":16839,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955659509,"difficulty":0.0044340491}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mildred knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mildred can now know that Eric can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mildred","Henry","Eric"],"index":48794,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998428762,"difficulty":0.001571238}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerri's card is shown to Jerri. Jerri's card is shown to Sophia. Sophia's card is shown to Sophia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Jerri can now know whether Sophia can know whether Jerri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jerri","Sophia"],"index":34876,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979900122,"difficulty":0.0020099878}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Eric can now know whether John can know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","John","Eric"],"index":58329,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999520421,"difficulty":0.000479579}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Kristopher can now know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Paul","Kristopher"],"index":17635,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959679842,"difficulty":0.0040320158}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kerry does not know whether Kelly is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"John can now know whether Kelly can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kerry","Kelly","John"],"index":6674,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deirdre's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Russ can now know that Deirdre can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Russ","Deirdre"],"index":53772,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997555614,"difficulty":0.0002444386}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Shane can now know whether Chelsea can know whether Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Shane","Chelsea"],"index":59838,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996997118,"difficulty":0.0003002882}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rudy does not know whether Martin is thirsty. It is publicly announced that Amanda is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Amanda can now know that Mark can know that Amanda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rudy","Amanda","Martin","Mark"],"index":30620,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9773237109,"difficulty":0.0226762891}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Don's forehead is muddy. It is publicly announced that James knows whether Don's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"James can now know whether Don can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Don"],"index":4044,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999682188,"difficulty":0.000317812}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesus knows whether or not everyone is thirsty. It is publicly announced that Edward knows whether Edward is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jesus can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edward","Jesus"],"index":58242,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999773562,"difficulty":0.000226438}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erick's card is shown to Erick. Charlene's card is shown to Erick. Erick's card is shown to Charlene. Charlene's card is shown to Charlene. Erick's card is shown to Jackie. Charlene's card is shown to Jackie. Stacy's card is shown to Stacy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Erick can now know that Jackie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erick","Charlene","Jackie","Stacy"],"index":55518,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981201291,"difficulty":0.0018798709}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwight's forehead is not muddy. It is publicly announced that Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Kevin can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kevin","Dwight"],"index":50942,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984607697,"difficulty":0.0015392303}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lloyd can now know whether Judy can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lloyd","Judy","Leonard","Eric"],"index":25636,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996024966,"difficulty":0.0003975034}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Nellie can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nellie","Michael","John","Pauline"],"index":65770,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.972604394,"difficulty":0.027395606}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hazel knows whether Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Michael can now know whether Janice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Hazel","Jim","Janice"],"index":41408,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997538924,"difficulty":0.0002461076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Veronica knows whether Veronica is thirsty. It is publicly announced that Maria does not know whether Veronica is thirsty. It is publicly announced that Calvin does not know whether Laurie is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Laurie can now know whether Maria can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Veronica","Laurie","Maria","Calvin"],"index":26120,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pedro's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Pedro can now know whether Brandi can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pedro","Howard","Jacqueline","Brandi"],"index":17743,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996476173,"difficulty":0.0003523827}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myung's card is shown to Kevin. Abel's card is shown to Kevin. Myung's card is shown to Myung. Kevin's card is shown to Abel. Abel's card is shown to Abel. Abel's card is shown to Douglas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Myung can now know whether Abel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Myung","Abel","Douglas"],"index":55166,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7965758443,"difficulty":1.7965758443}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kimberly can now know that Darryl can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","Evelyn","Darryl","Scotty"],"index":53533,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983508587,"difficulty":0.0016491413}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether or not everyone is thirsty. It is publicly announced that Crystal does not know whether Chad is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Eric can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Crystal","Chad","Eric","Stacey"],"index":54679,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980371594,"difficulty":0.0019628406}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Joseph. Stephen's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Stephen picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Stephen can now know whether Joseph can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Stephen"],"index":2221,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7717943192,"difficulty":0.2282056808}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynda's card is shown to Lynda. Stewart's card is shown to Lynda. Lynda's card is shown to Donald. Donald's card is shown to Donald. Bradley's card is shown to Bradley. Lynda's card is shown to Stewart. Donald's card is shown to Stewart. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether Stewart can know whether Bradley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lynda","Donald","Bradley","Stewart"],"index":19862,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998455286,"difficulty":0.001544714}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christina's card is shown to Kevin. Diane's card is shown to Marsha. Kevin's card is shown to Christina. Marsha's card is shown to Christina. Kevin's card is shown to Diane. Marsha's card is shown to Diane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know whether Marsha can know that Marsha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Marsha","Christina","Diane"],"index":41087,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.914968133,"difficulty":0.085031867}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stanley's card is shown to Kathryn. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathryn can now know whether Kathryn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathryn","Joshua","Stanley"],"index":57742,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8562967777,"difficulty":0.1437032223}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Patrick can now know whether Raymond can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Reginald","Raymond","Patrick"],"index":44512,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994522929,"difficulty":0.0005477071}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yesenia does not know whether Yesenia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gladys can now know that Gladys's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gladys","Leslie","Yesenia","Sharonda"],"index":20923,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965309501,"difficulty":0.0034690499}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Roy can now know whether Carl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roy","Carl"],"index":37341,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994764924,"difficulty":0.0005235076}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Delores can now know whether Michael can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Delores"],"index":32937,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9948328733,"difficulty":1.9948328733}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kyle does not know whether or not everyone is thirsty. It is publicly announced that Cindy knows whether someone is thirsty. It is publicly announced that Cindy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Cindy can now know that Cindy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andrea","Cindy","Kyle","Wilbert"],"index":67182,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9823447466,"difficulty":0.0176552534}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack does not know whether Jack's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Patrick can now know that Diane can know that Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diane","Karen","Patrick","Jack"],"index":67572,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976652861,"difficulty":0.0023347139}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether Norma's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentd knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Percy can now know that Norma can know whether Norma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danielle","John","Norma","Percy"],"index":52831,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995883107,"difficulty":0.0004116893}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lee does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Susie can now know whether Robert can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susie","Frances","Lee","Robert"],"index":41767,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6337243319,"difficulty":1.6337243319}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"James can now know that Dana can know that Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Dana","Donna","James"],"index":45029,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998108387,"difficulty":0.001891613}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Bonnie's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Curtis can now know whether Bonnie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Curtis","Bonnie","Michael"],"index":111,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995039701,"difficulty":0.0004960299}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kim does not know whether William is thirsty. It is publicly announced that William is not thirsty. It is publicly announced that William does not know whether Kim is thirsty. It is publicly announced that Kim knows whether William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know that Robert can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","William","Robert"],"index":63052,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997840524,"difficulty":0.0002159476}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to James. Mary's card is shown to James. James's card is shown to Jessica. Jessica's card is shown to Jessica. James's card is shown to Nancy. Mary's card is shown to Nancy. James's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Nancy can know whether Nancy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Jessica","Nancy","Mary"],"index":29591,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8289880753,"difficulty":0.1710119247}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy. It is publicly announced that Troy knows whether Amanda's forehead is muddy. It is publicly announced that Amanda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Thomas can now know whether Troy can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Troy","Emily","Amanda"],"index":53611,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9724267125,"difficulty":0.0275732875}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Elaine can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marcus","Elaine","Shannon"],"index":30160,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997459054,"difficulty":0.0002540946}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alan does not know whether Jerry is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jerry can now know that Gerald can know whether Alan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alan","Jerry","Gerald"],"index":64398,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9931451082,"difficulty":0.0068548918}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Brenda can now know that Lori can know that Brenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lori","Stacy","Michelle","Brenda"],"index":43195,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9628700614,"difficulty":0.0371299386}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Benjamin. Roger's card is shown to Benjamin. Benjamin's card is shown to Laura. Laura's card is shown to William. William's card is shown to William. Laura's card is shown to Roger. William's card is shown to Roger. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know whether Roger picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Benjamin","Laura","William","Roger"],"index":34397,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9473828673,"difficulty":1.9473828673}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Howard. Danny's card is shown to Howard. Howard's card is shown to Bonnie. Bonnie's card is shown to Bonnie. Bonnie's card is shown to Norman. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bonnie can now know that Danny can know that Howard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Howard","Danny","Bonnie","Norman"],"index":33867,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978049397,"difficulty":0.0021950603}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Nicole. Doris's card is shown to Nicole. Emma's card is shown to Doris. Nicole's card is shown to Emma. Emma's card is shown to Emma. It is publicly announced that someone picked a red card. It is publicly announced that Emma does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Doris can now know that Nicole can know that Doris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicole","Doris","Emma"],"index":15313,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6280497313,"difficulty":0.3719502687}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether Royce is thirsty. It is publicly announced that Royce does not know whether Stephen is thirsty. It is publicly announced that Stephen does not know whether Royce is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Delores can now know that Gilbert can know that Gilbert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Royce","Stephen","Delores","Gilbert"],"index":56744,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9616003036,"difficulty":0.0383996964}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paulette's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Paulette can now know whether Caroline can know that Caroline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","Caroline","Michael","Paulette"],"index":58837,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996340275,"difficulty":0.0003659725}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hope knows whether Robert's forehead is muddy. It is publicly announced that Robert's forehead is muddy. It is publicly announced that Maria does not know whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"William can now know that Robert can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","William","Hope","Robert"],"index":30401,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997124076,"difficulty":0.0002875924}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Berniece can now know that Lillian can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Berniece","James","Lillian"],"index":27278,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8775186539,"difficulty":0.1224813461}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know that Kimberly can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Megan","Kimberly","Thomas","Natasha"],"index":22549,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurie knows whether or not nobody's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy. It is publicly announced that Laurie does not know whether Laurie's forehead is muddy. It is publicly announced that Harry knows whether Harry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dorothy can now know whether Laurie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harry","Laurie","Dorothy"],"index":1230,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994309545,"difficulty":0.0005690455}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know whether Andrew can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Doris","Robert","Andrew"],"index":56280,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978038669,"difficulty":0.0021961331}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Karen. Michelle's card is shown to Paul. Karen's card is shown to Michelle. Paul's card is shown to Michelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know whether Karen can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Paul","Michelle"],"index":51865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978947043,"difficulty":0.0021052957}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Gerry can now know that Brad can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gerry","Margaret","Brad","Harold"],"index":58618,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984227419,"difficulty":0.0015772581}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jorge's card is shown to Jorge. Corey's card is shown to Jorge. Heather's card is shown to Heather. Corey's card is shown to Corey. It is publicly announced that someone picked a red card. It is publicly announced that Corey does not know whether Jorge picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Heather can now know that Corey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jorge","Heather","Corey"],"index":55914,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9369118214,"difficulty":0.0630881786}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Megan's card is shown to Sharon. Rosa's card is shown to Sharon. Sharon's card is shown to Megan. Megan's card is shown to Megan. Rosa's card is shown to Megan. Rosa's card is shown to Rosa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rosa can now know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Megan","Rosa"],"index":18097,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977532029,"difficulty":0.0022467971}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sammy's card is shown to Charles. Charles's card is shown to Sammy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Sammy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Sammy"],"index":15533,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997176528,"difficulty":0.0002823472}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leon's card is shown to Cassandra. Doris's card is shown to Judy. Leon's card is shown to Judy. Doris's card is shown to Doris. Doris's card is shown to Leon. It is publicly announced that someone picked a red card. It is publicly announced that Cassandra does not know whether Doris picked a red card. It is publicly announced that Doris picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Judy can now know that Doris can know whether Cassandra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cassandra","Judy","Doris","Leon"],"index":20989,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7829595208,"difficulty":0.2170404792}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pauline knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Pauline can now know whether John can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Pauline","Yolanda","Richard"],"index":31551,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999741137,"difficulty":0.000258863}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurice's card is shown to Maurice. Mary's card is shown to Maurice. Maurice's card is shown to Maria. Maria's card is shown to Maria. Maurice's card is shown to Mary. Matthew's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Maurice does not know whether Matthew picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Matthew can now know that Maurice can know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maurice","Maria","Matthew","Mary"],"index":14060,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932431579,"difficulty":0.0067568421}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Marion can now know that Elenora can know that Jamie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marion","Jamie","Elenora","Joseph"],"index":16250,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9303615689,"difficulty":0.0696384311}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorna's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"John can now know that Greg can know that Lorna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lorna","Greg","John"],"index":56058,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8594061136,"difficulty":0.1405938864}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Wanda. Wanda's card is shown to Janice. Janice's card is shown to Miguel. Miguel's card is shown to Miguel. Miguel's card is shown to Theodore. It is publicly announced that someone picked a red card. It is publicly announced that Theodore does not know whether Wanda picked a red card. It is publicly announced that Wanda does not know whether Janice picked a red card. It is publicly announced that Miguel knows whether Miguel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Theodore can now know whether Miguel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wanda","Janice","Miguel","Theodore"],"index":51126,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5444802642,"difficulty":0.4555197358}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann knows whether John's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] Agentc knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"John can now know whether Robin can know that Robin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sara","Robin","John","Ann"],"index":3963,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996573925,"difficulty":0.0003426075}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brittany does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"William can now know whether Brittany can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Brittany","Gloria"],"index":29826,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988687634,"difficulty":0.0011312366}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robin is thirsty. It is publicly announced that Robin does not know whether Craig is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robin can now know whether Craig can know whether Craig is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Craig","Robin"],"index":39973,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976032376,"difficulty":0.0023967624}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stuart's card is shown to Wanda. Minnie's card is shown to Wanda. Stuart's card is shown to Stuart. Minnie's card is shown to Stuart. Minnie's card is shown to Claudia. Stuart's card is shown to Minnie. It is publicly announced that someone picked a red card. It is publicly announced that Claudia does not know whether Stuart picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Minnie can now know that Stuart can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wanda","Stuart","Claudia","Minnie"],"index":5063,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9375711083,"difficulty":0.0624288917}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Callie can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Callie","Michael"],"index":59933,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984903336,"difficulty":0.0015096664}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Marisa. Bebe's card is shown to Marisa. Judy's card is shown to Sandra. Bebe's card is shown to Sandra. It is publicly announced that someone picked a red card. It is publicly announced that Judy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Marisa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marisa","Judy","Bebe","Sandra"],"index":46976,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982008934,"difficulty":0.0017991066}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Anthony. Earl's card is shown to Anthony. Earl's card is shown to Cristina. Kelly's card is shown to Kelly. Cristina's card is shown to Earl. Earl's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Kelly knows whether someone picked a red card. It is publicly announced that Anthony picked a red card. It is publicly announced that Cristina does not know whether Kelly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Kelly can now know that Earl can know whether Earl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Cristina","Kelly","Earl"],"index":47559,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.919166863,"difficulty":0.080833137}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter does not know whether Juanita is thirsty. It is publicly announced that Terry does not know whether Peter is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Juanita can now know whether Terry can know whether Terry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Juanita","Terry","Peter"],"index":6015,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998429358,"difficulty":0.001570642}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeff does not know whether Jeff's forehead is muddy. It is publicly announced that Cathy does not know whether Cathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know that Jeff can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeff","Cathy","James"],"index":20639,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9389615059,"difficulty":0.0610384941}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Edward can now know whether Larry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carmen","Maribel","Larry","Edward"],"index":11909,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996196032,"difficulty":0.0003803968}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doreen does not know whether Ricky is thirsty. It is publicly announced that Lorraine is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] Agentd knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"William can now know that Ricky can know that Lorraine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doreen","Lorraine","Ricky","William"],"index":23017,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9940516353,"difficulty":0.0059483647}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dixie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Felix can now know that Dixie can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Felix","Dixie","Cara"],"index":14689,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997441173,"difficulty":0.0002558827}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Jacqueline. Jacqueline's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Jesus does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jacqueline can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacqueline","Jesus","Carl","John"],"index":53617,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest knows whether Tommy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Monica can now know that Ernest can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tommy","Robert","Ernest","Monica"],"index":58875,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985303879,"difficulty":0.0014696121}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Katherine can now know whether Judy can know that Katherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Katherine","Judy"],"index":50340,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9890861511,"difficulty":0.0109138489}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bessie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jesus can now know that Brian can know that Jesus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Annette","Jesus","Brian","Bessie"],"index":29372,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7544406056,"difficulty":0.2455593944}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not everyone's forehead is muddy. It is publicly announced that Edward does not know whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Edward can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Christopher","Christian","Edward"],"index":28164,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997788072,"difficulty":0.0002211928}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Ignacio. Emily's card is shown to Judy. Emily's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Judy can now know that Ignacio picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ignacio","Judy","Emily","Michael"],"index":51989,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.995408833,"difficulty":0.004591167}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris does not know whether or not everyone's forehead is muddy. It is publicly announced that Doris knows whether Thelma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Thelma can now know whether Philip can know that Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doris","Doreen","Philip","Thelma"],"index":44105,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7191304564,"difficulty":0.2808695436}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Donald. Mary's card is shown to Donald. Robin's card is shown to Gary. Donald's card is shown to Gary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robin","Donald","Gary","Mary"],"index":6717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6223440766,"difficulty":0.3776559234}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chloe knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Brian can now know that Marguerite can know that Marguerite's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerry","Chloe","Brian","Marguerite"],"index":3403,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984439015,"difficulty":0.0015560985}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heather's card is shown to David. David's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that Heather knows whether Heather picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Heather can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Heather"],"index":65124,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9059901237,"difficulty":1.9059901237}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Megan does not know whether or not everyone's forehead is muddy. It is publicly announced that Michelle knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Michelle can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Megan","John","Michelle"],"index":9037,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997147918,"difficulty":0.0002852082}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alex's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Alex can now know that Pauline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Owen","Alex","Yolanda","Pauline"],"index":44222,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951783419,"difficulty":0.0048216581}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricardo's card is shown to Della. Della's card is shown to Ricardo. Ricardo's card is shown to Ricardo. Della's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Ricardo knows whether Ricardo picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ricardo can now know whether Della can know that Della picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Della","Ricardo","Stephen"],"index":64776,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7800415158,"difficulty":0.2199584842}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Marie. Marie's card is shown to Amber. Amber's card is shown to Amber. Suzanne's card is shown to Amber. Suzanne's card is shown to Suzanne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amber can now know that Suzanne can know whether Suzanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marie","Amber","Suzanne"],"index":417,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6510472894,"difficulty":0.3489527106}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Lori knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Michael can now know that Lori's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Lori","Dennis","Allen"],"index":43344,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996455431,"difficulty":0.003544569}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Michelle can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michelle","Frank","William"],"index":36229,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9898700118,"difficulty":0.0101299882}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Faye is thirsty. It is publicly announced that Mary is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(1) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Faye can now know whether John can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","John","Faye"],"index":21165,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989959598,"difficulty":0.0010040402}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marc's card is shown to Michael. Michael's card is shown to Kelli. Kelli's card is shown to Marc. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Kelli","Marc"],"index":17595,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953917265,"difficulty":0.0046082735}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harriet knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Charles can now know that Harriet can know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Patricia","Jason","Harriet"],"index":3312,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985313416,"difficulty":0.0014686584}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jolene's card is shown to Jolene. Dorothy's card is shown to Jolene. Daniel's card is shown to Dorothy. Dorothy's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Daniel does not know whether Daniel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Daniel can now know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jolene","Dorothy","Daniel"],"index":2492,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.977822721,"difficulty":1.977822721}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Amy. Beatrice's card is shown to Ernest. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amy","Daniel","Ernest","Beatrice"],"index":56498,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985161424,"difficulty":0.0014838576}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Conrad does not know whether or not everyone is thirsty. It is publicly announced that Esther knows whether Esther is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Esther can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Conrad","Esther","Steven","Joseph"],"index":61035,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969171286,"difficulty":0.0030828714}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Tyrone can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Tyrone","Michael","Gertrude"],"index":36267,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983683228,"difficulty":0.0016316772}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria knows whether or not nobody's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Victoria can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Victoria","Vincent","James"],"index":18425,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9825532436,"difficulty":0.0174467564}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judith does not know whether or not everyone is thirsty. It is publicly announced that Judith does not know whether or not everyone is thirsty. It is publicly announced that Michael knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Michael can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Judith"],"index":61111,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997240901,"difficulty":0.0002759099}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Mary can now know that Tina can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Charles","Tina","Mary"],"index":57028,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.995896697,"difficulty":0.004103303}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorraine knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Nicholas can now know that Natalie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charissa","Natalie","Lorraine","Nicholas"],"index":64676,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977949858,"difficulty":0.0022050142}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Sophia. Sophia's card is shown to Danielle. It is publicly announced that someone picked a red card. It is publicly announced that Danielle picked a red card. It is publicly announced that Sophia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Sophia can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sophia","Danielle"],"index":12407,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8928956985,"difficulty":1.8928956985}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jose can now know that Victoria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Mario","Jose","Robert"],"index":11228,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984507561,"difficulty":0.0015492439}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eileen does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Eileen can now know whether Geneva can know that Leslie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Geneva","Eileen","Leslie"],"index":35148,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9975172281,"difficulty":0.0024827719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Avelina knows whether Melvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"James can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Avelina","Melvin","John","James"],"index":54845,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993218184,"difficulty":0.0006781816}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Carol's card is shown to Michael. Carol's card is shown to Carol. Janet's card is shown to Carol. Michael's card is shown to Lucas. Carol's card is shown to Lucas. Michael's card is shown to Janet. Janet's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carol can now know that Janet can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Carol","Lucas","Janet"],"index":64362,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurie knows whether Laurie's forehead is muddy. It is publicly announced that Paula knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Paula can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laurie","Ernest","Paula","Heather"],"index":17467,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983249307,"difficulty":0.0016750693}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francisco is thirsty. It is publicly announced that Zack knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Eleanor can now know that Zack can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Zack","Mary","Francisco","Eleanor"],"index":16886,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981498718,"difficulty":0.0018501282}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carla's card is shown to Bryan. Jamie's card is shown to Robert. Robert's card is shown to Carla. Carla's card is shown to Carla. Bryan's card is shown to Jamie. It is publicly announced that someone picked a red card. It is publicly announced that Bryan does not know whether Jamie picked a red card. It is publicly announced that Robert picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(2) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Bryan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bryan","Robert","Carla","Jamie"],"index":61309,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998588264,"difficulty":0.001411736}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jill knows whether Karyl's forehead is muddy. It is publicly announced that Karyl knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Jill can now know that Karyl can know whether Jill's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Karyl","Jill"],"index":26743,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982398748,"difficulty":0.0017601252}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that Charles does not know whether Marion is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Chester knows whether Chester is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Chester can now know that Marion can know that Marion is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Chester","Marion","Charles"],"index":12066,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9301276207,"difficulty":0.0698723793}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Naomi's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Anthony can now know that Laura can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Timothy","Naomi","Laura"],"index":41236,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983875751,"difficulty":0.0016124249}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carol. Anthony's card is shown to Carol. Carol's card is shown to Bill. Anthony's card is shown to Bill. Bill's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know that Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carol","Bill","Anthony"],"index":18105,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980789423,"difficulty":0.0019210577}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Benjamin. Elizabeth's card is shown to Elizabeth. Benjamin's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Benjamin picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robert can now know that Benjamin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Benjamin","Elizabeth","Robert"],"index":9554,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997065663,"difficulty":0.0002934337}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew does not know whether or not everyone is thirsty. It is publicly announced that Matthew does not know whether Betty is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"James can now know whether Michael can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Betty","James","Michael"],"index":43586,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9972165823,"difficulty":0.0027834177}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christina knows whether or not everyone is thirsty. It is publicly announced that Karen is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Christina can now know that Karen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Karen","Christina"],"index":57666,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6214377284,"difficulty":1.6214377284}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Julian. Julian's card is shown to Gerald. Julian's card is shown to Karen. Gerald's card is shown to Karen. James's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Julian does not know whether Julian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Julian can now know that James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julian","Gerald","James","Karen"],"index":9272,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.988522768,"difficulty":0.011477232}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kurt's card is shown to Yuki. Yuki's card is shown to Kurt. Kurt's card is shown to Kurt. It is publicly announced that someone picked a red card. It is publicly announced that Kurt picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Kurt can now know whether Yuki can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Yuki","Kurt"],"index":16197,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cecelia is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] 0","hypothesis":"Cecelia can now know that Helen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cecelia","Lillie","Helen"],"index":7945,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9559585452,"difficulty":0.0440414548}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Ronald can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Ronald","Sharon","Jason"],"index":38409,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984110594,"difficulty":0.0015889406}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Edward's card is shown to Michael. Michael's card is shown to Cheryl. Jane's card is shown to Cheryl. Michael's card is shown to Jane. Edward's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Jane picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Michael can now know whether Jane can know that Jane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Cheryl","Jane","Edward"],"index":13257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9261645079,"difficulty":0.0738354921}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Frank can now know whether Eric can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leland","Bill","Frank","Eric"],"index":1067,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995774627,"difficulty":0.0004225373}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Francis. Virginia's card is shown to Todd. Francis's card is shown to Virginia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Francis can now know that Francis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francis","Todd","Virginia","Melissa"],"index":30362,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945462942,"difficulty":0.0054537058}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Mark can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Donald","Mary","Gladys"],"index":34514,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983078241,"difficulty":0.0016921759}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timmy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Harold can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harold","Bryan","Timmy","Eva"],"index":52716,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997420907,"difficulty":0.0002579093}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Steven. Tracey's card is shown to Steven. Tracey's card is shown to Tracey. It is publicly announced that someone picked a red card. It is publicly announced that Tracey does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Steven can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Steven","Tracey"],"index":9144,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979327917,"difficulty":0.0020672083}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Carlos can now know that Mallory can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carlos","Mallory"],"index":59185,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984787107,"difficulty":0.0015212893}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Eileen does not know whether Evelyn is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Eileen can now know whether David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","David","Evelyn","Eileen"],"index":17967,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9948585033,"difficulty":0.0051414967}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether James is thirsty. It is publicly announced that Pearl does not know whether or not everyone is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty. It is publicly announced that Russell does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Pearl can now know that James can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Russell","Pearl","John","James"],"index":778,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9831169844,"difficulty":0.0168830156}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anita knows whether Anita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Anita can now know that Bryan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Catherine","Anita","Bryan"],"index":249,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984270334,"difficulty":0.0015729666}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alma knows whether or not everyone's forehead is muddy. It is publicly announced that Alma does not know whether Alma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Charles can now know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Rudolph","Alma"],"index":34675,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9157204032,"difficulty":0.0842795968}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Patricia is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know whether David can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","David","Thomas","Patricia"],"index":53364,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976559877,"difficulty":0.0023440123}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irene does not know whether Timothy is thirsty. It is publicly announced that Irene does not know whether Diana is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Diana can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Timothy","Irene","Diana"],"index":4273,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984058738,"difficulty":0.0015941262}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brad's card is shown to Brad. Brad's card is shown to Jacalyn. Jacalyn's card is shown to Jacalyn. John's card is shown to Jacalyn. Brad's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card. It is publicly announced that Brad picked a black card. It is publicly announced that Jacalyn knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Brad can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brad","Jacalyn","John"],"index":24399,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985608459,"difficulty":0.0014391541}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tami can now know that Francina can know whether Francina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tami","Janet","Francina","Frances"],"index":22154,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.994127512,"difficulty":0.005872488}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Penney can know that Blake is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Penney","Michael","Blake","Christopher"],"index":19284,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9860199094,"difficulty":0.0139800906}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Amanda can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","Denise","Robert","Aaron"],"index":54467,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997163415,"difficulty":0.0002836585}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kent's card is shown to Victoria. Joshua's card is shown to Joshua. Victoria's card is shown to Rosemary. Joshua's card is shown to Rosemary. Joshua's card is shown to Kent. It is publicly announced that someone picked a red card. It is publicly announced that Joshua picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Joshua can now know that Kent can know whether Rosemary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victoria","Joshua","Rosemary","Kent"],"index":16433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6514199376,"difficulty":0.3485800624}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lyle's card is shown to Lyle. Lyle's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jason can now know that Lyle can know that Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lyle","Jason"],"index":16806,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962064028,"difficulty":0.0037935972}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Thomas can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Paula","Richard","Thomas"],"index":279,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Paul can now know that Mark can know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stacey","Mark","Paul"],"index":65648,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997430444,"difficulty":0.0002569556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad knows whether someone's forehead is muddy. It is publicly announced that Jonathan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jonathan can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chad","Jonathan","Nicholas","Margaret"],"index":33138,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9942715168,"difficulty":0.0057284832}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Jean's forehead is muddy. It is publicly announced that Steven's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jean can now know that Jean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Jean","Steven"],"index":55483,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9855938554,"difficulty":0.0144061446}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cassie does not know whether or not everyone's forehead is muddy. It is publicly announced that Jeremy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Jeremy can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Phillip","Nancy","Jeremy","Cassie"],"index":31191,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967486858,"difficulty":0.0032513142}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Rose can now know that Brigette can know that Rose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rose","Leona","Brigette"],"index":53614,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983292222,"difficulty":0.0016707778}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! 1 ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! 1 ] 0","hypothesis":"William can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brenda","William"],"index":2040,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997671247,"difficulty":0.0002328753}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darryl does not know whether or not everyone's forehead is muddy. It is publicly announced that Darryl's forehead is muddy. It is publicly announced that Darryl knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Michael can now know whether Darryl can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Darryl","Michael"],"index":29096,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988173842,"difficulty":0.0011826158}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Jason. James's card is shown to Jason. Shawn's card is shown to Susan. Jason's card is shown to Shawn. Susan's card is shown to Shawn. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Jason picked a red card. It is publicly announced that Shawn knows whether someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Susan can now know whether Shawn can know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Susan","Shawn","James"],"index":31175,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985780716,"difficulty":0.0014219284}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Lisa's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicolas knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Evelyn can now know that Lisa can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Melissa","Nicolas","Evelyn"],"index":45875,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997594953,"difficulty":0.0002405047}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bill knows whether or not everyone is thirsty. It is publicly announced that Silvia is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Bill can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Silvia","Bill"],"index":35225,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997293353,"difficulty":0.0002706647}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] 0","hypothesis":"Patricia can now know that Donna can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donna","Patricia"],"index":18664,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984600544,"difficulty":0.0015399456}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Jan can now know whether Jan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tommy","Faith","Jan"],"index":4340,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988397956,"difficulty":0.0011602044}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelo's card is shown to Angelo. Angelo's card is shown to Carmen. Carmen's card is shown to Carmen. Alicia's card is shown to Carmen. Angelo's card is shown to David. David's card is shown to David. David's card is shown to Alicia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Angelo can now know that Carmen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angelo","Carmen","David","Alicia"],"index":16541,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981466532,"difficulty":0.0018533468}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Barbara can now know that Angela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherry","Angela","Barbara"],"index":52949,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9613716602,"difficulty":0.0386283398}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Loretta knows whether Loretta is thirsty. It is publicly announced that Loretta is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Karen can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Tommy","Loretta"],"index":57833,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8071075678,"difficulty":1.8071075678}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Donald can now know that Jason can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roland","Jason","Veronica","Donald"],"index":63158,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997698665,"difficulty":0.0002301335}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy knows whether or not nobody is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Timothy can now know that Robert can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Timothy"],"index":13300,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9971469045,"difficulty":0.0028530955}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Christopher can now know that Mary can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Christopher","Mary"],"index":64280,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982808828,"difficulty":0.0017191172}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Johnny can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Janice","Florene","Johnny"],"index":37022,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9008425474,"difficulty":0.0991574526}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lola does not know whether Lola's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lola knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lola can now know that Dolores can know that Lola's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lola","Mary","Dolores"],"index":59009,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5324884653,"difficulty":1.5324884653}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pamela can now know that Helen can know that Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sherry","Pamela","Helen","Rita"],"index":62956,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983160496,"difficulty":0.0016839504}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori knows whether Harold's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Harold can now know that Lori can know whether Harold's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lori","Harold"],"index":6073,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995144606,"difficulty":0.0004855394}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Greg. John's card is shown to Greg. Greg's card is shown to Linda. John's card is shown to Linda. Kevin's card is shown to Kevin. Linda's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Greg knows whether or not nobody picked a red card. It is publicly announced that Greg picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 1 ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 1 ] 0","hypothesis":"Greg can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Greg","Linda","Kevin","John"],"index":65365,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977037311,"difficulty":0.0022962689}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Austin's card is shown to Angel. Angel's card is shown to Austin. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Angel can now know that Angel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angel","Annette","Austin"],"index":20027,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9564601779,"difficulty":0.0435398221}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nila's card is shown to Nila. Gloria's card is shown to Nila. Gloria's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that Gloria picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Nila can now know that Gloria can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nila","Gloria"],"index":42937,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984813333,"difficulty":0.0015186667}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Gerald. Sheila's card is shown to Gerald. Gerald's card is shown to Sheila. Elizabeth's card is shown to Sheila. Sheila's card is shown to Elizabeth. Gerald's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Sheila knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Sheila picked a black card. It is publicly announced that Gerald does not know whether Laura picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Gerald can now know whether Sheila can know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gerald","Sheila","Elizabeth","Laura"],"index":15580,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.96001333,"difficulty":1.96001333}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Julian can now know whether Sandra can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Julian","Richard"],"index":27918,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982149601,"difficulty":0.0017850399}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy. It is publicly announced that Donna knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Donna can now know whether James can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","James","Donna"],"index":31722,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Denise. Harold's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Harold knows whether or not nobody picked a red card. It is publicly announced that Harold does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Denise can now know whether Harold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Denise","Harold"],"index":31607,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9804172516,"difficulty":0.0195827484}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa does not know whether Agnes is thirsty. It is publicly announced that Joe does not know whether Teresa is thirsty. It is publicly announced that Agnes does not know whether Joe is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Teresa can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mario","Joe","Agnes","Teresa"],"index":41355,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999776423,"difficulty":0.000223577}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Alfredo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentb knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Susan can now know that Diane can know whether Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfredo","Susan","Diane","Daniel"],"index":32456,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997300506,"difficulty":0.0002699494}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francis knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Francis can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Francis","James"],"index":57590,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979736209,"difficulty":0.0020263791}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rochelle's card is shown to Rochelle. Lora's card is shown to Lora. Rochelle's card is shown to Jack. Lora's card is shown to Jack. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lora can now know whether Lora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rochelle","Lora","Jack"],"index":14484,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9014885426,"difficulty":0.0985114574}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Meghan's card is shown to William. Sara's card is shown to Sara. Meghan's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sara can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Sara","Meghan"],"index":40751,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943766594,"difficulty":0.0056233406}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan knows whether Jo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Bryan can now know that Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jo","Bryan","Patricia","Francine"],"index":17624,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978571534,"difficulty":0.0021428466}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Susan can now know that Anita can know that Anita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Susan","Anita"],"index":62281,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.971606791,"difficulty":0.028393209}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry's forehead is not muddy. It is publicly announced that Opal knows whether Jerry's forehead is muddy. It is publicly announced that Jerry knows whether Opal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Opal can now know whether Jerry can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Opal","Craig","Jerry"],"index":49250,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996930361,"difficulty":0.0003069639}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roseanna does not know whether Edward is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Theresa can now know that Tony is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Theresa","Roseanna","Edward","Tony"],"index":33246,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984519482,"difficulty":0.0015480518}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Jerry's forehead is muddy. It is publicly announced that Jerry knows whether Gary's forehead is muddy. It is publicly announced that Gary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] Agentb knows whether (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Gary can now know whether Betty can know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jerry","Gary","Betty"],"index":14302,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6459537745,"difficulty":1.6459537745}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joe does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Joe can now know whether Troy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Troy","Brian","Joe","Georgina"],"index":37396,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997119308,"difficulty":0.0002880692}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Jeremy. Jeremy's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Jeremy does not know whether Jeremy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jeremy can now know that Walter can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeremy","Walter"],"index":1813,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9193685055,"difficulty":1.9193685055}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Neil is not thirsty. It is publicly announced that David does not know whether Debra is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Neil can now know that Debra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cherryl","David","Debra","Neil"],"index":21509,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9945161939,"difficulty":0.0054838061}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Thomas can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Thomas","Charles"],"index":31008,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9374651909,"difficulty":0.0625348091}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Suzanne's card is shown to Suzanne. Suzanne's card is shown to Joseph. Suzanne's card is shown to Rhonda. Joseph's card is shown to Rhonda. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Willie picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Willie can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Suzanne","Willie","Joseph","Rhonda"],"index":27984,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.662130475,"difficulty":1.662130475}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvia's forehead is not muddy. It is publicly announced that Sylvia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Cory can now know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Cory","John","Sylvia"],"index":57016,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9902550578,"difficulty":0.0097449422}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Joseph's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether or not nobody picked a red card. It is publicly announced that Joseph knows whether Mary picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card. It is publicly announced that Mary knows whether Mary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joseph can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Mary"],"index":15846,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997854829,"difficulty":0.0002145171}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Amanda. Keisha's card is shown to Gayla. Ann's card is shown to Gayla. Ann's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Amanda knows whether or not nobody picked a red card. It is publicly announced that Ann picked a red card. It is publicly announced that Amanda does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Gayla can now know whether Amanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amanda","Gayla","Keisha","Ann"],"index":50733,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9403377175,"difficulty":1.9403377175}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luis's card is shown to Luis. Luis's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Luis knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Shannon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Luis","Shannon"],"index":15448,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997184873,"difficulty":0.0002815127}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristen is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kristen can now know whether John can know whether Leroy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Kristen","Leroy","John"],"index":3741,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992414713,"difficulty":0.0007585287}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether David is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Robert does not know whether David is thirsty. It is publicly announced that David knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Robert can now know that David can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","David"],"index":31549,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9918324947,"difficulty":0.0081675053}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tina does not know whether Faye is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Grace can now know whether Tina can know whether Grace is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Faye","Grace","Tina","Dorothy"],"index":33952,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979699254,"difficulty":0.0020300746}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jeffery can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Louis","Jeffery","David"],"index":11844,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984562397,"difficulty":0.0015437603}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Dan can now know whether Sonia can know whether Joanne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerard","Sonia","Joanne","Dan"],"index":21492,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992927313,"difficulty":0.0007072687}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Larry. Thomas's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Thomas can now know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Larry","John"],"index":9548,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9953676462,"difficulty":1.9953676462}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry knows whether Harry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Alexandra can now know whether Mildred's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harry","Monica","Mildred","Alexandra"],"index":47615,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995977283,"difficulty":0.0004022717}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Tamara can now know whether Doris can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Doris","Tamara"],"index":36083,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997494817,"difficulty":0.0002505183}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vincent's card is shown to Danielle. Gladys's card is shown to Billy. Gladys's card is shown to Gladys. Vincent's card is shown to Vincent. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gladys can now know that Billy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danielle","Billy","Gladys","Vincent"],"index":6721,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983293414,"difficulty":0.0016706586}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anita does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Dorothy","Robin","Anita"],"index":31039,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6126589179,"difficulty":0.3873410821}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clifford knows whether someone is thirsty. It is publicly announced that Patricia knows whether Clifford is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Patricia can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Clifford","Patricia"],"index":61663,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997147918,"difficulty":0.0002852082}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that Teresa knows whether Teresa picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Teresa can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Teresa","Bernard"],"index":2977,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999773562,"difficulty":0.000226438}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Debra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] 0","hypothesis":"Lyndsey can now know whether Jeff's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debra","Jeff","Lyndsey"],"index":9982,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997472167,"difficulty":0.0002527833}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Gary. Gary's card is shown to Diane. Gary's card is shown to Erin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Diana can now know whether Gary can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Diana","Diane","Erin"],"index":7393,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997710586,"difficulty":0.0002289414}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiffany does not know whether or not everyone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"William can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tiffany","Billy","William","Jack"],"index":33900,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997128844,"difficulty":0.0002871156}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Ellen. Mark's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Ellen knows whether Mark picked a red card. It is publicly announced that Ellen does not know whether Jeff picked a red card. It is publicly announced that David picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Jeff can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeff","Ellen","Mark","David"],"index":44419,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985877275,"difficulty":0.0014122725}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael is not thirsty. It is publicly announced that Michael does not know whether Kristen is thirsty. It is publicly announced that Sean does not know whether Daniel is thirsty. It is publicly announced that Sean does not know whether Daniel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Michael can now know that Kristen can know that Sean is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sean","Kristen","Michael","Daniel"],"index":9902,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9842045903,"difficulty":0.0157954097}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel does not know whether Rachel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rachel can now know whether Dennis can know whether Anita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rachel","Anita","Dennis","Cecile"],"index":63993,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994949102,"difficulty":0.0005050898}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Alan. Kevin's card is shown to Kevin. Jon's card is shown to Kevin. Alan's card is shown to Jon. Kevin's card is shown to Jon. It is publicly announced that someone picked a red card. It is publicly announced that Kevin picked a black card. It is publicly announced that Alan knows whether Alan picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jon can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alan","Kevin","Jon"],"index":29061,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Cecilia. Benjamin's card is shown to Cecilia. Benjamin's card is shown to Stephen. Cecilia's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Cecilia picked a red card. It is publicly announced that Benjamin does not know whether or not everyone picked a red card. It is publicly announced that Benjamin does not know whether Stephen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Stephen can now know that Cecilia can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cecilia","Stephen","Benjamin"],"index":9539,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980137348,"difficulty":0.0019862652}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Mildred. Savannah's card is shown to Mildred. Eva's card is shown to Savannah. Eva's card is shown to Lester. It is publicly announced that someone picked a red card. It is publicly announced that Eva does not know whether Mildred picked a red card. It is publicly announced that Savannah picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Savannah can now know that Mildred can know whether Eva picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mildred","Eva","Savannah","Lester"],"index":3185,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5005304217,"difficulty":1.5005304217}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aileen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Sierra can now know that Russell can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sierra","Glenn","Russell","Aileen"],"index":22474,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997323155,"difficulty":0.0002676845}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Roy can now know that Willie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Willie","Roy","Dani"],"index":19102,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985135198,"difficulty":0.0014864802}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"David can now know that Domingo can know that Anna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","David","Domingo","Anna"],"index":23326,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983242154,"difficulty":0.0016757846}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia does not know whether or not everyone is thirsty. It is publicly announced that Rose knows whether Rose is thirsty. It is publicly announced that Virginia does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Rose can now know whether Jesus can know whether Jesus is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rose","Virginia","Jesus"],"index":41494,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9955588579,"difficulty":0.0044411421}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Carol can now know that Barbara can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Keith","Carol","Barbara"],"index":14682,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997512698,"difficulty":0.0002487302}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ethel does not know whether Ethel's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Harry can now know whether Ethel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Harry","Ethel"],"index":8691,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994932413,"difficulty":0.0005067587}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allan does not know whether Barbara is thirsty. It is publicly announced that Betsy does not know whether Brandy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Brandy can now know that Barbara can know whether Allan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Allan","Brandy","Betsy"],"index":59592,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971206188,"difficulty":0.0028793812}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Curtis's forehead is not muddy. It is publicly announced that Robert's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Curtis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stanley","Robert","Curtis"],"index":63215,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984696507,"difficulty":0.0015303493}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herbert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Herbert can now know whether James can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Herbert","James"],"index":67053,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997699857,"difficulty":0.0002300143}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Timothy can now know that Shirley can know that Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Katherine","Shirley","Edward"],"index":5249,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9808127284,"difficulty":0.0191872716}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Mona is thirsty. It is publicly announced that Heidi does not know whether Elnora is thirsty. It is publicly announced that Mona knows whether Mona is thirsty. It is publicly announced that Mona knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Elnora can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mona","Elnora","Heidi","John"],"index":554,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980787039,"difficulty":0.0019212961}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Dennis's card is shown to Joy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Joy","Dennis"],"index":30617,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966729879,"difficulty":0.0033270121}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Riley can now know that Ruth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruth","Barbara","Riley","Lucille"],"index":6641,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984413981,"difficulty":0.0015586019}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harvey knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Shantell can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harvey","Crystal","David","Shantell"],"index":21765,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998007834,"difficulty":0.001992166}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy. It is publicly announced that Jasper knows whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jasper can now know whether Peter can know that Andrea's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Jasper","Andrea","Peter"],"index":48745,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9970658422,"difficulty":0.0029341578}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Vanessa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Vanessa can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deborah","James","Vanessa"],"index":60803,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994749427,"difficulty":0.0005250573}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Russel's card is shown to Florence. Michael's card is shown to Michael. Michael's card is shown to Kathryn. Russel's card is shown to Kathryn. Florence's card is shown to Russel. Michael's card is shown to Russel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kathryn can now know whether Russel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Florence","Michael","Kathryn","Russel"],"index":32329,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9744707942,"difficulty":0.0255292058}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether Dale is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Dale can now know whether Dorothy can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beryl","Dale","Dorothy"],"index":64276,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997754693,"difficulty":0.0002245307}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Linda is thirsty. It is publicly announced that Alma does not know whether Richard is thirsty. It is publicly announced that Linda does not know whether Alma is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Alma can now know whether Alma is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Alma","Linda"],"index":52653,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986752868,"difficulty":0.0013247132}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose knows whether or not everyone's forehead is muddy. It is publicly announced that Rose knows whether or not nobody's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Rose can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rose","James"],"index":15206,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969424605,"difficulty":0.0030575395}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin knows whether Kevin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kevin can now know that Craig can know that Kevin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brendan","Kevin","Craig"],"index":60241,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9928962588,"difficulty":0.0071037412}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Lawrence can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lawrence","Mary","Roger"],"index":35467,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969671369,"difficulty":0.0030328631}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lori","Greg","Sean","Robert"],"index":3438,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5299447179,"difficulty":0.4700552821}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward is thirsty. It is publicly announced that Edward is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! 1 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Edward can now know whether Harlan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edward","Harlan"],"index":35050,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9358111024,"difficulty":1.9358111024}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andy knows whether Herbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Andy can now know that Herbert can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Andy","Herbert","Betty"],"index":19621,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995087385,"difficulty":0.0004912615}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl does not know whether Brian is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"Samatha can now know that Gregory can know whether Gregory is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Carl","Gregory","Samatha"],"index":7367,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9970867038,"difficulty":0.0029132962}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeremy does not know whether or not everyone is thirsty. It is publicly announced that Jeremy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Oscar can now know whether Jeremy can know that Oscar is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Oscar","Jeremy"],"index":28920,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9683876634,"difficulty":0.0316123366}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gene knows whether Gene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether Peggy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gene","Mary","Peggy","Sandra"],"index":39208,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99962008,"difficulty":0.00037992}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Louise. Arthur's card is shown to Lois. Arthur's card is shown to Eileen. Lois's card is shown to Eileen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louise can now know that Lois picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arthur","Louise","Lois","Eileen"],"index":62747,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982892871,"difficulty":0.0017107129}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Hazel's card is shown to James. John's card is shown to Hazel. Hazel's card is shown to Hazel. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"John can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","James","Hazel"],"index":42761,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984912872,"difficulty":0.0015087128}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandra's card is shown to Beulah. Beulah's card is shown to Sandra. It is publicly announced that someone picked a red card. It is publicly announced that Beulah does not know whether Norma picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Norma can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Beulah","Norma","Sandra"],"index":15245,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9862357974,"difficulty":0.0137642026}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] 0","hypothesis":"Jennifer can now know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jennifer","Willie"],"index":54039,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8090672493,"difficulty":1.8090672493}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Richard. Timothy's card is shown to Timothy. Michael's card is shown to Michael. Michael's card is shown to Dana. Dana's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Dana does not know whether Richard picked a red card. It is publicly announced that Richard does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Dana can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Timothy","Michael","Dana"],"index":29476,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983386993,"difficulty":0.0016613007}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tana knows whether Faye's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Arnulfo can now know that Tana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tana","Phyllis","Faye","Arnulfo"],"index":5677,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982764721,"difficulty":0.0017235279}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vaughn does not know whether Mary is thirsty. It is publicly announced that Bella does not know whether Georgiana is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Bella can now know that Mary can know that Georgiana is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Vaughn","Georgiana","Bella"],"index":39585,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965058565,"difficulty":0.0034941435}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita does not know whether Paul is thirsty. It is publicly announced that Anita does not know whether Diana is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Anita can now know that Paul is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anita","Paul","Diana"],"index":46547,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974084496,"difficulty":0.0025915504}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Carolyn can now know that Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rose","Karen","Carolyn"],"index":14230,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982669353,"difficulty":0.0017330647}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tanya does not know whether Tanya's forehead is muddy. It is publicly announced that Clemmie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clemmie","Tanya","John"],"index":6849,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979438186,"difficulty":0.0020561814}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that Monica does not know whether Monica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know that Monica can know that Monica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Donna","Monica"],"index":55656,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9810617566,"difficulty":0.0189382434}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Katherine. Timothy's card is shown to Katherine. Susan's card is shown to Susan. Timothy's card is shown to Joseph. Katherine's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susan can now know that Joseph can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katherine","Susan","Joseph","Timothy"],"index":44015,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997162223,"difficulty":0.0002837777}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandi knows whether Brandi is thirsty. It is publicly announced that Mary does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Brandi can now know that Mary can know whether Brandi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brandi","John","Mary"],"index":66613,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9890770912,"difficulty":0.0109229088}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerri knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Gerri can now know whether Nancy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kelly","Nancy","Jonathon","Gerri"],"index":27197,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978165627,"difficulty":0.0021834373}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Amy"],"index":46326,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983522892,"difficulty":0.0016477108}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ebony knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Daisy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gayle","Ebony","Daisy"],"index":29225,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980870485,"difficulty":0.0019129515}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mitchell's card is shown to Alice. Victoria's card is shown to Alice. Alice's card is shown to Mitchell. Mitchell's card is shown to Mitchell. Victoria's card is shown to Mitchell. Alice's card is shown to Victoria. It is publicly announced that someone picked a red card. It is publicly announced that Mitchell knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Alice can now know that Mitchell can know that Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alice","Mitchell","Victoria"],"index":16893,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954727292,"difficulty":0.0045272708}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Joe knows whether Theresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Theresa can now know whether Francisco can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joe","Francisco","Theresa"],"index":7903,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ron knows whether Ron's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Ron can now know that Katie can know whether Jess's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katie","Tina","Jess","Ron"],"index":45774,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997335076,"difficulty":0.0002664924}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kathleen can now know whether George can know that Marcia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcia","Kathleen","George","Alma"],"index":7475,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9969905615,"difficulty":0.0030094385}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"John can now know that Ana can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ana","Laura","John"],"index":2594,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974567294,"difficulty":0.0025432706}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Greg knows whether Lorna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Lorna can now know that Jeane can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Greg","Lorna","Jeane"],"index":14059,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982432127,"difficulty":0.0017567873}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felice's card is shown to Thomas. Thomas's card is shown to Zina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Zina","Felice"],"index":26008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998380661,"difficulty":0.001619339}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Aurea can now know whether Tonja can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tonja","Aurea","Linda","Kevin"],"index":35425,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997839332,"difficulty":0.0002160668}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rachel can now know that Jaime can know whether Arnold's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jaime","Arnold","Bernard","Rachel"],"index":11603,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997490048,"difficulty":0.0002509952}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Phillip knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Joyce can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Paul","Phillip","Joyce"],"index":34462,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997834563,"difficulty":0.0002165437}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wesley knows whether Kathryn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kathryn can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathryn","Wesley","Shirley"],"index":23225,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997614026,"difficulty":0.0002385974}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jose can now know whether Karen can know whether Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Jose","Karen"],"index":1911,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998759985,"difficulty":0.001240015}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marina does not know whether Mildred is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Steve can now know whether Marina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Mildred","Marina","Steve"],"index":15310,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9938796759,"difficulty":0.0061203241}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Emma. Clifton's card is shown to Clifton. Thelma's card is shown to Clifton. Thelma's card is shown to Pamela. Pamela's card is shown to Thelma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clifton can now know that Thelma can know whether Emma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emma","Clifton","Pamela","Thelma"],"index":45853,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8804495335,"difficulty":0.1195504665}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Maurice can now know that Jack's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sarah","Maurice","Sherry","Jack"],"index":34396,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967941642,"difficulty":0.0032058358}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melanie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentb knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Martina can now know whether Mckinley can know whether Mckinley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melanie","Martina","Eric","Mckinley"],"index":57760,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9939823747,"difficulty":0.0060176253}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Evelyn. Kenneth's card is shown to Evelyn. Linda's card is shown to Linda. Kenneth's card is shown to Linda. Kenneth's card is shown to Kenneth. Lisa's card is shown to Kenneth. Lisa's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Evelyn can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Evelyn","Linda","Kenneth","Lisa"],"index":16768,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848333001,"difficulty":0.0151666999}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether Damon is thirsty. It is publicly announced that Damon does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Mark can now know that Nancy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Nancy","Charles","Damon"],"index":40043,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982157946,"difficulty":0.0017842054}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Eric can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eric","Gloria"],"index":33274,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983763695,"difficulty":0.0016236305}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Armando's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Willie can now know whether Armando can know whether Willie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peggy","Willie","Alice","Armando"],"index":3363,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997195601,"difficulty":0.0002804399}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Sharon. Joanne's card is shown to Joanne. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether Sharon picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Sharon can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sharon","Joanne"],"index":32866,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985960126,"difficulty":0.0014039874}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Bethany can now know that Adam can know whether Adam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Adam","Bethany"],"index":25176,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995698333,"difficulty":0.0004301667}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"John can now know whether Robert can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Jeremy","Mildred","Robert"],"index":10046,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997541308,"difficulty":0.0002458692}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy. It is publicly announced that Jeffrey knows whether Kelly's forehead is muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Emma can now know whether Jennifer can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Jeffrey","Emma","Kelly"],"index":22704,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993891716,"difficulty":0.0006108284}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether someone's forehead is muddy. It is publicly announced that Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Velma can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Velma","Janet","Deborah"],"index":13034,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982934594,"difficulty":0.0017065406}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ladonna's card is shown to Pedro. Pedro's card is shown to Ladonna. Harry's card is shown to Ladonna. Pedro's card is shown to Harry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pedro can now know whether Ladonna can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pedro","Ladonna","Harry"],"index":32587,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997118115,"difficulty":0.0002881885}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Roberta can now know that Robert can know that Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roberta","Brian","Robert","Marianne"],"index":27997,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982971549,"difficulty":0.0017028451}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Roman can now know whether Donald can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roman","Donald","Kelly","Robert"],"index":16803,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994114637,"difficulty":0.0005885363}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joshua's card is shown to Joshua. Joshua's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donna can now know that Joshua can know whether Donna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Donna","Madge"],"index":37177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9384871125,"difficulty":0.0615128875}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"William can now know that Daniel can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daniel","William"],"index":39896,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997546077,"difficulty":0.0002453923}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Pamelia can now know whether Pamelia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bradley","Dorothy","Pamelia"],"index":50060,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9957106113,"difficulty":0.0042893887}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Lou can now know whether Timothy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Oscar","James","Lou","Timothy"],"index":40201,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5770302415,"difficulty":0.4229697585}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phillip knows whether Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jean can now know whether Kathy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phillip","Kathy","Jean","Shaunda"],"index":14626,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997653365,"difficulty":0.0002346635}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Holly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Brian can now know that Mark can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Holly","Mark","Natalia"],"index":23359,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marguerite does not know whether Marguerite's forehead is muddy. It is publicly announced that Thelma knows whether Marguerite's forehead is muddy. It is publicly announced that Diane knows whether Diane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Diane can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diane","Marguerite","Thelma"],"index":18886,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997664094,"difficulty":0.0002335906}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darrell does not know whether or not everyone is thirsty. It is publicly announced that Darrell does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Darrell can now know that Charles can know that Lucille is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darrell","Lucille","Charles","Cory"],"index":24901,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6907815933,"difficulty":0.3092184067}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Enid's card is shown to Enid. Enid's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Enid can now know whether John can know whether Enid picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Enid","John"],"index":11563,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988695979,"difficulty":0.0011304021}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte does not know whether or not everyone is thirsty. It is publicly announced that Charlotte knows whether Charlotte is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Harry can now know that Charlotte can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Harry","Charlotte"],"index":43807,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997826219,"difficulty":0.0002173781}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether Gloria's forehead is muddy. It is publicly announced that Connie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Eugene can now know whether Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Connie","Susan","Eugene","Gloria"],"index":42154,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994664788,"difficulty":0.0005335212}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilburn can now know that Tiffany can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tiffany","Wilburn","Bradley","Sharon"],"index":1044,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984433055,"difficulty":0.0015566945}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria does not know whether Maria's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Edmund can now know that Maria can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edmund","Maria","John"],"index":19313,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985338449,"difficulty":0.0014661551}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Ollie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diana","Mark","Ollie"],"index":64020,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998536706,"difficulty":0.001463294}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Jean. Elizabeth's card is shown to Jean. Jean's card is shown to Regina. Regina's card is shown to Regina. Elizabeth's card is shown to Regina. David's card is shown to Regina. Regina's card is shown to Elizabeth. David's card is shown to Elizabeth. Jean's card is shown to David. Elizabeth's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Regina can now know that Jean can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jean","Regina","Elizabeth","David"],"index":36809,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5916931033,"difficulty":1.5916931033}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Joann. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"David can now know whether Joann can know whether Joann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joann","David"],"index":22343,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9950187206,"difficulty":0.0049812794}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina knows whether or not nobody's forehead is muddy. It is publicly announced that Wayne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Christina can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christina","Eva","Wayne"],"index":51158,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983899593,"difficulty":0.0016100407}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"William can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bridgett","William","Heather","James"],"index":30007,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984421134,"difficulty":0.0015578866}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know whether Enrique can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stephanie","James","Pearl","Enrique"],"index":54727,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8631983995,"difficulty":0.1368016005}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that David can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edith","David","Barbara","John"],"index":43747,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985210299,"difficulty":0.0014789701}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jimmy can now know whether Elizabeth can know that Jimmy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmy","Jeremy","Elizabeth"],"index":21797,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994466901,"difficulty":0.0005533099}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Roman can now know whether Evan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martin","Evan","Jeff","Roman"],"index":3046,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995619655,"difficulty":0.0004380345}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is muddy. It is publicly announced that Hilary's forehead is not muddy. It is publicly announced that Nancy knows whether Hilary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Nancy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hilary","Nancy","Sheri"],"index":26701,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981947541,"difficulty":0.0018052459}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether Elizabeth is thirsty. It is publicly announced that Moriah is thirsty. It is publicly announced that Elizabeth knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Moriah can now know that Paul can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Moriah","Elizabeth"],"index":19552,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997858405,"difficulty":0.0002141595}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Van's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Van's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Helen can now know that Maureen can know that Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Van","Helen","Maureen"],"index":10009,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9568879604,"difficulty":0.0431120396}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mack knows whether Mack's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Alesia can now know whether Mack can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mack","Alesia"],"index":36852,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996929169,"difficulty":0.0003070831}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Maria can now know that Eleanor can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Sheila","Eleanor","Doris"],"index":5746,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9840524197,"difficulty":0.0159475803}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Constance knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Arlene can now know that Sierra can know whether Constance's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sierra","Arlene","Constance","Mayra"],"index":37212,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997342229,"difficulty":0.0002657771}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Doris. Andrew's card is shown to Melissa. Doris's card is shown to Andrew. Melissa's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Andrew knows whether or not everyone picked a red card. It is publicly announced that Doris knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Doris can now know that Andrew can know that Doris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Doris","Melissa","Andrew"],"index":12232,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6045072675,"difficulty":0.3954927325}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Carlos is thirsty. It is publicly announced that John is not thirsty. It is publicly announced that Penny knows whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Penny can now know whether Benjamin can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Benjamin","Penny","Carlos"],"index":58654,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9929100871,"difficulty":0.0070899129}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know that Benjamin can know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amy","George","Marjorie","Benjamin"],"index":60835,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985094666,"difficulty":0.0014905334}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglass's forehead is muddy. It is publicly announced that Joann knows whether Douglass's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Douglass","John","Joann"],"index":47653,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984521866,"difficulty":0.0015478134}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth does not know whether Ruth's forehead is muddy. It is publicly announced that Dennis does not know whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Ruth can now know that Dennis can know whether Dennis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Christopher","Ruth"],"index":33454,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9141944647,"difficulty":0.0858055353}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jill does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Timothy can now know that Jennifer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jill","Jennifer","Brandon","Timothy"],"index":24791,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9452982545,"difficulty":0.0547017455}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether or not everyone is thirsty. It is publicly announced that Gay knows whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Patricia can now know that Barbara can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Barbara","Patricia","Gay"],"index":10997,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997199178,"difficulty":0.0002800822}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony is not thirsty. It is publicly announced that Anthony knows whether Anthony is thirsty. It is publicly announced that Anthony does not know whether Shirley is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Anthony can now know that Alma can know that Anthony is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Shirley","Alma"],"index":66049,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7915706038,"difficulty":0.2084293962}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Betty knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Janet can now know that Betty can know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alan","Betty","Janet"],"index":812,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9907435775,"difficulty":0.0092564225}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alfredo is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Eileen can now know that Ken can know whether Ken is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eileen","Ken","Wesley","Alfredo"],"index":55364,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985548854,"difficulty":0.0014451146}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Chad's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Chad can now know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Chad","Kristen","Patricia"],"index":9352,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997288585,"difficulty":0.0002711415}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gene's card is shown to Gene. Joseph's card is shown to Gene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Gene can now know that Gene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gene","Joseph"],"index":20814,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9924824834,"difficulty":0.0075175166}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Rose. Rose's card is shown to Norene. Kerri's card is shown to Norene. It is publicly announced that someone picked a red card. It is publicly announced that Rose knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Norene can now know whether Rose can know whether Rose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rose","Norene","Kerri"],"index":12077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997192204,"difficulty":0.002807796}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether Gladys's forehead is muddy. It is publicly announced that Gladys's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Matthew can now know that Terry can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Matthew","Terry","Gladys"],"index":44237,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976798892,"difficulty":0.0023201108}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Vivian. Brian's card is shown to Brian. Vivian's card is shown to Thomas. Brian's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Vivian does not know whether or not everyone picked a red card. It is publicly announced that Brian knows whether Brian picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Vivian can now know whether Thomas can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vivian","Brian","Thomas"],"index":639,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997732043,"difficulty":0.0002267957}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lynsey can now know whether Charlie can know that Li's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louise","Charlie","Lynsey","Li"],"index":4084,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984347224,"difficulty":0.0015652776}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether Luke's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brenda","Luke","Florence","John"],"index":45027,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980569482,"difficulty":0.0019430518}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice does not know whether Janice's forehead is muddy. It is publicly announced that Janice does not know whether Janice's forehead is muddy. It is publicly announced that Janice's forehead is not muddy. It is publicly announced that Johnny does not know whether Johnny's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Johnny can now know whether Stanley can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stanley","Janice","Johnny"],"index":5797,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catherine does not know whether Deanna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Deanna can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anne","Deanna","Catherine","Dawn"],"index":15571,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998247385,"difficulty":0.001752615}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeff's forehead is not muddy. It is publicly announced that Preston does not know whether Preston's forehead is muddy. It is publicly announced that Preston knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Jeff can now know whether Preston can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Jeff","Preston"],"index":48989,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9954965115,"difficulty":0.0045034885}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"John can now know whether Joel can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joel","John"],"index":36010,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emilia does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick knows whether Aurelio's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Aurelio can now know that Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Phyllis","Patrick","Aurelio","Emilia"],"index":49367,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5698689222,"difficulty":1.5698689222}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know whether Mirella can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Maria","Joseph","Mirella"],"index":51966,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997101426,"difficulty":0.0002898574}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Earlene knows whether Victor's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Donna can now know whether Victor can know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Victor","Louis","Earlene","Donna"],"index":37395,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997068048,"difficulty":0.0002931952}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to George. Judy's card is shown to George. Magnolia's card is shown to George. Magnolia's card is shown to Magnolia. It is publicly announced that someone picked a red card. It is publicly announced that Gregory does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gregory can now know whether Magnolia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Gregory","Judy","Magnolia"],"index":17619,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6888420582,"difficulty":0.3111579418}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brent knows whether Brent's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Marie can now know whether Edwin can know that Carolyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Brent","Carolyn","Edwin"],"index":11907,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996476173,"difficulty":0.0003523827}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dustin's card is shown to Dustin. Lance's card is shown to Dustin. Kathleen's card is shown to Dustin. Dustin's card is shown to Lance. Kathleen's card is shown to Lance. Lauren's card is shown to Lance. Dustin's card is shown to Lauren. Lance's card is shown to Lauren. Kathleen's card is shown to Lauren. It is publicly announced that someone picked a red card. It is publicly announced that Lance does not know whether Lance picked a red card. It is publicly announced that Lauren picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,3,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,3,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Kathleen can now know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dustin","Lance","Kathleen","Lauren"],"index":43513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7111709118,"difficulty":0.2888290882}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Casey's card is shown to Edith. Michael's card is shown to Edith. Edith's card is shown to Michael. Edith's card is shown to John. Casey's card is shown to John. Michael's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Edith does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Edith can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edith","Casey","Michael","John"],"index":44489,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7458631992,"difficulty":1.7458631992}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Roberta can now know whether Daniel can know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Danielle","Roberta","Daniel"],"index":42861,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6417082548,"difficulty":1.6417082548}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"James can now know that David can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Robert","David"],"index":51795,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9707631469,"difficulty":0.0292368531}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Sal knows whether Sal is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Sal can now know whether Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sal","Mary","Elmer"],"index":34860,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941520095,"difficulty":0.0058479905}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denise's card is shown to Sierra. Denise's card is shown to Tracey. Tracey's card is shown to Tracey. Dianna's card is shown to Tracey. Dianna's card is shown to Dianna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Denise can now know that Sierra can know that Denise picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sierra","Denise","Tracey","Dianna"],"index":37381,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967018962,"difficulty":0.0032981038}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lynn can now know whether Douglas can know that Steve's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","Lynn","Jamie","Steve"],"index":48813,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988875985,"difficulty":0.0011124015}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard does not know whether Leonard's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Leonard can now know that Benjamin can know whether Leonard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Benjamin","Leonard","Brett"],"index":47216,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995891452,"difficulty":0.0004108548}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario knows whether or not nobody's forehead is muddy. It is publicly announced that Lisa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Lisa can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Samuel","Lisa","Mario"],"index":19557,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985384941,"difficulty":0.0014615059}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jesus can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Jesus","Millard","Carol"],"index":34777,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994279623,"difficulty":0.005720377}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jessica knows whether Williams's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jessica can now know that Williams's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessica","Damian","Williams"],"index":60375,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9930154085,"difficulty":0.0069845915}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Frank is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Frank does not know whether Linnea is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Frank can now know whether Linnea is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Linnea","Frank","Richard"],"index":53302,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9877681136,"difficulty":0.0122318864}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether Mary is thirsty. It is publicly announced that Sallie knows whether Sallie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mary can now know whether Sallie can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Sallie"],"index":39509,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9979812503,"difficulty":1.9979812503}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kerry's card is shown to Jeffrey. Sheryl's card is shown to Kerry. Kerry's card is shown to Sheryl. Sheryl's card is shown to Sheryl. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Kerry can now know that Jeffrey can know whether Kerry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeffrey","Kerry","Sheryl"],"index":46558,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9266192317,"difficulty":0.0733807683}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martin does not know whether or not everyone's forehead is muddy. It is publicly announced that Jake's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentd knows whether (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Jake can now know whether Martin can know that Jake's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christine","Esther","Martin","Jake"],"index":37113,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9156130552,"difficulty":0.0843869448}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorcas's card is shown to Carolyn. Kimberly's card is shown to Dorcas. Catherine's card is shown to Catherine. Kimberly's card is shown to Catherine. Catherine's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberly can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carolyn","Dorcas","Catherine","Kimberly"],"index":2373,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Marie can now know that Kevin can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marie","Lois","Aurelio","Kevin"],"index":62644,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966025352,"difficulty":0.0033974648}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elise's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Frederic can now know whether Jenifer can know whether Josie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jenifer","Elise","Josie","Frederic"],"index":43556,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997233748,"difficulty":0.0002766252}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kyle does not know whether Jeffrey is thirsty. It is publicly announced that Jeffrey does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Mae can now know whether Jeffrey can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeffrey","Mae","Kyle"],"index":61417,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9963082075,"difficulty":0.0036917925}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olivia's card is shown to Olivia. Michael's card is shown to Olivia. Olivia's card is shown to Wanda. Michael's card is shown to Wanda. Wanda's card is shown to Leona. Leona's card is shown to Leona. Wanda's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Wanda knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Olivia can now know that Michael can know that Olivia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Olivia","Wanda","Leona","Michael"],"index":65259,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967097044,"difficulty":0.0032902956}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Scott does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Alan can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Scott","Alan"],"index":28865,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997283816,"difficulty":0.0002716184}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jenna is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jenna can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Thomas","Jenna"],"index":26961,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9029400945,"difficulty":1.9029400945}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know whether Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sarah","Jennifer","Thomas","David"],"index":8241,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99975425,"difficulty":0.00024575}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bertha's card is shown to Joseph. Joseph's card is shown to Joseph. Adam's card is shown to Joseph. Craig's card is shown to Joseph. Adam's card is shown to Adam. Craig's card is shown to Adam. Joseph's card is shown to Craig. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joseph can now know whether Bertha can know that Bertha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bertha","Joseph","Adam","Craig"],"index":54455,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6361852884,"difficulty":1.6361852884}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Shirley can now know that Janine can know that Janine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shirley","Janine","Barbara"],"index":21747,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.993401587,"difficulty":0.006598413}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Mark's forehead is muddy. It is publicly announced that Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"William can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sarah","Ashley","William","Mark"],"index":47724,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7195760012,"difficulty":0.2804239988}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy. It is publicly announced that Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Daniel can now know whether Ofelia can know that Ofelia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Ofelia","Christopher"],"index":53554,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5610366464,"difficulty":0.4389633536}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis does not know whether Ricky is thirsty. It is publicly announced that Dennis does not know whether Ricky is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Ricky can now know that Dennis can know whether Clara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ricky","Clara","Dennis","Barbara"],"index":55189,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9911661744,"difficulty":0.0088338256}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Nicholas. Evan's card is shown to Evan. Kim's card is shown to Evan. Evan's card is shown to Kim. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kim can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nicholas","Evan","Kim"],"index":44146,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997273088,"difficulty":0.0002726912}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Annie. Barbara's card is shown to Annie. Douglas's card is shown to Apryl. Apryl's card is shown to Douglas. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Annie does not know whether Douglas picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Douglas can now know whether Annie can know that Apryl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annie","Apryl","Douglas","Barbara"],"index":55021,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9406459332,"difficulty":0.0593540668}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Margaret can now know whether Helena can know whether Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helena","Matthew","Margaret"],"index":36260,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997169375,"difficulty":0.0002830625}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that May knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"May can now know whether Vanessa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["May","Vanessa","James"],"index":43668,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997470975,"difficulty":0.0002529025}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Linda can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erma","Lowell","Geoffrey","Linda"],"index":18659,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983743429,"difficulty":0.0016256571}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to Alberta. Priscilla's card is shown to Carey. Carey's card is shown to Priscilla. It is publicly announced that someone picked a red card. It is publicly announced that Priscilla does not know whether Priscilla picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Priscilla can now know whether Carey can know that Carey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alberta","Carey","Priscilla","Martha"],"index":7370,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8101632595,"difficulty":0.1898367405}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Willis. Mary's card is shown to Willis. Mary's card is shown to Elaine. Willis's card is shown to Patrick. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patrick can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willis","Elaine","Patrick","Mary"],"index":48276,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985571504,"difficulty":0.0014428496}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jonathan can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tina","James","Jonathan"],"index":45541,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9917116165,"difficulty":0.0082883835}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Herbert knows whether Herbert is thirsty. It is publicly announced that Lupe does not know whether or not everyone is thirsty. It is publicly announced that Elizabeth does not know whether or not everyone is thirsty. It is publicly announced that Stacey does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Herbert can now know that Stacey can know whether Stacey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stacey","Lupe","Elizabeth","Herbert"],"index":15179,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986302853,"difficulty":0.0013697147}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Richard can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Peggy","Elizabeth","Richard"],"index":583,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9758090377,"difficulty":0.0241909623}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Aaron knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Aaron can now know whether Bertha can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aaron","Lorine","Bertha","Marion"],"index":9715,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997768998,"difficulty":0.0002231002}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Derek knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Lee can now know whether Derek can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Derek","Lee"],"index":54715,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997385144,"difficulty":0.0002614856}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herbert does not know whether Herbert's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jewel can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Phyllis","Annette","Herbert","Jewel"],"index":65901,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8597151637,"difficulty":0.1402848363}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know that Emily can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","James","Emily","Michael"],"index":34281,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984612465,"difficulty":0.0015387535}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Alexander. Alexander's card is shown to Alexander. Jose's card is shown to Melody. Eric's card is shown to Jose. Alexander's card is shown to Jose. Melody's card is shown to Jose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melody can now know whether Eric can know that Jose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Alexander","Melody","Jose"],"index":47167,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9298086166,"difficulty":0.0701913834}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Robert. Ashley's card is shown to Eugene. Robert's card is shown to James. Eugene's card is shown to James. Eugene's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know whether Ashley can know that Ashley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Eugene","James","Ashley"],"index":57160,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9701828957,"difficulty":0.0298171043}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Timothy. Timothy's card is shown to Jeffrey. Daniel's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Timothy can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Timothy","Darlene","Daniel","Jeffrey"],"index":1148,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas is not thirsty. It is publicly announced that Thomas does not know whether Amber is thirsty. It is publicly announced that Shawn does not know whether Catherine is thirsty. It is publicly announced that Shawn does not know whether Catherine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Shawn can now know whether Catherine can know that Amber is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shawn","Amber","Thomas","Catherine"],"index":17901,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9879106283,"difficulty":0.0120893717}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mae's card is shown to Ruben. Mae's card is shown to Mae. Amelia's card is shown to Amelia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mae can now know that Alan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruben","Alan","Mae","Amelia"],"index":17889,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983335137,"difficulty":0.0016664863}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Robert. Robert's card is shown to Katherine. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Katherine can now know that Robert can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Katherine"],"index":41697,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.973605454,"difficulty":0.026394546}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Joslyn. Joslyn's card is shown to Catherine. Catherine's card is shown to Catherine. David's card is shown to Catherine. Catherine's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Joslyn does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joslyn can now know that David can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joslyn","Catherine","David"],"index":7161,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9931628704,"difficulty":0.0068371296}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Julian can now know whether Joann can know that Julian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Teresa","Joann","Julian"],"index":12739,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6251995564,"difficulty":1.6251995564}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joe is thirsty. It is publicly announced that James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 1 ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 1 ] 0","hypothesis":"Henry can now know that Dennis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Henry","Dennis","Joe"],"index":65091,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9607707858,"difficulty":0.0392292142}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know whether Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","John","Julie"],"index":55497,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9924921393,"difficulty":0.0075078607}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Florence's card is shown to Florence. Joycelyn's card is shown to Florence. Florence's card is shown to Brittany. James's card is shown to Joycelyn. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Joycelyn can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florence","Brittany","Joycelyn","James"],"index":37506,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974796176,"difficulty":0.0025203824}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Michael can now know that Kristina can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kristina","Michael","Shirley"],"index":26982,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983465672,"difficulty":0.0016534328}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlie does not know whether Brandy is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Charlie can now know whether Bonita can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charlie","Bonita","Kristy","Brandy"],"index":32235,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9967893362,"difficulty":0.0032106638}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sade does not know whether Regina is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Thelma knows whether someone is thirsty. It is publicly announced that Regina does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Sade can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thelma","Sade","Regina"],"index":40955,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997726083,"difficulty":0.0002273917}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Iris knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Joseph can now know that William can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Joseph","Iris"],"index":14042,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983899593,"difficulty":0.0016100407}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hazel does not know whether or not everyone is thirsty. It is publicly announced that Leonard does not know whether Tracy is thirsty. It is publicly announced that Leonard does not know whether Tracy is thirsty. It is publicly announced that Leonard does not know whether Steve is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] Agentc knows whether (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Hazel can now know whether Steve can know that Leonard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steve","Leonard","Hazel","Tracy"],"index":61980,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9889293313,"difficulty":0.0110706687}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric does not know whether or not everyone's forehead is muddy. It is publicly announced that Eric does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Eric can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sylvia","Eric"],"index":41730,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9786636829,"difficulty":1.9786636829}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerrie does not know whether Jerrie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jerrie","Mary","Sally"],"index":61394,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973787069,"difficulty":0.0026212931}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry does not know whether Ana is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Randy can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Randy","Ana"],"index":9486,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953913689,"difficulty":0.0046086311}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Joan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 2 ] 0","hypothesis":"David can now know that Julie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Joan","Michelle","Julie"],"index":53131,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9939773083,"difficulty":0.0060226917}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Annette can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Florinda","James","Annette","Paul"],"index":54285,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954807758,"difficulty":0.0045192242}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Coy's card is shown to Coy. Kerry's card is shown to Coy. Coy's card is shown to Michelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michelle can now know whether Coy can know whether Coy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Coy","Michelle","Kerry"],"index":35144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970217347,"difficulty":0.0029782653}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristina's card is shown to William. William's card is shown to Philip. Diana's card is shown to Philip. Kristina's card is shown to Diana. Diana's card is shown to Diana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Philip can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Kristina","Philip","Diana"],"index":66545,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997271895,"difficulty":0.0002728105}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Trisha can now know whether Errol can know that Carter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Trisha","Carter","Cedric","Errol"],"index":2650,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996863604,"difficulty":0.0003136396}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Victoria can now know that Gerald can know that Victoria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Victoria","Gerald","Jaime"],"index":57224,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973210692,"difficulty":0.0026789308}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothea knows whether someone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dorothea can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Scott","Dorothea","Rebecca"],"index":10785,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998487711,"difficulty":0.001512289}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rhonda does not know whether or not everyone is thirsty. It is publicly announced that Rhonda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Orlando can now know that John can know that Orlando is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Rhonda","Orlando"],"index":33029,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7712990642,"difficulty":1.7712990642}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Bertha's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sharon","John","James","Bertha"],"index":17099,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9912310243,"difficulty":1.9912310243}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sara knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Stephen can now know whether Sara can know whether Sara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stephen","Sara"],"index":6769,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9626507759,"difficulty":0.0373492241}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonio's card is shown to Antonio. Bradley's card is shown to Antonio. Antonio's card is shown to Bradley. Bradley's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Bradley does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Bradley can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Antonio","Bradley","Jane"],"index":33149,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999771893,"difficulty":0.000228107}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie knows whether Randy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Randy can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marjorie","Dexter","Randy","James"],"index":16697,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984305501,"difficulty":0.0015694499}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Kimberly. Todd's card is shown to Lucy. Kimberly's card is shown to Todd. Louise's card is shown to Todd. Kimberly's card is shown to Louise. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberly can now know whether Lucy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Lucy","Todd","Louise"],"index":52383,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997738004,"difficulty":0.0002261996}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether or not everyone is thirsty. It is publicly announced that Melissa knows whether Melissa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Zachary can now know that Jennifer can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Zachary","Melissa","Jennifer"],"index":22241,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997077584,"difficulty":0.0002922416}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Misty can now know whether David can know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Randy","David","Misty"],"index":13525,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997105002,"difficulty":0.0002894998}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann does not know whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","Ann","George","David"],"index":14831,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979254007,"difficulty":0.0020745993}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Esther","John","Richard","Joseph"],"index":45352,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985608459,"difficulty":0.0014391541}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Austin's card is shown to Miles. Miles's card is shown to Austin. Austin's card is shown to Austin. It is publicly announced that someone picked a red card. It is publicly announced that Austin picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Austin can now know whether Miles can know that Miles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Miles","Austin"],"index":25113,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.859811306,"difficulty":0.140188694}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Kenneth can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Kenneth"],"index":36576,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998478353,"difficulty":0.001521647}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jean is not thirsty. It is publicly announced that Jean does not know whether Amanda is thirsty. It is publicly announced that Linda does not know whether Amanda is thirsty. It is publicly announced that Linda knows whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jean can now know that Alma can know that Linda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jean","Linda","Amanda","Alma"],"index":16999,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9620428681,"difficulty":0.0379571319}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth does not know whether Paul is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kenneth can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Caroline","Paul","Robert"],"index":51784,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985963702,"difficulty":0.0014036298}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sheila does not know whether Louise is thirsty. It is publicly announced that Bruce does not know whether Sheila is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Bruce can now know that Louise is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bruce","Edward","Sheila","Louise"],"index":48571,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9940542579,"difficulty":0.0059457421}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. Lamonica's card is shown to Cindy. Brian's card is shown to Cindy. Sean's card is shown to Cindy. Lamonica's card is shown to Lamonica. Cindy's card is shown to Brian. Cindy's card is shown to Sean. Brian's card is shown to Sean. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether Brian picked a red card. It is publicly announced that Cindy knows whether Brian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:2 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Sean can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cindy","Lamonica","Brian","Sean"],"index":10423,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997263551,"difficulty":0.0002736449}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Laura can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","Charlotte","John"],"index":8791,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986471534,"difficulty":0.0013528466}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan's forehead is muddy. It is publicly announced that Leticia's forehead is not muddy. It is publicly announced that Susan knows whether Leticia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Leticia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leticia","Susan","Lacy"],"index":40297,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984878302,"difficulty":0.0015121698}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Bonnie can now know that James can know that Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","James","Bonnie","Cathy"],"index":1288,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973275661,"difficulty":0.0026724339}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Woodrow is not thirsty. It is publicly announced that Woodrow does not know whether June is thirsty. It is publicly announced that Mamie does not know whether June is thirsty. It is publicly announced that Mamie knows whether Mamie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mamie can now know that Stefan can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Woodrow","Mamie","June","Stefan"],"index":4291,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6101703048,"difficulty":1.6101703048}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Angela. Richard's card is shown to Richard. Richard's card is shown to Susie. Susie's card is shown to Susie. It is publicly announced that someone picked a red card. It is publicly announced that Richard picked a black card. It is publicly announced that Susie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 3 ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 3 ] 0","hypothesis":"Angela can now know whether Susie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Richard","Susie"],"index":21686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenn's forehead is muddy. It is publicly announced that Glenn's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Glenn can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Irene","Barbara","Glenn"],"index":16752,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979947805,"difficulty":0.0020052195}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lois knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Kayla can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lacy","Kayla","Lois"],"index":40345,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981530309,"difficulty":0.0018469691}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Janet. Scott's card is shown to Scott. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Janet picked a red card. It is publicly announced that Scott picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] Agentc knows that (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that Janet can know that Gilbert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Scott","Mary","Gilbert"],"index":22754,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9781858921,"difficulty":0.0218141079}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alta's card is shown to Robert. Alta's card is shown to George. George's card is shown to Maria. Maria's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know that Robert can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alta","Robert","George","Maria"],"index":25265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9854387045,"difficulty":0.0145612955}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether someone's forehead is muddy. It is publicly announced that Larry knows whether Michaela's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Michaela can know whether Michaela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Beatrice","Michaela","Larry"],"index":45283,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9606028199,"difficulty":0.0393971801}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lucy can now know whether Susan can know that Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucy","John","Anthony","Susan"],"index":32183,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987001419,"difficulty":0.0012998581}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugenia's card is shown to Erik. Erik's card is shown to Eugenia. Eugenia's card is shown to Eugenia. It is publicly announced that someone picked a red card. It is publicly announced that Eugenia knows whether someone picked a red card. It is publicly announced that Erik knows whether someone picked a red card. It is publicly announced that Eugenia knows whether Erik picked a red card. It is publicly announced that Eugenia knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Eugenia can now know whether Erik picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Erik","Eugenia"],"index":47366,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6383838058,"difficulty":0.3616161942}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Juanita is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Dana can now know that Mary can know that Juanita is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juanita","Mary","Gregory","Dana"],"index":60794,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978581071,"difficulty":0.0021418929}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josephine does not know whether Josephine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Josephine can now know whether Christine can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Josephine","Christine","Antonio"],"index":7902,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9118524194,"difficulty":0.0881475806}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether or not everyone's forehead is muddy. It is publicly announced that Lindsay knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Paul can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gail","Lindsay","Paul"],"index":59358,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9656013846,"difficulty":0.0343986154}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jesse","Anna","Brian","Jason"],"index":52632,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997834563,"difficulty":0.0002165437}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmy does not know whether or not everyone is thirsty. It is publicly announced that Jimmy knows whether or not nobody is thirsty. It is publicly announced that Donna knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Christopher can now know whether Christopher is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Donna","Christopher","Jimmy"],"index":41320,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9957387447,"difficulty":0.0042612553}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Zoe is thirsty. It is publicly announced that John does not know whether Zachary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] Agentc knows that (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"John can now know that Zachary can know whether Helen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Zoe","John","Zachary"],"index":45021,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967954755,"difficulty":0.0032045245}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Inez knows whether James's forehead is muddy. It is publicly announced that Inez's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Inez can now know whether James can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Walter","Inez","James"],"index":224,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9222236276,"difficulty":0.0777763724}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Helene's forehead is muddy. It is publicly announced that Sebastian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Melvin can now know that Sebastian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melvin","Sebastian","William","Helene"],"index":20294,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9890224934,"difficulty":0.0109775066}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aubrey knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Pamela can now know that Veola's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karon","Aubrey","Veola","Pamela"],"index":37044,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9325400591,"difficulty":0.0674599409}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kayla's card is shown to Kayla. Tonya's card is shown to Tonya. Marie's card is shown to Tonya. Kayla's card is shown to Marie. Tonya's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Tonya picked a black card. It is publicly announced that Kayla knows whether Kayla picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Marie can now know that Tonya picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kayla","Tonya","Marie"],"index":14451,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9132278562,"difficulty":0.0867721438}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Lee can now know that Mary can know that Lee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Terry","Lee"],"index":39370,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8786053658,"difficulty":0.1213946342}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caroline's card is shown to Caroline. Caroline's card is shown to Tatiana. Caroline's card is shown to Elinor. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Caroline can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Caroline","Tatiana","Elinor"],"index":12303,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997100234,"difficulty":0.0002899766}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Geneva can now know whether Roy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donna","Roy","Geneva"],"index":48951,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978558421,"difficulty":0.0021441579}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn does not know whether Thomas is thirsty. It is publicly announced that Francis does not know whether Thomas is thirsty. It is publicly announced that Francis does not know whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Francis can now know that Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Thomas","Francis"],"index":30204,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9886921644,"difficulty":0.0113078356}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isaiah knows whether Mark's forehead is muddy. It is publicly announced that Isaiah knows whether Isaiah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Isaiah can now know that Mark can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Micaela","Isaiah","Mark"],"index":2078,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968248606,"difficulty":0.0031751394}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruthie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Luis can now know that Debra can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Ruthie","Luis","Sophie"],"index":6304,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997467399,"difficulty":0.0002532601}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Donald. Donald's card is shown to David. David's card is shown to David. Rose's card is shown to David. Donald's card is shown to Rose. Rose's card is shown to Rose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether Donald can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","David","Rose"],"index":15461,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7856598496,"difficulty":0.2143401504}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennie does not know whether Judy is thirsty. It is publicly announced that Judy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Jennie can now know that Jennie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennie","Judy","Dorothy"],"index":53525,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9780628085,"difficulty":1.9780628085}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether or not nobody's forehead is muddy. It is publicly announced that Dana knows whether Dana's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dana can now know whether Patrick can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dana","Patrick"],"index":10173,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996026158,"difficulty":0.0003973842}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew does not know whether or not everyone's forehead is muddy. It is publicly announced that Wayne knows whether Wayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Andrew can now know whether Wayne can know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wayne","Cori","Andrew"],"index":40270,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6798593402,"difficulty":1.6798593402}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Telma can now know whether Terry can know whether Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michel","Terry","Telma","Ralph"],"index":28638,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9890040755,"difficulty":0.0109959245}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Regena can now know that William can know that Regena's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Regena","William"],"index":33294,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983843565,"difficulty":0.0016156435}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"David can now know that Wanda can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Wanda","David"],"index":8903,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9564461112,"difficulty":1.9564461112}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy. It is publicly announced that Bess's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"James can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Bess","Mark","Oscar"],"index":50826,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997286201,"difficulty":0.0002713799}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christina is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] 0","hypothesis":"Melissa can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christina","Pedro","Melissa"],"index":65031,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997900128,"difficulty":0.0002099872}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thanh does not know whether Thanh's forehead is muddy. It is publicly announced that Cynthia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Toni can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cynthia","Toni","Wendy","Thanh"],"index":7212,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997230172,"difficulty":0.0002769828}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Brian. Brian's card is shown to Bianca. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know whether Karen can know that Karen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Karen","Bianca"],"index":59263,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.530318737,"difficulty":0.469681263}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darren's card is shown to Russell. Russell's card is shown to Darren. Russell's card is shown to Nelda. Darren's card is shown to Nelda. Nelda's card is shown to Nelda. It is publicly announced that someone picked a red card. It is publicly announced that Nelda knows whether Darren picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Darren can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Russell","Darren","Nelda"],"index":35790,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984511137,"difficulty":0.0015488863}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keitha's card is shown to Keitha. It is publicly announced that someone picked a red card. It is publicly announced that Keitha knows whether someone picked a red card. It is publicly announced that Keitha does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Keitha can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Keitha","Andrew"],"index":34733,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.920984149,"difficulty":1.920984149}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ginger can now know that Tisha can know whether Tisha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tisha","Ginger","Dorothy","Leticia"],"index":60728,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931413531,"difficulty":0.0068586469}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margareta is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Julian can now know whether Margareta is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Julian","Margareta"],"index":34153,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9255492091,"difficulty":0.0744507909}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. David's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Joshua picked a red card. It is publicly announced that Joshua knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"David can now know whether Joshua can know that Joshua picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Joshua"],"index":42806,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8432079554,"difficulty":0.1567920446}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tony knows whether Charles is thirsty. It is publicly announced that Charles is thirsty. It is publicly announced that Charles knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Tony can now know whether Charles can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tony","Charles"],"index":51908,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993840456,"difficulty":0.0006159544}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Thomas. Carmen's card is shown to Carmen. Carmen's card is shown to Judy. It is publicly announced that someone picked a red card. It is publicly announced that Thomas picked a red card. It is publicly announced that Thomas knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Carmen can now know whether Judy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Carmen","Judy"],"index":8893,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janet is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Beth can now know whether Janet can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Beth","Linda","Janet"],"index":60332,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6230164766,"difficulty":0.3769835234}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"John can now know whether Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","John"],"index":1955,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999637723,"difficulty":0.000362277}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula knows whether someone is thirsty. It is publicly announced that Emily does not know whether Whitney is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Paula knows whether Paula is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Whitney can now know whether Charles can know that Paula is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Whitney","Charles","Paula","Emily"],"index":12709,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.986123085,"difficulty":0.013876915}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Angelita's card is shown to Angelita. Isela's card is shown to Angelita. Jennifer's card is shown to Isela. Angelita's card is shown to Isela. It is publicly announced that someone picked a red card. It is publicly announced that Angelita picked a black card. It is publicly announced that Jennifer knows whether Jennifer picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Isela can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Angelita","Isela"],"index":5829,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982178807,"difficulty":0.0017821193}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Lewis can now know that Cleo can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lewis","Kenneth","Cleo"],"index":57068,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984459281,"difficulty":0.0015540719}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jared knows whether Hilda's forehead is muddy. It is publicly announced that Hilda knows whether someone's forehead is muddy. It is publicly announced that Hilda's forehead is muddy. It is publicly announced that Jared does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jared can now know whether Hilda can know whether Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hilda","Kelly","Jared"],"index":62835,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999076128,"difficulty":0.000923872}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Clark can now know whether Christine can know whether Clark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christine","Dorothy","Henry","Clark"],"index":16231,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997161031,"difficulty":0.0002838969}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina's forehead is not muddy. It is publicly announced that Christina's forehead is not muddy. It is publicly announced that James knows whether Christina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Christina can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Alfred","Christina"],"index":51413,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99828583,"difficulty":0.00171417}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allene does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Allene can now know that Winnie can know whether Tommy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Winnie","Allene","Tommy","Thomas"],"index":49906,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7928478718,"difficulty":0.2071521282}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Connie can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Connie","James"],"index":19193,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9100959897,"difficulty":1.9100959897}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phyllis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Gregory can now know whether Michael can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phyllis","Gregory","Michael"],"index":63518,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997335076,"difficulty":0.0002664924}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerome does not know whether or not everyone's forehead is muddy. It is publicly announced that Frank knows whether Jerome's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agenta knows that (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Frank can now know that Jerome can know whether Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Asley","Ronald","Jerome"],"index":37215,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993311167,"difficulty":0.0006688833}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Domingo's forehead is muddy. It is publicly announced that Vivian knows whether Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Vivian can now know that Vivian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Timothy","Vivian","Domingo"],"index":1102,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969651103,"difficulty":0.0030348897}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bradley's card is shown to Joseph. Joseph's card is shown to Carl. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Carl picked a red card. It is publicly announced that Carl does not know whether Bradley picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Joseph can now know whether Carl can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Carl","Bradley"],"index":64748,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.942825377,"difficulty":1.942825377}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tamika's card is shown to Lori. Lori's card is shown to Douglas. Tamika's card is shown to Douglas. Lori's card is shown to Tamika. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Douglas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lori","Douglas","Tamika"],"index":30142,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997263551,"difficulty":0.0002736449}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dustin can now know whether Henry can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Laurence","Wendy","Dustin"],"index":44180,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9885370731,"difficulty":0.0114629269}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernestine's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Eunice can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eunice","Ernestine","Josiah"],"index":48032,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996899366,"difficulty":0.0003100634}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carol. Rita's card is shown to Carol. Carol's card is shown to Rita. Rita's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Rita knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Rita can now know whether Carol can know that Rita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carol","Rita"],"index":4877,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9201204181,"difficulty":0.0798795819}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janis knows whether Janis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that Janis can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Robert","Janis"],"index":21976,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983715415,"difficulty":0.0016284585}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alicia's card is shown to Teodoro. Carlos's card is shown to Alicia. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Teodoro can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carlos","Teodoro","Alicia"],"index":23257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7831429839,"difficulty":0.2168570161}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know whether Michael can know that Kim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","Paul","Michael"],"index":1252,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996880293,"difficulty":0.0003119707}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Robert. Linda's card is shown to Linda. Gregory's card is shown to Linda. Linda's card is shown to Mark. Mark's card is shown to Mark. Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Linda","Mark","Gregory"],"index":24417,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6357839108,"difficulty":0.3642160892}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherill's card is shown to Betty. William's card is shown to Betty. Charles's card is shown to Sherill. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Betty can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Sherill","William","Charles"],"index":63504,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9625682235,"difficulty":0.0374317765}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Christopher. Christopher's card is shown to Lois. Julie's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Lois picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Julie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Christopher","Lois","Scott"],"index":24619,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982497096,"difficulty":0.0017502904}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy. It is publicly announced that Linda knows whether Willie's forehead is muddy. It is publicly announced that Linda's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Willie can now know that Linda can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Willie"],"index":37996,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997567534,"difficulty":0.0002432466}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rafaela's card is shown to Barbara. Barbara's card is shown to Corrine. Barbara's card is shown to Rafaela. It is publicly announced that someone picked a red card. It is publicly announced that Corrine does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Rafaela can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Corrine","Rafaela"],"index":4917,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7504850626,"difficulty":1.7504850626}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jack knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Elizabeth can now know that Eugene can know that Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Elizabeth","Eugene","Jack"],"index":60872,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9803863168,"difficulty":0.0196136832}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is muddy. It is publicly announced that Philip knows whether someone's forehead is muddy. It is publicly announced that Christopher knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Philip can now know whether Jesse can know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Jesse","Philip"],"index":33155,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987819791,"difficulty":0.0012180209}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonny knows whether Betty's forehead is muddy. It is publicly announced that Betty knows whether Betty's forehead is muddy. It is publicly announced that Bonny knows whether Bonny's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Bonny can now know that Bonny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bonny","Betty"],"index":22442,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9925807714,"difficulty":0.0074192286}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"William can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Charmaine","Anita","Helen"],"index":1250,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984684587,"difficulty":0.0015315413}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle does not know whether Danielle's forehead is muddy. It is publicly announced that Danielle does not know whether Danielle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Joseph can now know that Danielle can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margery","Danielle","Joseph"],"index":67655,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997076392,"difficulty":0.0002923608}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason does not know whether Alvin is thirsty. It is publicly announced that Jason does not know whether Helen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jason can now know whether Alvin can know whether Jason is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alvin","Jason","Helen"],"index":38710,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984123707,"difficulty":0.0015876293}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Marie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Thomas","Marie","Joan"],"index":33236,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985669255,"difficulty":0.0014330745}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tiffany does not know whether Sandra is thirsty. It is publicly announced that Sandra is thirsty. It is publicly announced that Sandra knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Tiffany can now know whether John can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tiffany","Sandra","John"],"index":37307,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994907379,"difficulty":0.0005092621}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bret knows whether someone's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"John can now know that Bret's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mae","John","Bret","Lee"],"index":50221,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9910976887,"difficulty":0.0089023113}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elmer does not know whether Christopher is thirsty. It is publicly announced that Christopher does not know whether Margot is thirsty. It is publicly announced that Treva knows whether Treva is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Elmer can now know that Treva is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Elmer","Treva","Margot"],"index":57105,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955138564,"difficulty":0.0044861436}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Christine. Lois's card is shown to Christine. Christine's card is shown to Lois. It is publicly announced that someone picked a red card. It is publicly announced that Christine knows whether Lois picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Christine can now know that Lois can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Christine","Lois"],"index":57426,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983329177,"difficulty":0.0016670823}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Natalie's forehead is muddy. It is publicly announced that Patrick knows whether someone's forehead is muddy. It is publicly announced that Natalie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Natalie can now know that Mark can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Natalie","Mark","Patrick"],"index":20337,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997264743,"difficulty":0.0002735257}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Claude's card is shown to Claude. Jeff's card is shown to Mae. Mae's card is shown to Jeff. Jeff's card is shown to Jeff. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Claude can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Claude","Mae","Jeff"],"index":6891,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985710382,"difficulty":0.0014289618}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ryan knows whether someone is thirsty. It is publicly announced that Tressie knows whether or not nobody is thirsty. It is publicly announced that Louis knows whether Louis is thirsty. It is publicly announced that Tressie does not know whether Ryan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Todd can now know that Louis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","Louis","Tressie","Todd"],"index":35171,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9943085313,"difficulty":0.0056914687}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mike knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Shirley can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robin","Shirley","Octavia","Mike"],"index":19266,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Shelia can now know that David can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Shelia"],"index":54108,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether someone's forehead is muddy. It is publicly announced that Ines's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] 0","hypothesis":"Ines can now know that Anna can know that Ines's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anna","Ines"],"index":34590,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9499734044,"difficulty":0.0500265956}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerri knows whether Kerri's forehead is muddy. It is publicly announced that Edna knows whether Derek's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Derek can now know that Edna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Derek","Kerri","Carol","Edna"],"index":35940,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980282187,"difficulty":0.0019717813}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Bruce can now know whether Alton can know whether Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alton","Bruce","George","Sandra"],"index":65577,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997141957,"difficulty":0.0002858043}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ethel's card is shown to Nancy. Martha's card is shown to Martha. Nancy's card is shown to Ethel. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Martha can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Martha","Ethel","David"],"index":3411,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997692704,"difficulty":0.0002307296}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that David can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","David","Betty","Norbert"],"index":15464,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998433888,"difficulty":0.001566112}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerald knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Albert can now know that Ethel can know that Ethel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Albert","Jerald","William","Ethel"],"index":62670,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980667233,"difficulty":0.0019332767}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janella knows whether Janella's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Judy can now know that Shannon can know that Shannon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Justin","Judy","Janella","Shannon"],"index":24584,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983780384,"difficulty":0.0016219616}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rick knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Cassie can now know whether Rick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cassie","Rick","Lakesha","Gerald"],"index":37964,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997345805,"difficulty":0.0002654195}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is muddy. It is publicly announced that Cora does not know whether Cora's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Noelle can now know whether Cora's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Eva","Noelle","Cora"],"index":65990,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995703101,"difficulty":0.0004296899}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Corey. Michael's card is shown to Donald. Michael's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether or not nobody picked a red card. It is publicly announced that Donald picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 2 ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 2 ] 0","hypothesis":"Corey can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Corey","Donald","Michael","Christine"],"index":65386,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982649684,"difficulty":0.0017350316}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susanna's card is shown to David. Donald's card is shown to David. Patrick's card is shown to Susanna. David's card is shown to Susanna. Donald's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susanna can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","David","Susanna","Donald"],"index":63091,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6298699379,"difficulty":1.6298699379}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Donald can now know that Jason can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Ralph","Jason"],"index":61895,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori does not know whether Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Yesenia can now know whether Lori can know that Yesenia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lori","Eric","Yesenia","Matthew"],"index":48553,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7549633384,"difficulty":0.2450366616}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ana does not know whether or not everyone is thirsty. It is publicly announced that Helen is not thirsty. It is publicly announced that Helen knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Helen can now know whether Ana can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ana","Helen"],"index":48939,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997733235,"difficulty":0.0002266765}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reda does not know whether or not everyone's forehead is muddy. It is publicly announced that Reda does not know whether Reda's forehead is muddy. It is publicly announced that Reda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Reda can now know that Marsha can know that Reda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Reda","Marsha"],"index":26939,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9516533017,"difficulty":1.9516533017}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether or not nobody's forehead is muddy. It is publicly announced that Gladys's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] 0","hypothesis":"Eileen can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eileen","William","Robin","Gladys"],"index":33348,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9940115809,"difficulty":0.0059884191}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Joseph can now know whether Suzette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joseph","Suzette"],"index":39123,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9763145447,"difficulty":0.0236854553}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether China is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Richard can now know that Jeff can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeff","Richard","Donna","China"],"index":2764,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9800907969,"difficulty":0.0199092031}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Erik knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Erik can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Timothy","Adam","Erik","Fabiola"],"index":57867,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.994468689,"difficulty":0.005531311}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrice does not know whether Patrice's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Harold knows whether or not everyone's forehead is muddy. It is publicly announced that Harold's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Patrice can now know that Andrew can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Harold","Patrice","Andrew"],"index":29570,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985312223,"difficulty":0.0014687777}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Patricia's forehead is muddy. It is publicly announced that Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Robert can now know that Patricia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Patricia"],"index":39287,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985235333,"difficulty":0.0014764667}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to George. Christopher's card is shown to Christopher. George's card is shown to Connie. It is publicly announced that someone picked a red card. It is publicly announced that Connie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Connie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Christopher","Connie"],"index":54287,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997237325,"difficulty":0.0002762675}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Laura can now know that Juan can know that Billy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Juan","Billy","Eugene"],"index":13931,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997998178,"difficulty":0.002001822}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shala's forehead is not muddy. It is publicly announced that Eduardo's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Shala can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Eduardo","Shala"],"index":27637,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9409304857,"difficulty":0.0590695143}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Denise does not know whether Brandon is thirsty. It is publicly announced that Brandon knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jill can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Denise","Jill","Brandon","Melissa"],"index":18390,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966369867,"difficulty":0.0033630133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Arlene can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arlene","Charles","Alberto","Joel"],"index":53668,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982866645,"difficulty":0.0017133355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Michelle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Michelle can now know whether Kyle can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Kyle","Michelle","David"],"index":26579,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995211363,"difficulty":0.0004788637}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn does not know whether or not everyone is thirsty. It is publicly announced that Evelyn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Patsy can now know that Evelyn can know whether Patsy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alicia","Evelyn","Patsy"],"index":38994,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7570368648,"difficulty":1.7570368648}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Victoria does not know whether Roxie is thirsty. It is publicly announced that Roxie does not know whether Phillip is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Roxie can now know that Roxie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Rita","Phillip","Roxie"],"index":57517,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9031811357,"difficulty":0.0968188643}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Michael does not know whether Eleanor is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Michael can now know whether Eleanor is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eleanor","Michael","Rosalyn"],"index":25376,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9883897305,"difficulty":0.0116102695}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bonita does not know whether or not everyone is thirsty. It is publicly announced that Joshua knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Bonita can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joshua","Bonita","Agnes"],"index":5946,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955698848,"difficulty":0.0044301152}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harrison's card is shown to Harrison. Anne's card is shown to Anne. Harrison's card is shown to Miguel. Anne's card is shown to Miguel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anne can now know whether Harrison can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harrison","Anne","Miguel"],"index":36460,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9926395416,"difficulty":0.0073604584}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Willie. Ruby's card is shown to Willie. Willie's card is shown to Rick. Arlene's card is shown to Ruby. Arlene's card is shown to Arlene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rick can now know whether Willie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Rick","Ruby","Arlene"],"index":9854,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9930576086,"difficulty":0.0069423914}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernard's card is shown to Paul. Paul's card is shown to Bernard. It is publicly announced that someone picked a red card. It is publicly announced that Bernard does not know whether Bernard picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Bernard can now know whether Paul can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Bernard"],"index":43212,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Kimi knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Christy can now know whether Douglas can know whether Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimi","Christy","Douglas"],"index":52873,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996587038,"difficulty":0.0003412962}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Amy's card is shown to Jessie. Jessie's card is shown to Jessie. It is publicly announced that someone picked a red card. It is publicly announced that Jessie knows whether Jessie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Amy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Amy","Jessie"],"index":7797,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986280203,"difficulty":0.0013719797}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Margaret can now know whether Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Margaret","William","Nancy"],"index":44993,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.975333333,"difficulty":0.024666667}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linnie","Patricia","Kim","Linda"],"index":5204,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984215498,"difficulty":0.0015784502}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Russell knows whether Russell is thirsty. It is publicly announced that Patricia knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Timothy can now know whether Russell is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Timothy","Russell"],"index":34847,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9654849172,"difficulty":0.0345150828}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald is thirsty. It is publicly announced that Ronald does not know whether Susan is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Susan can now know that Ronald can know whether Susan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Susan","Ronald"],"index":37050,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5277237892,"difficulty":0.4722762108}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentd knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Donald can now know whether Myra can know that Billy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Myra","Eva","Billy","Donald"],"index":26895,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996408224,"difficulty":0.0003591776}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samuel does not know whether Larry is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Larry can now know whether Kevin can know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Samuel","Kevin","Polly"],"index":7386,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9965762496,"difficulty":0.0034237504}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Viola's card is shown to Barbara. Kristel's card is shown to Kristel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","John","Kristel","Viola"],"index":22400,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962278605,"difficulty":0.0037721395}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maude's card is shown to Maude. Maude's card is shown to Pamela. Bertram's card is shown to Pamela. Maude's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Maude does not know whether Bertram picked a red card. It is publicly announced that Gregory knows whether or not everyone picked a red card. It is publicly announced that Maude does not know whether Pamela picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Pamela can now know that Gregory can know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maude","Pamela","Gregory","Bertram"],"index":12875,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.727339685,"difficulty":0.272660315}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phyllis's card is shown to William. Krystal's card is shown to Krystal. Phyllis's card is shown to Krystal. Krystal's card is shown to Phyllis. Phyllis's card is shown to Phyllis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Krystal can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Krystal","Phyllis"],"index":58003,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin does not know whether Allen is thirsty. It is publicly announced that Allen does not know whether Justin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Micheal can now know whether Allen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allen","Julian","Justin","Micheal"],"index":29423,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974400997,"difficulty":0.0025599003}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jeffrey can now know whether Annabelle can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Annabelle","Jeffrey","Robin"],"index":52943,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997802377,"difficulty":0.0002197623}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerri's card is shown to Gerri. Gary's card is shown to Gerri. Gerri's card is shown to Wanita. Gerri's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gerri can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gerri","Wanita","Gary"],"index":4628,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997729659,"difficulty":0.0002270341}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria's forehead is muddy. It is publicly announced that Terrence knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentd knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sarah can now know whether Terrence can know whether Renee's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terrence","Maria","Renee","Sarah"],"index":29979,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994532466,"difficulty":0.0005467534}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Violet's card is shown to David. David's card is shown to Joseph. Violet's card is shown to Joseph. Joseph's card is shown to Velma. David's card is shown to Violet. Velma's card is shown to Violet. It is publicly announced that someone picked a red card. It is publicly announced that Violet does not know whether Violet picked a red card. It is publicly announced that David knows whether or not nobody picked a red card. It is publicly announced that Velma picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Velma can now know whether Joseph can know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Joseph","Velma","Violet"],"index":28006,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9952924252,"difficulty":1.9952924252}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wesley's card is shown to Bernard. Bernard's card is shown to Vaughn. Charles's card is shown to Vaughn. Wesley's card is shown to Wesley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernard","Charles","Vaughn","Wesley"],"index":37296,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977887869,"difficulty":0.0022112131}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether Christine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Denise can now know that Christine can know whether Denise's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christine","Denise"],"index":4111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997252822,"difficulty":0.0002747178}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilyn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Bryan can now know that Jackie can know whether Marilyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Marilyn","Jackie","Bryan"],"index":67305,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990075231,"difficulty":0.0009924769}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Brent can now know that Mary can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Brent","Israel","Lewis"],"index":32266,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983397722,"difficulty":0.0016602278}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Johnnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Robert can now know whether Donald can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Laura","Robert","Johnnie"],"index":6704,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995991588,"difficulty":0.0004008412}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Patricia's card is shown to Douglas. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Douglas knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Douglas picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Douglas can now know whether Patricia can know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Douglas"],"index":46651,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9475482702,"difficulty":0.0524517298}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Pamela can now know that James can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Pamela","Alejandro","Guadalupe"],"index":27421,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983648658,"difficulty":0.0016351342}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether or not everyone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Sharon can now know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sheryl","Earline","Sharon"],"index":7734,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8884583712,"difficulty":1.8884583712}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Peggy. Rachel's card is shown to Peggy. Peggy's card is shown to Rachel. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Peggy can now know that Peggy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peggy","Gerald","Rachel"],"index":21479,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9407271743,"difficulty":0.0592728257}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Tara can now know that Kevin can know that Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tara","Kevin","Jose"],"index":58702,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982238412,"difficulty":0.0017761588}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esperanza does not know whether Esperanza's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Alice can now know that Esperanza can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Esperanza","Greg","Jennifer","Alice"],"index":17596,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983478785,"difficulty":0.0016521215}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ryan does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ryan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Mark","Ryan"],"index":30246,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982299209,"difficulty":0.0017700791}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judith is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Maria can now know whether Judith can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Judith","Malcom"],"index":58460,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5482020974,"difficulty":0.4517979026}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Clarence. Gertrude's card is shown to Barbara. Barbara's card is shown to Gertrude. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Alice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Barbara can now know whether Clarence can know that Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clarence","Barbara","Alice","Gertrude"],"index":32101,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9422849417,"difficulty":0.0577150583}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Claude can now know whether Pauline can know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Pauline","Claude","Linda"],"index":39537,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996743202,"difficulty":0.0003256798}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judith does not know whether Denise is thirsty. It is publicly announced that Fannie does not know whether Judith is thirsty. It is publicly announced that Denise does not know whether Fannie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Denise can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judith","Fannie","Denise"],"index":47983,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984935522,"difficulty":0.0015064478}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth does not know whether or not everyone's forehead is muddy. It is publicly announced that Ruth knows whether Joshua's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ruth can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ruth","Joshua"],"index":26410,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997256398,"difficulty":0.0002743602}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nadine knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Nadine can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Priscilla","Nadine","Edwin"],"index":26709,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972231388,"difficulty":0.0027768612}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annette knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Gregory can now know that Annette can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Annette","Gregory"],"index":9228,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99976331,"difficulty":0.00023669}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patsy knows whether someone's forehead is muddy. It is publicly announced that Patsy knows whether Allison's forehead is muddy. It is publicly announced that Allison's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"Patsy can now know whether Pamela can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Allison","Pamela","Patsy"],"index":14563,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995825887,"difficulty":0.0004174113}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Craig can now know whether Dion can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joy","Dion","Craig"],"index":60957,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda does not know whether or not everyone's forehead is muddy. It is publicly announced that Deborah knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Brenda can now know whether Deborah can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deborah","Carlos","Brenda"],"index":15709,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999694705,"difficulty":0.000305295}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rick's forehead is not muddy. It is publicly announced that Barbara's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Barbara can now know that Regenia can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Regenia","Rick","Colleen","Barbara"],"index":48330,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982417822,"difficulty":0.0017582178}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorie knows whether Lorie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Terry can now know whether James can know whether Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terry","Lorie","Violet","James"],"index":23781,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987454414,"difficulty":0.0012545586}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jennifer can now know whether Michael can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Jennifer","Michael"],"index":37636,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997192025,"difficulty":0.0002807975}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Johnny is thirsty. It is publicly announced that Kimberly does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Johnny can now know that Kimberly can know that Johnny is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fredrick","Johnny","Sally","Kimberly"],"index":26988,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8864148259,"difficulty":0.1135851741}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. Yesenia's card is shown to Andrea. Yesenia's card is shown to Yesenia. Robert's card is shown to Yesenia. Evelyn's card is shown to Robert. Yesenia's card is shown to Evelyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrea can now know that Robert can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrea","Yesenia","Robert","Evelyn"],"index":47880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962383509,"difficulty":0.0037616491}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linwood's card is shown to Linwood. Alice's card is shown to Linwood. Dustin's card is shown to Alice. Alice's card is shown to Dustin. Dustin's card is shown to Dustin. It is publicly announced that someone picked a red card. It is publicly announced that Linwood does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Latasha can now know whether Alice can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Latasha","Linwood","Alice","Dustin"],"index":30623,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Brenda can now know whether Charles can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fredrick","Merlin","Brenda","Charles"],"index":38033,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996464252,"difficulty":0.0003535748}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Emery can now know that Emery's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sue","Emery","Maria","Estelle"],"index":17948,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952940345,"difficulty":0.0047059655}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Angelica. Troy's card is shown to Angelica. Angelica's card is shown to Mary. Troy's card is shown to Mary. Mary's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that Angelica does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Angelica can now know that Mary can know that Troy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angelica","Mary","Troy"],"index":31857,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6703234911,"difficulty":1.6703234911}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Terry is thirsty. It is publicly announced that Margaret is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Margaret can now know that John can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","John","Richard","Terry"],"index":13523,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961370826,"difficulty":0.0038629174}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matilda's card is shown to Clifton. Raymond's card is shown to Clifton. Matilda's card is shown to Matilda. Raymond's card is shown to Matilda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clifton can now know whether Matilda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clifton","Matilda","Raymond"],"index":58943,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9566532373,"difficulty":0.0433467627}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Celesta does not know whether Celesta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vernon","John","Celesta"],"index":11385,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996964395,"difficulty":0.003035605}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Jason. Scot's card is shown to Jason. Jason's card is shown to Scot. It is publicly announced that someone picked a red card. It is publicly announced that Cecil knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Cecil can now know that Jason can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cecil","Jason","Scot"],"index":42945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983091354,"difficulty":0.0016908646}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Dalton. Dalton's card is shown to Daniel. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Daniel knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Dalton can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dalton","Daniel"],"index":472,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981289506,"difficulty":0.0018710494}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Danny can now know that Roosevelt can know that Dorothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Danny","Dorothy","Roosevelt"],"index":54084,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8708095551,"difficulty":0.1291904449}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Estela's card is shown to Fran. Crystal's card is shown to Fran. Fran's card is shown to Donald. Donald's card is shown to Estela. Estela's card is shown to Estela. Donald's card is shown to Crystal. Estela's card is shown to Crystal. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Crystal can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fran","Donald","Estela","Crystal"],"index":60602,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983482361,"difficulty":0.0016517639}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that Megan does not know whether Megan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Megan can now know whether Thomas can know whether Sue's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sue","Thomas","Megan"],"index":33787,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991777539,"difficulty":0.0008222461}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gwendolyn knows whether Sun's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Gwendolyn can now know that Sun's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sun","Gwendolyn","Leah","John"],"index":37002,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973567724,"difficulty":0.0026432276}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Shirley can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","Colleen","Sallie","John"],"index":10775,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985387325,"difficulty":0.0014612675}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Gerald can now know that Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sharonda","Terry","Deborah","Gerald"],"index":40307,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9963095784,"difficulty":0.0036904216}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Matthew can now know whether Michael can know that Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jacqueline","Michael","Matthew"],"index":32259,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990879297,"difficulty":0.0009120703}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elba knows whether Elba's forehead is muddy. It is publicly announced that Elba's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] Agentb knows that (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Rachel can now know that Frank can know that Karen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Rachel","Elba","Karen"],"index":61600,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9831114411,"difficulty":1.9831114411}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heike's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agentc knows that (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Isiah can now know that Janet can know that Stephen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heike","Stephen","Isiah","Janet"],"index":65263,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9366492033,"difficulty":0.0633507967}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Theresa. William's card is shown to Theresa. Dorothy's card is shown to Dorothy. Dorothy's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether Theresa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"William can now know whether Theresa can know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Theresa","Dorothy","William"],"index":16416,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986467957,"difficulty":0.0013532043}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darell can now know that Douglas can know whether Russell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Buddy","Darell","Douglas","Russell"],"index":22002,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997429252,"difficulty":0.0002570748}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christine does not know whether Esther is thirsty. It is publicly announced that Christine does not know whether or not everyone is thirsty. It is publicly announced that Christine does not know whether Esther is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Christine can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Esther","Donald","Christine"],"index":32500,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996949434,"difficulty":0.0003050566}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sadie knows whether Sadie's forehead is muddy. It is publicly announced that Patricia knows whether or not everyone's forehead is muddy. It is publicly announced that Barbara knows whether Sadie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Barbara can now know whether Sadie can know that Dora's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Sadie","Barbara","Dora"],"index":17594,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.995341301,"difficulty":0.004658699}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether someone's forehead is muddy. It is publicly announced that Laura does not know whether Laura's forehead is muddy. It is publicly announced that Angelina does not know whether or not everyone's forehead is muddy. It is publicly announced that Margaret knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Margaret can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Margaret","Lucy","Angelina"],"index":49622,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978564382,"difficulty":0.0021435618}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Judy can now know whether Kelli's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerald","Jessica","Judy","Kelli"],"index":3738,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997319579,"difficulty":0.0002680421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andre's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Clyde can now know that Andre can know that Andre's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Andre","Clyde","Michael"],"index":49928,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9751351476,"difficulty":0.0248648524}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria is not thirsty. It is publicly announced that Maria is not thirsty. It is publicly announced that Clay does not know whether Jeffery is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jeffery can now know that Ted can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffery","Clay","Ted","Maria"],"index":60624,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984746575,"difficulty":0.0015253425}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to Darryl. Paula's card is shown to Brenda. Jesus's card is shown to Paula. Paula's card is shown to Paula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darryl can now know whether Brenda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darryl","Jesus","Brenda","Paula"],"index":50039,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8025647402,"difficulty":0.1974352598}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kelvin can now know that Allan can know whether Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelvin","Margaret","Allan"],"index":56534,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999727428,"difficulty":0.000272572}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Lane's card is shown to Robert. Willie's card is shown to Robert. Robert's card is shown to Willard. Willard's card is shown to Willard. Willard's card is shown to Willie. Willie's card is shown to Willie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Lane can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Lane","Willard","Willie"],"index":58733,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8495690823,"difficulty":0.1504309177}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlene's card is shown to Marlene. James's card is shown to Marlene. Betsy's card is shown to Woodrow. Woodrow's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Betsy can now know whether Marlene can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marlene","Betsy","Woodrow","James"],"index":15839,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985845089,"difficulty":0.0014154911}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Micheal's card is shown to Stuart. Stuart's card is shown to Julie. Julie's card is shown to Julie. Sarah's card is shown to Julie. Micheal's card is shown to Julie. Julie's card is shown to Sarah. Stuart's card is shown to Micheal. It is publicly announced that someone picked a red card. It is publicly announced that Sarah does not know whether Stuart picked a red card. It is publicly announced that Stuart knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Stuart can now know whether Micheal can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stuart","Julie","Sarah","Micheal"],"index":1076,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lula's card is shown to Lula. Anthony's card is shown to Lula. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether Lula picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Lula can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lula","Anthony"],"index":56124,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isabel does not know whether Sarah is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Isabel can now know whether James can know whether Isabel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Isabel","Katharine","James","Sarah"],"index":18368,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983844757,"difficulty":0.0016155243}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Alan. Margaret's card is shown to Alan. Alan's card is shown to Hazel. Hazel's card is shown to Hazel. Margaret's card is shown to Hazel. Alan's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Hazel knows whether or not nobody picked a red card. It is publicly announced that Alan does not know whether Hazel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alan","Hazel","Margaret"],"index":64021,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9755772352,"difficulty":0.0244227648}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aimee does not know whether Aimee's forehead is muddy. It is publicly announced that Kathleen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jennifer can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Aimee","Kathleen"],"index":19413,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976328611,"difficulty":0.0023671389}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether Elbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Carolyn can now know that Elbert can know whether Trudy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Trudy","Elbert","Agnes","Carolyn"],"index":63548,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997255206,"difficulty":0.0002744794}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether Charles is thirsty. It is publicly announced that Diane does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Diane can now know whether Francis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diane","Steven","Francis","Charles"],"index":9736,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8971748352,"difficulty":0.1028251648}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Katherine can now know whether Audrey can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Katherine","Audrey"],"index":61629,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996904135,"difficulty":0.0003095865}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that German's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"German can now know that John can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Abe","John","German","Roy"],"index":20154,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997832179,"difficulty":0.0002167821}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"James can now know that Madeline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Madeline","James","John"],"index":74,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9840797782,"difficulty":0.0159202218}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Anne can now know whether Raymond can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Raymond","Anne"],"index":67680,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997296929,"difficulty":0.0002703071}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry does not know whether or not everyone is thirsty. It is publicly announced that Tod does not know whether Greg is thirsty. It is publicly announced that Tod does not know whether Greg is thirsty. It is publicly announced that Tod does not know whether Gina is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Gina can now know that Larry can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gina","Tod","Larry","Greg"],"index":50241,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997130036,"difficulty":0.0002869964}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy. It is publicly announced that Micah does not know whether Micah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Marie can now know whether Richard can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marie","Jose","Micah","Richard"],"index":11029,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7871510386,"difficulty":1.7871510386}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shanika knows whether Shawn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Shawn can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arturo","Shanika","Shawn","Tony"],"index":5348,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996705055,"difficulty":0.0003294945}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jarrod does not know whether Katherine is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Mary is thirsty. It is publicly announced that Jarrod knows whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Sara can now know that Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sara","Mary","Jarrod","Katherine"],"index":53509,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7278474569,"difficulty":1.7278474569}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lewis knows whether Anna's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Lewis can now know that Anna can know that Lewis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anna","Lewis"],"index":59375,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980060458,"difficulty":0.0019939542}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacob knows whether Jacob's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lamar can now know whether Juan can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jacob","Juan","Sylvia","Lamar"],"index":31995,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996902943,"difficulty":0.0003097057}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that Paul can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Larry","Paul"],"index":30557,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983600974,"difficulty":0.0016399026}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Michelle can now know that Robert can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Pearl","Theresa","Robert"],"index":25923,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Mary. Frank's card is shown to Mary. Judy's card is shown to Michael. Michael's card is shown to Judy. Judy's card is shown to Judy. Mary's card is shown to Frank. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Judy can now know whether Frank can know that Judy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Michael","Judy","Frank"],"index":30787,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9230240583,"difficulty":0.0769759417}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Logan can now know that Ollie can know that Logan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melissa","Logan","Ollie","Jennifer"],"index":38075,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984757304,"difficulty":0.0015242696}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Rosanna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentc knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Michael can now know whether Robert can know that Rosanna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Charles","Michael","Rosanna"],"index":57473,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983299375,"difficulty":0.0016700625}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Misty does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Misty can now know that Danielle can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Samantha","Misty","Danielle","Gladys"],"index":52139,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.975566566,"difficulty":0.024433434}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erna does not know whether Nicolas is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Erna can now know whether Amanda can know that Amanda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Erna","Nicolas","Amanda"],"index":52349,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.706358552,"difficulty":0.293641448}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lorraine is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know that Christopher can know whether Lorraine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Lorraine","Anna","Patricia"],"index":60179,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8124216199,"difficulty":0.1875783801}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Catherine. James's card is shown to James. Catherine's card is shown to Susan. James's card is shown to Howard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susan can now know whether Catherine can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","James","Susan","Howard"],"index":52162,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9119984508,"difficulty":0.0880015492}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ja's card is shown to Ja. Amy's card is shown to Ja. Tiffany's card is shown to Ja. Amy's card is shown to Amy. Tiffany's card is shown to Tiffany. It is publicly announced that someone picked a red card. It is publicly announced that Amy does not know whether Tiffany picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Ja can now know whether Tiffany can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ja","Amy","Tiffany"],"index":23990,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997039437,"difficulty":0.0002960563}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dawn can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gary","Mary","Sharon","Dawn"],"index":23446,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997705817,"difficulty":0.0002294183}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Edith knows whether Edith's forehead is muddy. It is publicly announced that Kenneth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Kenneth can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edith","Kenneth"],"index":13791,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996316433,"difficulty":0.0003683567}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know that Joseph can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Vanessa","David"],"index":67034,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993017912,"difficulty":0.0006982088}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Troy's card is shown to Troy. Tiffany's card is shown to Antone. Troy's card is shown to Tiffany. Tiffany's card is shown to Tiffany. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Antone can now know whether Tiffany can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Troy","Antone","Tiffany"],"index":23234,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Wanda","Michael"],"index":27823,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985964894,"difficulty":0.0014035106}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reba does not know whether Reba's forehead is muddy. It is publicly announced that Reba does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Reba can now know whether Reba's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Christina","Reba"],"index":37727,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8218337297,"difficulty":1.8218337297}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Diane can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Della","Diane","Darren","Melissa"],"index":56592,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997304082,"difficulty":0.0002695918}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Lori can now know that Lori's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Lori","Diane","Kenneth"],"index":22259,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.97556144,"difficulty":0.02443856}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arnold knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Raymond can now know that Sean can know that Sean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Arnold","Raymond","Sean"],"index":30192,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998329699,"difficulty":0.001670301}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andres's card is shown to Andres. Andres's card is shown to James. Andres's card is shown to Timothy. James's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Andres picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andres","James","Timothy"],"index":19688,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6465066075,"difficulty":0.3534933925}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alton does not know whether Helen is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty. It is publicly announced that Helen is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Alton can now know that Alton is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","John","Alton"],"index":41505,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9689621925,"difficulty":1.9689621925}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Ramon. Kevin's card is shown to Paul. Ramon's card is shown to Kevin. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that Kevin can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ramon","Paul","Kevin"],"index":58131,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9344931841,"difficulty":0.0655068159}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"James can now know whether Scott can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Scott","Krista"],"index":42935,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6874642372,"difficulty":0.3125357628}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kurt knows whether Kurt's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"William can now know that Kurt can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Kurt","James","Paul"],"index":705,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985334873,"difficulty":0.0014665127}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Douglas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Douglas can now know that Delbert can know that Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Delbert","Douglas","Michael"],"index":632,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981879592,"difficulty":0.0018120408}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Brenda can now know whether Connie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brenda","Bernice","Gregory","Connie"],"index":30699,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992509484,"difficulty":0.0007490516}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dale can now know that Kyle can know that Stasia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kyle","Carmen","Stasia","Dale"],"index":6033,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981648326,"difficulty":0.0018351674}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Albert does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Clyde can now know whether Sylvia can know that Clyde is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clyde","William","Albert","Sylvia"],"index":27016,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9809935093,"difficulty":0.0190064907}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Corey knows whether or not nobody is thirsty. It is publicly announced that Corey does not know whether Ricky is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Ricky can now know that Gia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Corey","Ricky","Gia"],"index":47641,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976179004,"difficulty":0.0023820996}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher knows whether or not everyone is thirsty. It is publicly announced that Christopher knows whether or not nobody is thirsty. It is publicly announced that Christopher knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Dorothy can now know that Christopher can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Christopher"],"index":36428,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Cole can now know that Ronald can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Cole","Tamela","Lloyd"],"index":34779,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999759376,"difficulty":0.000240624}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephenie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Denise can now know that Stephenie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephenie","Jenny","Reginald","Denise"],"index":31889,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.697238028,"difficulty":1.697238028}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sanford's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sanford's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Mattie can now know that Pamela can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sanford","Pamela","Mattie"],"index":43121,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985535741,"difficulty":0.0014464259}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dallas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Christine can now know that Anne can know that Heather's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Heather","Anne","Dallas"],"index":43308,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9210805893,"difficulty":0.0789194107}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vincent does not know whether Robert is thirsty. It is publicly announced that Monica does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Claudia can now know whether Robert can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Claudia","Vincent","Robert","Monica"],"index":57569,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997031093,"difficulty":0.0002968907}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Mildred can now know whether John can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Mildred"],"index":54175,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996700287,"difficulty":0.0003299713}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vernon does not know whether Vernon's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Vernon can now know that Charles can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Vernon"],"index":25116,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.992831707,"difficulty":1.992831707}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Arthur can now know whether Kevin can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Arthur"],"index":45360,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997258782,"difficulty":0.0002741218}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to Amber. Heather's card is shown to Heather. Ryan's card is shown to Heather. Heather's card is shown to Ryan. Ryan's card is shown to Ryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ryan can now know that Amber can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amber","Heather","Ryan"],"index":51127,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997788072,"difficulty":0.0002211928}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy. It is publicly announced that Brittany knows whether Julia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Julia can now know that Luis can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Luis","Richard","Julia","Brittany"],"index":8366,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997745156,"difficulty":0.0002254844}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Neal can now know that Carol can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carol","Neal"],"index":37762,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9933460951,"difficulty":0.0066539049}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Georgia can now know that Tracy can know that Tracy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracy","Georgia","Edward"],"index":20437,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9955744743,"difficulty":0.0044255257}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Susie can now know that Jody can know that Nicholas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nicholas","Susie","Jody","John"],"index":57293,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9951717257,"difficulty":0.0048282743}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Percy's card is shown to Maria. Maria's card is shown to Dexter. Percy's card is shown to Dexter. Maria's card is shown to Percy. Dexter's card is shown to Percy. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Maria picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Dexter knows whether Percy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Maria can now know whether Percy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maria","Dexter","Percy"],"index":47563,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7200214863,"difficulty":0.2799785137}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Renate's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Renate can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Robert","Renate","Herbert"],"index":39314,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9915354252,"difficulty":0.0084645748}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Donna does not know whether Lillian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Lillian can now know whether James can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Donna","Lillian","Linda"],"index":29266,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8127522469,"difficulty":0.1872477531}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Madeline does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Derek can now know whether Madeline can know that Mike's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mike","Madeline","Derek","Jane"],"index":56994,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983363748,"difficulty":0.0016636252}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Patricia can now know that Daniel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Daniel","Barry"],"index":55587,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984458089,"difficulty":0.0015541911}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna does not know whether Jeffrey is thirsty. It is publicly announced that Jeffrey does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Paul can now know whether Donna can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Donna","Paul"],"index":18393,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9536709785,"difficulty":1.9536709785}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alyce is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Alyce can now know that Donna can know whether Kimberly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","Donna","Alyce","Jerry"],"index":55918,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9467543364,"difficulty":0.0532456636}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Ryan can now know that Steven can know that Mattie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ryan","Steven","Mattie"],"index":14840,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.943457365,"difficulty":0.056542635}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Conrad's card is shown to Conrad. Conrad's card is shown to Amy. Conrad's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Debra does not know whether Amy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Conrad can now know whether Amy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Conrad","Amy","Debra"],"index":10962,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.941513896,"difficulty":0.058486104}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Emmett. Christopher's card is shown to Michele. Christopher's card is shown to Christopher. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michele can now know that Emmett can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emmett","Michele","Christopher","Catherine"],"index":40841,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997178912,"difficulty":0.0002821088}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gertrude's card is shown to Gertrude. Raymond's card is shown to Gertrude. Gertrude's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Elvin does not know whether Elvin picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Elvin can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gertrude","Elvin","Raymond"],"index":58938,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984931946,"difficulty":0.0015068054}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gary can now know whether Blake's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Blake","Christopher","Gary","Candice"],"index":34002,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997408986,"difficulty":0.0002591014}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Glenda can now know that Julius can know that Julius's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Glenda","Julius","Robert"],"index":28162,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998287499,"difficulty":0.001712501}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Malcolm knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Malcolm can now know that Marylin can know that Russell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Malcolm","Marylin","Russell"],"index":5589,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985449314,"difficulty":0.0014550686}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Audra does not know whether Audra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Donald can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Audra","Laurel"],"index":1053,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7333136201,"difficulty":0.2666863799}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosemary's forehead is muddy. It is publicly announced that Megan knows whether or not everyone's forehead is muddy. It is publicly announced that Richard knows whether Rosemary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Megan can now know that Megan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Megan","Richard","Rosemary"],"index":2476,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7821345925,"difficulty":1.7821345925}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Andrew can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Andrew","Christopher","Wanda"],"index":52007,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998495698,"difficulty":0.001504302}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlene is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Charlene can now know that Rebeca is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charlene","Rebeca"],"index":6505,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9494875669,"difficulty":0.0505124331}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamela's card is shown to Pamela. Walter's card is shown to Walter. Leon's card is shown to Walter. Walter's card is shown to Leon. Leon's card is shown to Leon. It is publicly announced that someone picked a red card. It is publicly announced that Pamela does not know whether Walter picked a red card. It is publicly announced that Leon knows whether Walter picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Pamela can now know whether Walter can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Walter","Leon"],"index":52016,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7632947564,"difficulty":1.7632947564}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roberta's card is shown to Roberta. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan does not know whether Roberta picked a red card. It is publicly announced that Roberta picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] 0","hypothesis":"Roberta can now know that Jonathan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roberta","Jonathan"],"index":29331,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6906194687,"difficulty":1.6906194687}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alan does not know whether or not everyone is thirsty. It is publicly announced that Ruben does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know whether Alan can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Alan","Ruben"],"index":1065,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9647502899,"difficulty":0.0352497101}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mona knows whether Derek's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Patricia can now know that Derek can know that Mona's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mona","Maggie","Patricia","Derek"],"index":21344,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985135198,"difficulty":0.0014864802}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Joy can now know whether Rick can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Rick","Charlene","Joy"],"index":48593,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9946934581,"difficulty":0.0053065419}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Rhonda can now know whether Eloise can know that Rhonda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Randy","Rhonda","Eloise","Katherine"],"index":31990,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8338835239,"difficulty":0.1661164761}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicole does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Antony can now know whether John can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christina","Nicole","John","Antony"],"index":56453,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994418025,"difficulty":0.0005581975}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca does not know whether or not everyone's forehead is muddy. It is publicly announced that Emma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] 0","hypothesis":"Nicole can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rebecca","Nicole","Emma"],"index":21734,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982594848,"difficulty":0.0017405152}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy. It is publicly announced that Robert knows whether Elliott's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Robert can now know that Elliott can know that Tracy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elliott","Tracy","Robert"],"index":29316,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9785019159,"difficulty":0.0214980841}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Cheryl is thirsty. It is publicly announced that David is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Benjamin can now know whether Cheryl can know whether Benjamin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Benjamin","Cheryl"],"index":10930,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9982951283,"difficulty":1.9982951283}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Lottie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justine","David","Sona","Lottie"],"index":29514,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985460043,"difficulty":0.0014539957}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Robert is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Virgil can now know that Marvin can know that Virgil is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Marvin","Charles","Virgil"],"index":4563,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9939285517,"difficulty":0.0060714483}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delia's card is shown to Delia. Rachel's card is shown to Delia. Lisa's card is shown to Rachel. Shirley's card is shown to Shirley. Shirley's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Rachel does not know whether Shirley picked a red card. It is publicly announced that Shirley does not know whether Rachel picked a red card. It is publicly announced that Shirley does not know whether Rachel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Delia can now know whether Delia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Delia","Rachel","Shirley","Lisa"],"index":65825,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8246149421,"difficulty":0.1753850579}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennie's card is shown to Tiffany. Jennie's card is shown to Jennie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Jennie can now know that Tiffany can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tiffany","Jennie"],"index":9557,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997698665,"difficulty":0.0002301335}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Janet. Janet's card is shown to Tuyet. Tuyet's card is shown to Tuyet. Janet's card is shown to Julianne. Julianne's card is shown to Julianne. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Tuyet picked a red card. It is publicly announced that Tuyet does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Tuyet can now know that Jo can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Tuyet","Jo","Julianne"],"index":65145,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976494908,"difficulty":0.0023505092}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tressa knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Alberto can now know whether Tressa can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alberto","Tressa"],"index":5221,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997702241,"difficulty":0.0002297759}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] 0","hypothesis":"Joseph can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Patrick"],"index":49151,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997629523,"difficulty":0.0002370477}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sharon can now know whether Scott can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Scott","Carol"],"index":52606,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9778416157,"difficulty":0.0221583843}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nina's card is shown to Nina. David's card is shown to Nina. David's card is shown to Colleen. Nina's card is shown to David. Connie's card is shown to David. Connie's card is shown to Connie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that Nina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nina","Colleen","David","Connie"],"index":33359,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979842901,"difficulty":0.0020157099}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann's forehead is muddy. It is publicly announced that Lissette knows whether or not everyone's forehead is muddy. It is publicly announced that Kirsten knows whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lissette can now know that Kirsten's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lissette","Kirsten","Ann"],"index":24415,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5419270992,"difficulty":1.5419270992}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russel knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Stephen can now know whether Ronald can know whether Russel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Russel","Ronald","Patricia"],"index":62903,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996970892,"difficulty":0.0003029108}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether or not nobody's forehead is muddy. It is publicly announced that Jason's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Rachel can now know whether Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jason","Rachel"],"index":44961,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997527003,"difficulty":0.0002472997}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Veronica is thirsty. It is publicly announced that Isabel is not thirsty. It is publicly announced that Naomi does not know whether Andre is thirsty. It is publicly announced that Veronica does not know whether Naomi is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Naomi can now know whether Andre can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Veronica","Naomi","Andre","Isabel"],"index":51336,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996993542,"difficulty":0.0003006458}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Lilia. Charles's card is shown to Lilia. Lilia's card is shown to Doris. Doris's card is shown to Doris. Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Doris knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Doris can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lilia","Doris","Charles"],"index":21195,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984989166,"difficulty":0.0015010834}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Elias. Elias's card is shown to Elias. Eric's card is shown to Matthew. Elias's card is shown to Matthew. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Eric does not know whether Matthew picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Elias can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Elias","Leigh","Matthew"],"index":14671,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932268262,"difficulty":0.0067731738}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristi's card is shown to Beryl. Beryl's card is shown to Joann. Kristi's card is shown to Joann. Beryl's card is shown to Walter. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beryl can now know whether Beryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beryl","Joann","Kristi","Walter"],"index":16996,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9073963761,"difficulty":1.9073963761}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rosa can now know whether Charlotte can know that Charlotte is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rosa","Clayton","Jules","Charlotte"],"index":44680,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8416959643,"difficulty":0.1583040357}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Charles can now know that Amber can know that Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Amber","Charles"],"index":42064,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9242052436,"difficulty":0.0757947564}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Sandra can now know that Sheila's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sheila","Margarita","Edna","Sandra"],"index":10518,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9057542086,"difficulty":0.0942457914}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Phillip can now know whether Richard can know whether Phillip's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Tasha","Phillip","George"],"index":65856,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997137189,"difficulty":0.0002862811}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Kyle. Donald's card is shown to Kyle. George's card is shown to Valerie. Donald's card is shown to Valerie. Valerie's card is shown to Donald. Donald's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether Valerie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kyle","Valerie","George","Donald"],"index":25305,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995644689,"difficulty":0.0004355311}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Emily's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Krista can now know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Emily","Agustin","Krista"],"index":39357,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994984865,"difficulty":0.0005015135}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yvonne's card is shown to Sharon. Leonard's card is shown to Carl. Sharon's card is shown to Yvonne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know whether Leonard can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leonard","Sharon","Carl","Yvonne"],"index":5554,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995824695,"difficulty":0.0004175305}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ida's card is shown to Ida. Donald's card is shown to Ida. Timothy's card is shown to Jeanette. Ida's card is shown to Jeanette. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Ida does not know whether Donald picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Ida can now know that Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Ida","Jeanette","Donald"],"index":26338,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946684241,"difficulty":0.0053315759}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Janet can now know that Shari can know whether Gilberto's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gilberto","Janet","Shari"],"index":56397,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997295737,"difficulty":0.0002704263}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Brenda can now know that Jane can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brenda","Melanie","Jane"],"index":58961,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983227849,"difficulty":0.0016772151}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly does not know whether Jesse is thirsty. It is publicly announced that Kelly does not know whether or not everyone is thirsty. It is publicly announced that Zulema knows whether Kelly is thirsty. It is publicly announced that Jesse does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Zulema can now know that Jesse can know that Kelly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Zulema","Kelly","Jesse"],"index":11671,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6430658102,"difficulty":1.6430658102}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sonia does not know whether Marta is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Sonia can now know whether Marta can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marta","Cindy","Sonia"],"index":19421,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7576981187,"difficulty":0.2423018813}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Rachel does not know whether Roger is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Roger can now know that Janet can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Rachel","Roger","Stacy"],"index":38838,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983754158,"difficulty":0.0016245842}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Dave. Dave's card is shown to Kenneth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Dave can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dave","Kenneth"],"index":12014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997672439,"difficulty":0.0002327561}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vicky's card is shown to Vicky. Jacquelyn's card is shown to Vicky. Arthur's card is shown to Vicky. Jacquelyn's card is shown to Jacquelyn. Robert's card is shown to Jacquelyn. Arthur's card is shown to Arthur. Robert's card is shown to Arthur. Jacquelyn's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Arthur can now know that Jacquelyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vicky","Jacquelyn","Arthur","Robert"],"index":27556,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976246953,"difficulty":0.0023753047}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Mignon does not know whether Mignon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether Doris can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mignon","Robert","Doris"],"index":59507,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958367348,"difficulty":0.0041632652}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise knows whether someone's forehead is muddy. It is publicly announced that Daniel knows whether Eugenia's forehead is muddy. It is publicly announced that Eugenia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Evelyn can now know whether Eugenia can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louise","Daniel","Evelyn","Eugenia"],"index":51011,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997016788,"difficulty":0.0002983212}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Jose's forehead is muddy. It is publicly announced that Jose knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Tommy","Maryann","Joseph"],"index":26189,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.516191721,"difficulty":0.483808279}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Bill can now know whether Derek can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Bill","Derek","Clarence"],"index":11722,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5623898506,"difficulty":1.5623898506}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esther knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Margaret knows whether Margaret's forehead is muddy. It is publicly announced that Esther knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Margaret can now know whether Esther can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Margaret","Esther"],"index":5425,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9925515652,"difficulty":0.0074484348}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roy knows whether someone is thirsty. It is publicly announced that Gail does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Roy can now know whether Patrick can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jenny","Roy","Patrick","Gail"],"index":39938,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Efrain knows whether Efrain is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Efrain can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Efrain","Catherine"],"index":61953,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997819066,"difficulty":0.0002180934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Theresa can now know that Marilyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Theresa","Jamie","Marilyn"],"index":31021,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9254105687,"difficulty":0.0745894313}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Heather knows whether Heather's forehead is muddy. It is publicly announced that Dennis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Heather can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Heather","Dennis"],"index":48389,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9923496246,"difficulty":0.0076503754}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shelley can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","John","Shelley","Andre"],"index":45385,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997527003,"difficulty":0.0002472997}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Cheryl can now know that Carlton can know that Cheryl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carlton","Cheryl"],"index":62621,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978494644,"difficulty":0.0021505356}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Eugene's forehead is muddy. It is publicly announced that Elisabeth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Elisabeth can now know that Eugene can know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elisabeth","Steven","Eugene","George"],"index":31940,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963161349,"difficulty":0.0036838651}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Debra can now know that Maria can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Debra","Peter","Joshua","Maria"],"index":43369,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984526634,"difficulty":0.0015473366}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yolanda does not know whether or not everyone's forehead is muddy. It is publicly announced that Ryan knows whether someone's forehead is muddy. It is publicly announced that Yolanda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Felicia can now know that Yolanda can know whether Yolanda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joe","Yolanda","Ryan","Felicia"],"index":1079,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6892066002,"difficulty":1.6892066002}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha does not know whether Gisela is thirsty. It is publicly announced that Stephen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Kevin can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Kevin","Martha","Gisela"],"index":23506,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984676242,"difficulty":0.0015323758}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adam knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ines can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ines","Jennifer","Manuel","Adam"],"index":66411,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984715581,"difficulty":0.0015284419}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roger is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Mike can now know that Roger can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roger","Mike","Shirley"],"index":52037,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6579154134,"difficulty":0.3420845866}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"William can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Robert","William"],"index":24769,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999732554,"difficulty":0.000267446}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristi knows whether Kristi's forehead is muddy. It is publicly announced that Katherine knows whether Kristi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Denise can now know that Richard can know that Denise's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katherine","Kristi","Denise","Richard"],"index":9297,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976873398,"difficulty":0.0023126602}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert knows whether or not everyone's forehead is muddy. It is publicly announced that Sheldon's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Sheldon can now know that Albert can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Albert","Sheldon"],"index":61013,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997603297,"difficulty":0.0002396703}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario knows whether Colin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Colin can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Colin","Robert","Mario","Randy"],"index":42216,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9789901376,"difficulty":0.0210098624}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wayne does not know whether Mark is thirsty. It is publicly announced that Melinda does not know whether Mark is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Mark can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Wayne","Melinda","Lester"],"index":38505,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985800982,"difficulty":0.0014199018}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stuart can now know that Robert can know whether Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Margaret","Stuart"],"index":3251,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997447133,"difficulty":0.0002552867}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Randy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Randy can now know that Darwin can know that Darwin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Randy","Darwin"],"index":10917,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980238676,"difficulty":0.0019761324}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leroy's card is shown to Elizabeth. Michelle's card is shown to Elizabeth. Elizabeth's card is shown to Leroy. It is publicly announced that someone picked a red card. It is publicly announced that Leroy does not know whether Michelle picked a red card. It is publicly announced that Elizabeth does not know whether Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Leroy can now know that Elizabeth can know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","Leroy","Michelle"],"index":35000,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9813162088,"difficulty":0.0186837912}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Jose. Jose's card is shown to Rosemary. Rosemary's card is shown to Rosemary. Hershel's card is shown to Rosemary. Rosemary's card is shown to Hershel. Dewayne's card is shown to Dewayne. It is publicly announced that someone picked a red card. It is publicly announced that Dewayne picked a red card. It is publicly announced that Jose picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Jose can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Rosemary","Hershel","Dewayne"],"index":55863,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5286673903,"difficulty":0.4713326097}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Darlene. It is publicly announced that someone picked a red card. It is publicly announced that Darlene does not know whether Darlene picked a red card. It is publicly announced that Darlene knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Darlene can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Darlene","Mattie"],"index":33750,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986076951,"difficulty":0.0013923049}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glen's card is shown to Glen. Norma's card is shown to Glen. Jennifer's card is shown to Glen. Glen's card is shown to Norma. Glen's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Norma can now know whether Norma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Glen","Norma","Jennifer"],"index":20995,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9758415222,"difficulty":1.9758415222}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether someone's forehead is muddy. It is publicly announced that Debra knows whether Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Andrew can now know whether Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eloise","Debra","Andrew"],"index":16286,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995825887,"difficulty":0.0004174113}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Mary. Guadalupe's card is shown to Guadalupe. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card. It is publicly announced that Guadalupe does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Guadalupe can now know that Mary can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Guadalupe"],"index":53409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997833371,"difficulty":0.0002166629}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucia does not know whether Sean is thirsty. It is publicly announced that Lucia does not know whether Peggy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sean can now know that Lucia can know that Peggy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sean","Peggy","Lucia"],"index":16283,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951104522,"difficulty":0.0048895478}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to Kenneth. Gregory's card is shown to Kenneth. Frank's card is shown to Victoria. Frank's card is shown to Gregory. Kenneth's card is shown to Frank. Victoria's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Kenneth can now know whether Gregory can know that Frank picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Victoria","Gregory","Frank"],"index":31561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9229015112,"difficulty":0.0770984888}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Carol knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Carol can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nettie","Elizabeth","Carol"],"index":66687,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Brandon. Christopher's card is shown to Brandon. Christopher's card is shown to John. Christopher's card is shown to Orlando. It is publicly announced that someone picked a red card. It is publicly announced that Orlando does not know whether Brandon picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Orlando can now know that John can know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brandon","John","Orlando","Christopher"],"index":51822,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949937463,"difficulty":0.0050062537}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacia does not know whether Clifford is thirsty. It is publicly announced that Shannon does not know whether Stacia is thirsty. It is publicly announced that Stacia does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Stacia can now know that Clifford is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shannon","Stacia","Clifford","Brian"],"index":9263,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8663981557,"difficulty":0.1336018443}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rae's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Linda can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Wanda","Linda","Rae"],"index":27188,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986060262,"difficulty":0.0013939738}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know that Lori can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laura","Lori","Maria","Whitney"],"index":34333,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997437596,"difficulty":0.0002562404}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Kevin. Joseph's card is shown to Joseph. Kevin's card is shown to Lynn. Lynn's card is shown to Lynn. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Kevin picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Lynn can now know whether Kevin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Joseph","Lynn"],"index":44520,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5872446299,"difficulty":1.5872446299}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rob does not know whether Justine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Justine can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fred","Mary","Justine","Rob"],"index":35432,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958059788,"difficulty":0.0041940212}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shawn's card is shown to Robert. Robert's card is shown to Shawn. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shawn can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Shawn","Anthony"],"index":54623,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985221028,"difficulty":0.0014778972}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherri does not know whether Sherri's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Hazel can now know that Ana's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ana","Hazel","Sherri"],"index":23935,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9907192588,"difficulty":0.0092807412}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Donald can now know whether Harold can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rafael","Edward","Harold","Donald"],"index":2644,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995340109,"difficulty":0.0004659891}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stephanie can now know that Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Celia","Stephanie","Christopher"],"index":32361,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931714535,"difficulty":0.0068285465}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dolores's card is shown to Michael. Michael's card is shown to Dolores. It is publicly announced that someone picked a red card. It is publicly announced that Dolores picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Dolores"],"index":45436,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997285008,"difficulty":0.0002714992}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether Kenny is thirsty. It is publicly announced that Kenny is not thirsty. It is publicly announced that Brenda is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] 0","hypothesis":"Kenny can now know that Brenda can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenny","Brenda","John","Anthony"],"index":23647,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984723926,"difficulty":0.0015276074}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Albert. Katherine's card is shown to Albert. Marie's card is shown to Marie. Katherine's card is shown to Marie. Albert's card is shown to Sheila. Marie's card is shown to Sheila. Katherine's card is shown to Sheila. Sheila's card is shown to Katherine. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1,2,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1,2,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sheila can now know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Albert","Marie","Sheila","Katherine"],"index":15456,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975205064,"difficulty":0.0024794936}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha does not know whether Martha's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Shanon can now know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Martha","Shanon","Kevin"],"index":266,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8559267521,"difficulty":0.1440732479}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kent does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Kent can now know that John can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Kent"],"index":8560,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark is not thirsty. It is publicly announced that Mark knows whether Mark is thirsty. It is publicly announced that Mark does not know whether Joe is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Victor can now know that Mark can know that Joe is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Joe","Victor"],"index":39627,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9403069615,"difficulty":0.0596930385}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marisol knows whether someone's forehead is muddy. It is publicly announced that Esperanza knows whether Esperanza's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Esperanza can now know that Lori's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Esperanza","Lori","Marisol","Teresa"],"index":51004,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99804914,"difficulty":0.00195086}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Vivian can now know that Mary can know that Vivian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Vivian","Sherry","Dale"],"index":66857,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9425497651,"difficulty":0.0574502349}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Andrew. Andrew's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether Andrew picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Andrew can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Andrew","Mary"],"index":36221,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999722898,"difficulty":0.000277102}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Judith knows whether Judith's forehead is muddy. It is publicly announced that Troy knows whether Judith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Judith can now know that Steve can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steve","Judith","Troy"],"index":3143,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Petra's card is shown to James. James's card is shown to Julia. Petra's card is shown to Julia. Julia's card is shown to Petra. Petra's card is shown to Petra. It is publicly announced that someone picked a red card. It is publicly announced that Julia knows whether or not everyone picked a red card. It is publicly announced that Julia knows whether Petra picked a red card. It is publicly announced that Julia knows whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"James can now know that Petra can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Julia","Petra"],"index":41954,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6401252151,"difficulty":1.6401252151}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that Robert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"David can now know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","David","William"],"index":37422,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7526664138,"difficulty":1.7526664138}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Eddie can now know that Wayne can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Wayne","Eddie"],"index":2555,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983355403,"difficulty":0.0016644597}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillian does not know whether Lillian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lillian can now know whether James can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Lillian","Linda","Richard"],"index":32749,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9158238769,"difficulty":0.0841761231}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hope knows whether Hope is thirsty. It is publicly announced that Margaret does not know whether Hope is thirsty. It is publicly announced that Ingrid does not know whether Dolores is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Margaret can now know that Dolores can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hope","Dolores","Margaret","Ingrid"],"index":29567,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997137189,"difficulty":0.0002862811}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald does not know whether Hilda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Alfred can now know whether Donald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hilda","Alfred","Donald"],"index":25695,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9739304185,"difficulty":0.0260695815}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roger knows whether Madeline's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Regina can now know whether Madeline can know whether Roger's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Madeline","Helen","Roger","Regina"],"index":62384,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Evelyn can now know whether Jeffrey can know that Dorothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Mildred","Dorothy","Evelyn"],"index":54943,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9869673848,"difficulty":0.0130326152}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Anthony can now know whether Megan can know that Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Megan","Anthony","Frederick"],"index":51289,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9920497537,"difficulty":0.0079502463}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel knows whether Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Andrew can now know that Joel can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joel","Andrew","Jessica"],"index":48886,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9919338226,"difficulty":0.0080661774}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernest's card is shown to Alan. Alan's card is shown to Ernest. Alan's card is shown to David. Ernest's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Alan can now know that Ernest picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alan","Ernest","David"],"index":26316,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953243732,"difficulty":0.0046756268}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernice knows whether Nicole's forehead is muddy. It is publicly announced that Bernice knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Morris can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elmer","Morris","Nicole","Bernice"],"index":34260,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998565495,"difficulty":0.001434505}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeanette's card is shown to Jeanette. Kim's card is shown to Jeanette. Jeanette's card is shown to Arron. Jeanette's card is shown to Kim. Kim's card is shown to Kim. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Arron can now know that Jeanette can know whether Arron picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeanette","Arron","Kim"],"index":39693,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8512917757,"difficulty":0.1487082243}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George does not know whether or not everyone's forehead is muddy. It is publicly announced that George does not know whether George's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kyung can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["George","Kyung"],"index":53089,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9591286182,"difficulty":0.0408713818}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samuel does not know whether Sherry is thirsty. It is publicly announced that Samuel does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Kay can now know that Samuel can know whether Kay is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Samuel","Sherry","Ida","Kay"],"index":49731,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7085527778,"difficulty":0.2914472222}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Joseph. Joseph's card is shown to Thelma. It is publicly announced that someone picked a red card. It is publicly announced that Thelma picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Thelma can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Thelma"],"index":56504,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Noel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Noel can now know whether Sheri's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Noel","Sheri","Cedric"],"index":36554,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995651841,"difficulty":0.0004348159}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hazel's card is shown to Lillian. Dorothy's card is shown to Curtis. Hazel's card is shown to Dorothy. Dorothy's card is shown to Hazel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Curtis can now know that Lillian can know that Lillian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lillian","Curtis","Dorothy","Hazel"],"index":59499,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980024695,"difficulty":0.0019975305}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alejandro does not know whether Alejandro's forehead is muddy. It is publicly announced that Ruben knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ruben can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nicole","Alejandro","Ruben"],"index":64584,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997110963,"difficulty":0.0002889037}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Susana can now know that Joel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joel","Dorothy","Susana"],"index":47179,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.995474875,"difficulty":0.004525125}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dirk knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] 0","hypothesis":"Vesta can now know whether Dirk can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thu","Vesta","Phillis","Dirk"],"index":64002,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996232986,"difficulty":0.0003767014}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George does not know whether or not everyone's forehead is muddy. It is publicly announced that Melissa knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"George can now know whether Melissa can know that Doloris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melissa","Jordan","Doloris","George"],"index":24260,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9934501648,"difficulty":0.0065498352}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Donna can now know that Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michelle","Donna"],"index":67563,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984093308,"difficulty":0.0015906692}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Marcos can now know that Shirley can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Shirley","Marcos"],"index":37028,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984576702,"difficulty":0.0015423298}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy. It is publicly announced that Catherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] 0","hypothesis":"Catherine can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Melanie","Catherine","Eleanor"],"index":53924,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978870749,"difficulty":0.0021129251}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Norman. Shaun's card is shown to Shaun. William's card is shown to Shaun. Norman's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Shaun does not know whether Michael picked a red card. It is publicly announced that Michael does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Shaun can now know whether Michael can know that Shaun picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Norman","Michael","Shaun","William"],"index":54045,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9188594818,"difficulty":1.9188594818}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Timothy can now know whether Kelly can know that Germaine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Germaine","Doris","Timothy","Kelly"],"index":66565,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9977830052,"difficulty":0.0022169948}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernice's card is shown to Bernice. Bernice's card is shown to Barbara. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Bernice does not know whether Barbara picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Barbara can now know whether Bernice can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bernice","Barbara"],"index":19605,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995125532,"difficulty":0.0004874468}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angela does not know whether Tiffany is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Angela can now know whether John can know that Tiffany is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Angela","Tiffany"],"index":12214,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9897917509,"difficulty":0.0102082491}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julia's card is shown to Julia. Julia's card is shown to Darrell. Julia's card is shown to Bertha. Darrell's card is shown to Bertha. It is publicly announced that someone picked a red card. It is publicly announced that Julia knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Julia can now know whether Bertha can know whether Darrell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julia","Darrell","Bertha"],"index":21537,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983897209,"difficulty":0.0016102791}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terrell's card is shown to Patricia. Patricia's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Terrell can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Terrell","Patricia","John"],"index":49530,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983489513,"difficulty":0.0016510487}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monty does not know whether Monty's forehead is muddy. It is publicly announced that Arlene does not know whether Arlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Karlene can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karlene","Monty","Arlene"],"index":13247,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997720122,"difficulty":0.0002279878}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Harold can now know whether Dennis can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dennis","Harold"],"index":22892,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999771893,"difficulty":0.000228107}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danyelle knows whether Ulysses's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Danyelle can now know that Ulysses can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ulysses","Danyelle"],"index":30248,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997550845,"difficulty":0.0002449155}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Enrique's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Enrique can now know that Jason can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Enrique","Jason","Forest"],"index":34879,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996151924,"difficulty":0.0003848076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darren does not know whether Darren's forehead is muddy. It is publicly announced that Andreas's forehead is muddy. It is publicly announced that Donald knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Andreas can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andreas","Donald","Meghan","Darren"],"index":46467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9351127148,"difficulty":0.0648872852}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy. It is publicly announced that Roger does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Roger can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roger","Robert","Barbara","Tabitha"],"index":47465,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979194999,"difficulty":0.0020805001}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Rosa can now know whether Kelly can know whether Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Kelly","Rosa","Peter"],"index":51626,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993453622,"difficulty":0.0006546378}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ray's card is shown to Ray. Willie's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Willie knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Ray can now know that Willie can know that Willie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ray","Willie"],"index":40057,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9544275403,"difficulty":0.0455724597}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know that Jan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerry","Joanna","Carl","Jan"],"index":62540,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983244538,"difficulty":0.0016755462}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Louis. Cheryl's card is shown to Teresa. Teresa's card is shown to Teresa. Lucy's card is shown to Teresa. Lucy's card is shown to Lucy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louis can now know that Teresa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Cheryl","Teresa","Lucy"],"index":61521,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997810721,"difficulty":0.0002189279}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathleen is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Glenn can now know whether Kathleen can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Glenn","Kathleen","Jesus"],"index":31556,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997783303,"difficulty":0.0002216697}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby does not know whether Bobby's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Rebekah can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Denise","Rebekah","Bobby"],"index":42545,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8817731738,"difficulty":0.1182268262}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether Janet's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ronald can now know whether Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Janet","Ronald"],"index":23757,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9911208749,"difficulty":0.0088791251}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Ilana's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"Ilana can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Renee","Ilana","Jordan","Donald"],"index":29878,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997772574,"difficulty":0.0002227426}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Beulah can now know whether Doris can know that Beulah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Doris","Beulah"],"index":63336,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994218349,"difficulty":0.0005781651}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew does not know whether Matthew's forehead is muddy. It is publicly announced that Maude knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Maude can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Scott","Matthew","Carrie","Maude"],"index":23141,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983541965,"difficulty":0.0016458035}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maurice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Howard can now know whether Beverly can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Maurice","Howard","Dolores"],"index":41827,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Don's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Don can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Allison","Lawrence","Don"],"index":17579,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9950352907,"difficulty":0.0049647093}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Janet. Aurelia's card is shown to Janet. Janet's card is shown to Aurelia. It is publicly announced that someone picked a red card. It is publicly announced that Janet knows whether Janet picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Aurelia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Janet","Aurelia"],"index":35576,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Marion. James's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marion can now know that James can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marion","James","Maria"],"index":33152,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996980429,"difficulty":0.0003019571}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sallie does not know whether Janet is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that William is thirsty. It is publicly announced that Sallie knows whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] (Agenta knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Susan can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Susan","William","Sallie","Janet"],"index":47024,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999785006,"difficulty":0.000214994}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric does not know whether or not everyone's forehead is muddy. It is publicly announced that Eric knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Eric can now know whether Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Laura","Eric"],"index":42406,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5596865416,"difficulty":0.4403134584}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Colin knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"James can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Colin","James"],"index":25782,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997584224,"difficulty":0.0002415776}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Pauline. Pauline's card is shown to Gregory. Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Pauline knows whether Gregory picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Gregory can now know whether Pauline can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pauline","Gregory"],"index":29053,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9961498976,"difficulty":0.0038501024}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosemary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Bertha can now know whether Emily can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosemary","Emily","Walter","Bertha"],"index":18060,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995799661,"difficulty":0.0004200339}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to William. Josephine's card is shown to Josephine. Roy's card is shown to Roy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Josephine can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Josephine","Roy"],"index":64434,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983421564,"difficulty":0.0016578436}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Deborah. Maria's card is shown to Deborah. Maria's card is shown to Janet. Deborah's card is shown to Rose. Janet's card is shown to Maria. Rose's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janet can now know that Deborah can know that Deborah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Janet","Rose","Maria"],"index":28619,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969409108,"difficulty":0.0030590892}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Celia. Celia's card is shown to Janice. Janice's card is shown to Janice. Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gregory can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Celia","Janice","Gregory"],"index":10050,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983812571,"difficulty":0.0016187429}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Martha can now know whether Gale can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Ismael","Martha","Gale"],"index":39205,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997517467,"difficulty":0.0002482533}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether David's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"David can now know that Mary can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","David"],"index":16986,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Eduardo. Eduardo's card is shown to Michelle. Michelle's card is shown to Michelle. John's card is shown to Michelle. Michelle's card is shown to Kathleen. Eduardo's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eduardo","Michelle","Kathleen","John"],"index":26975,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979617596,"difficulty":0.0020382404}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Jason. Tammie's card is shown to Tammie. Tammie's card is shown to Richard. Jason's card is shown to Tifany. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tifany can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Tammie","Richard","Tifany"],"index":60133,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.718083322,"difficulty":0.281916678}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether Mary is thirsty. It is publicly announced that Joseph knows whether Joseph is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mary can now know that Joseph can know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Joseph"],"index":47764,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9964117408,"difficulty":0.0035882592}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ron does not know whether Joshua is thirsty. It is publicly announced that Ron does not know whether or not everyone is thirsty. It is publicly announced that Ron does not know whether Marilyn is thirsty. It is publicly announced that Joshua does not know whether Marilyn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Joshua can now know whether Marilyn can know whether Marilyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marilyn","James","Joshua","Ron"],"index":26396,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9963131547,"difficulty":0.0036868453}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Michael can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Shannon"],"index":37518,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984086156,"difficulty":0.0015913844}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ervin can now know whether Ramon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jodi","Ervin","Ramon","Jesse"],"index":44125,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995738864,"difficulty":0.0004261136}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Leonard. Leonard's card is shown to Gloria. Leonard's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leonard can now know that Leonard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leonard","Gloria","Nancy"],"index":21043,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967926145,"difficulty":0.0032073855}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Miles's card is shown to Jackie. Betty's card is shown to Jackie. Jackie's card is shown to Betty. Betty's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Jackie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Miles can now know whether Jackie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","Miles","Betty"],"index":41576,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roman's card is shown to William. Madelene's card is shown to William. William's card is shown to Roman. Roman's card is shown to Roman. William's card is shown to James. Madelene's card is shown to James. William's card is shown to Madelene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Madelene can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Roman","James","Madelene"],"index":5628,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983960986,"difficulty":0.0016039014}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesse does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Timothy can now know that Jesse can know that Jesse's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jesse","Timothy"],"index":37033,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8736605048,"difficulty":1.8736605048}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Cara can now know whether Fred can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Fred","Richard","Cara"],"index":27242,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994677901,"difficulty":0.0005322099}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martin is not thirsty. It is publicly announced that Barbara knows whether Martin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Barbara can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Martin","Barbara","Judi"],"index":12025,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9759952426,"difficulty":1.9759952426}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roscoe knows whether Roscoe is thirsty. It is publicly announced that Roscoe is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Helen can now know that Helen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Katherine","Roscoe"],"index":56036,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.98456949,"difficulty":0.01543051}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Morris does not know whether Morris's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Linda can now know whether Morris can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucius","Morris","Linda"],"index":4485,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8313450813,"difficulty":1.8313450813}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robbie's card is shown to Ernest. Ruth's card is shown to Ruth. Laurie's card is shown to Robbie. Ernest's card is shown to Robbie. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ruth can now know whether Laurie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laurie","Ernest","Ruth","Robbie"],"index":66004,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997705817,"difficulty":0.0002294183}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Eddie knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Eddie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eddie","Linda","Marlon"],"index":42667,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997211099,"difficulty":0.0002788901}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Mark knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Mary can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joann","Mary","Julia","Mark"],"index":44179,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9945901632,"difficulty":0.0054098368}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. William's card is shown to John. John's card is shown to Janis. John's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that William can know that Janis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Janis","William"],"index":43890,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981354475,"difficulty":0.0018645525}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether Jason's forehead is muddy. It is publicly announced that Jason's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Joan can now know whether Jason can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joan","Jason"],"index":49819,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995544553,"difficulty":0.0004455447}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know that Jerry can know whether Lillie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","William","Lillie","Patricia"],"index":10588,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.992454648,"difficulty":0.007545352}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kayla's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"James can now know that Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dolores","Kayla","Carlos","James"],"index":7295,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994548142,"difficulty":0.005451858}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanette's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Ruby can now know whether Carol can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Jeanette","Carol"],"index":31321,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997814298,"difficulty":0.0002185702}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Kevin can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marilyn","Virginia","Kevin","Charles"],"index":14150,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985163808,"difficulty":0.0014836192}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Everett does not know whether or not everyone's forehead is muddy. It is publicly announced that Everett knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Joseph can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Everett","Joseph"],"index":34138,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997202754,"difficulty":0.0002797246}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marta does not know whether Bennett is thirsty. It is publicly announced that Melissa does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Marta can now know that Bennett can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Marta","Melissa","Bennett"],"index":23251,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997783303,"difficulty":0.0002216697}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey knows whether or not nobody is thirsty. It is publicly announced that Bernadette does not know whether Jeffrey is thirsty. It is publicly announced that Judy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bernadette can now know that Judy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bernadette","Jeffrey","Judy"],"index":57978,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9918420315,"difficulty":0.0081579685}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Juanita. Robert's card is shown to Juanita. Juanita's card is shown to Abigail. Robert's card is shown to Abigail. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juanita can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Anna","Robert","Abigail"],"index":65728,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5763085485,"difficulty":1.5763085485}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Jerry. Jerry's card is shown to Katelyn. Katelyn's card is shown to Katelyn. Jerry's card is shown to Ida. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jerry can now know whether Ida can know whether Katelyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jerry","Katelyn","Ida"],"index":65182,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985995889,"difficulty":0.0014004111}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon does not know whether Gordon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gordon can now know whether Lucinda can know whether Malcolm's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gordon","Malcolm","Lucinda"],"index":51680,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994992018,"difficulty":0.0005007982}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Shaun can now know that Anthony can know that Toby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shaun","Anthony","Terry","Toby"],"index":8463,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6912950873,"difficulty":0.3087049127}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory's forehead is muddy. It is publicly announced that Gregory's forehead is muddy. It is publicly announced that Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agentd knows that (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Fred can now know that Gregory can know that Deborah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gregory","Warren","Deborah","Fred"],"index":44821,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8296507001,"difficulty":1.8296507001}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edna knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Amy can now know that Timothy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Edna","Amy"],"index":22130,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997039437,"difficulty":0.0002960563}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that Clinton does not know whether or not everyone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"David can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Clinton","David"],"index":40359,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944022298,"difficulty":0.0055977702}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda's forehead is muddy. It is publicly announced that Brenda knows whether someone's forehead is muddy. It is publicly announced that Richard knows whether Willie's forehead is muddy. It is publicly announced that Jon does not know whether Jon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Richard can now know that Jon can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Richard","Jon","Brenda"],"index":17727,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990021586,"difficulty":0.0009978414}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell knows whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Darrell can now know that Douglas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rose","Douglas","Darrell","Troy"],"index":33945,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980828762,"difficulty":0.0019171238}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Bryant can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Keith","Bryant"],"index":65903,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997748733,"difficulty":0.0002251267}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Timothy. Dana's card is shown to Timothy. Dorothy's card is shown to Margaret. Margaret's card is shown to Dana. Timothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Margaret does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Dorothy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Margaret","Dana","Dorothy"],"index":37927,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6912122965,"difficulty":1.6912122965}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gisele's card is shown to Gisele. Margarita's card is shown to Gisele. Gisele's card is shown to Margarita. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Margarita can now know that Gisele can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gisele","Margarita"],"index":55948,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985381365,"difficulty":0.0014618635}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether Irma's forehead is muddy. It is publicly announced that Charles knows whether Irma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Angela can now know that Charles can know that Irma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Irma","Charles"],"index":64462,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973342419,"difficulty":0.0026657581}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Danny knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Lisa can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Maria","Danny"],"index":5090,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997653365,"difficulty":0.0002346635}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Fay does not know whether Brandon is thirsty. It is publicly announced that Irma knows whether or not everyone is thirsty. It is publicly announced that Irma does not know whether Fay is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Fay can now know that Irma can know that Fay is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brandon","Fay","Irma"],"index":10843,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7269983888,"difficulty":0.2730016112}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine knows whether Gale's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Geraldine can now know whether Christopher can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Gale","Geraldine"],"index":38928,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997635484,"difficulty":0.0002364516}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacob does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jacob can now know whether Scott can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Scott","Andrew","Jacob"],"index":23423,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9842277765,"difficulty":0.0157722235}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Susan knows whether Elisa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Elisa can now know whether Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Susan","Elisa"],"index":4971,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993983507,"difficulty":0.0006016493}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether Claudette's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Sharon can now know that Victoria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Victoria","Sharon","Claudette"],"index":10888,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983564019,"difficulty":0.0016435981}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Millie. Wanda's card is shown to Millie. Wanda's card is shown to Wanda. Candace's card is shown to Wanda. Millie's card is shown to Candace. It is publicly announced that someone picked a red card. It is publicly announced that Candace does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Wanda can now know that Millie can know whether Wanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Millie","Wanda","Candace"],"index":44101,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6392011046,"difficulty":0.3607988954}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Rhonda. Ann's card is shown to Rhonda. Ann's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Rhonda knows whether Rhonda picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Rhonda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rhonda","Michael","Ann"],"index":45190,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9961723685,"difficulty":1.9961723685}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marvin does not know whether Cheryl is thirsty. It is publicly announced that Jerry does not know whether Marvin is thirsty. It is publicly announced that Jerry does not know whether Cheryl is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Marvin can now know whether Jerry can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cheryl","Marvin","Jerry"],"index":19445,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975771308,"difficulty":0.0024228692}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy. It is publicly announced that Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] 0","hypothesis":"Tony can now know that Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kenneth","Tony","Stevie"],"index":24310,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9547481537,"difficulty":0.0452518463}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martin knows whether Martin is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Martin can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Martin","Rebecca"],"index":49154,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984529018,"difficulty":0.0015470982}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Nancy can now know whether Barbara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barbara","Larry","Ted","Nancy"],"index":23751,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9943658113,"difficulty":0.0056341887}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Marjorie can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marjorie","Raymond"],"index":2889,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997840524,"difficulty":0.0002159476}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Loris can now know that Charles can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Loris","Benjamin"],"index":22770,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983187914,"difficulty":0.0016812086}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Brian. Heather's card is shown to Brian. Pete's card is shown to Brian. Heather's card is shown to Christopher. Heather's card is shown to Heather. Heather's card is shown to Pete. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether Christopher picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Christopher can now know that Brian can know that Brian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Christopher","Heather","Pete"],"index":42704,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8851546645,"difficulty":0.1148453355}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wesley's card is shown to Ruth. Tim's card is shown to Tim. James's card is shown to Tim. Ruth's card is shown to Wesley. Wesley's card is shown to Wesley. James's card is shown to Wesley. Ruth's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:1,3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:1,3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know whether Tim can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Tim","Wesley","James"],"index":27466,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996047616,"difficulty":0.0003952384}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Wesley is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jennifer can now know whether Wesley can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bryan","Wesley","Jennifer","Reuben"],"index":9474,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7176356912,"difficulty":0.2823643088}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Christian's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Donald can now know whether Christian can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donald","Christian"],"index":55530,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994161129,"difficulty":0.0005838871}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Phillip. Phillip's card is shown to Geraldine. Therese's card is shown to Geraldine. Phillip's card is shown to Therese. Therese's card is shown to Therese. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Therese can now know whether Geraldine can know whether Geraldine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phillip","Geraldine","Therese"],"index":63449,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9862902761,"difficulty":0.0137097239}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Raymond. Don's card is shown to Don. Juan's card is shown to Don. Keri's card is shown to Juan. Keri's card is shown to Keri. It is publicly announced that someone picked a red card. It is publicly announced that Raymond does not know whether Keri picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Raymond can now know whether Juan can know that Don picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Don","Juan","Keri"],"index":66967,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.981380403,"difficulty":0.018619597}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether Vanesa's forehead is muddy. It is publicly announced that Hilda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Hilda can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vanesa","Andrew","Hilda","Stephanie"],"index":33756,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Krystal's forehead is not muddy. It is publicly announced that Krystal's forehead is not muddy. It is publicly announced that Lisa knows whether Krystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Chad can now know whether Chad's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lisa","Chad","Krystal"],"index":35016,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6889272332,"difficulty":0.3110727668}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Debra can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deborah","Debra","Matthew"],"index":52414,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997819066,"difficulty":0.0002180934}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know whether Gary can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Gary","Kenneth"],"index":64314,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9543623924,"difficulty":0.0456376076}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence knows whether Annis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Henry can now know that Clarence can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Henry","Annis","Clarence"],"index":34061,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997499585,"difficulty":0.0002500415}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucina's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Geraldine can now know whether Corey can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geraldine","Corey","Lucina","Scott"],"index":58348,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracey's card is shown to Tracey. Deborah's card is shown to Tracey. Tracey's card is shown to Nancy. Tracey's card is shown to Deborah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nancy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tracey","Nancy","Deborah"],"index":23003,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997244477,"difficulty":0.0002755523}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dora knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesse","Dora","William","Theresa"],"index":9409,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8553433418,"difficulty":0.1446566582}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edwin knows whether Edwin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Edwin can now know that Evelyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Gwendolyn","Edwin"],"index":39789,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984439015,"difficulty":0.0015560985}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Birdie knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Birdie can now know whether Mark can know whether Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Birdie","Jeanie"],"index":22221,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995936751,"difficulty":0.0004063249}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlon's card is shown to James. Larry's card is shown to James. Marlon's card is shown to Marlon. James's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Larry can now know whether James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Marlon","Larry"],"index":13390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9954624772,"difficulty":0.0045375228}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Scott is thirsty. It is publicly announced that Blanche does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Blanche can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Blanche","Scott","Robert"],"index":42274,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5422586799,"difficulty":0.4577413201}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Leslie can now know whether Grace can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Kathleen","Grace","Leslie"],"index":25552,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99957937,"difficulty":0.00042063}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Shirley can now know that James can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Benjamin","Shirley"],"index":5795,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997407794,"difficulty":0.0002592206}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Willard. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Charles can now know that Willard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Willard"],"index":42762,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975761771,"difficulty":0.0024238229}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Gerald. Nicole's card is shown to Gerald. Nicole's card is shown to Nicole. Anna's card is shown to Nicole. Nicole's card is shown to Anna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anna can now know whether Gerald can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gerald","Nicole","Anna"],"index":30892,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether or not nobody's forehead is muddy. It is publicly announced that Sharon knows whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Deborah can now know that Sharon can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sharon","Deborah"],"index":51486,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984408021,"difficulty":0.0015591979}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Clifford knows whether or not nobody's forehead is muddy. It is publicly announced that Michael knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Michael can now know whether Clifford can know whether Clifford's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Clifford","Brian","Michael"],"index":38139,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996440411,"difficulty":0.0003559589}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Jessica can now know whether Nina can know whether Jessica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Christina","Nina"],"index":52420,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999730289,"difficulty":0.000269711}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Cindy. Carly's card is shown to Carly. It is publicly announced that someone picked a red card. It is publicly announced that Cindy does not know whether Carly picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Cindy can now know that Carly can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cindy","Carly"],"index":62347,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997106194,"difficulty":0.0002893806}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Susan can now know whether Kimberly can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Frances","Johanna","Susan"],"index":14460,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996974468,"difficulty":0.0003025532}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that Alisha can know whether Alisha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Douglas","Kathlyn","Alisha"],"index":28849,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996122718,"difficulty":0.0003877282}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Todd can now know whether Jesus can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Todd","Jesus","Brenda"],"index":3243,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997571111,"difficulty":0.0002428889}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Norman. Janet's card is shown to Janet. Laurie's card is shown to Carla. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Carla picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Janet can now know that Norman can know that Carla picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laurie","Norman","Janet","Carla"],"index":57163,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958608747,"difficulty":0.0041391253}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ashley does not know whether Rebecca is thirsty. It is publicly announced that Ashley does not know whether Larry is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Rebecca can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ashley","Larry","Rebecca"],"index":17986,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9914616346,"difficulty":0.0085383654}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Natalie can now know that Lina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Natalie","Dawn","Lina"],"index":49907,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.7310472131,"difficulty":0.2689527869}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse does not know whether Mercedes is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Mercedes can now know whether William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stanley","William","Jesse","Mercedes"],"index":66703,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970797896,"difficulty":0.0029202104}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Jennifer can now know that Joy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joy","Jennifer","Grover","Brianne"],"index":44470,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984242916,"difficulty":0.0015757084}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sonia knows whether Tammi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tammi","William","Jerry","Sonia"],"index":17347,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985260963,"difficulty":0.0014739037}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Andrew. Betsy's card is shown to Andrew. Andrew's card is shown to Betsy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lynda can now know whether Andrew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lynda","Andrew","Betsy"],"index":170,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997742772,"difficulty":0.0002257228}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sylvia's card is shown to Sylvia. Sylvia's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Sylvia does not know whether Ruth picked a red card. It is publicly announced that Sylvia knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Ruth can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sylvia","Ruth"],"index":59865,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9774000049,"difficulty":0.0225999951}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Serena's card is shown to James. William's card is shown to Gregory. Serena's card is shown to Gregory. William's card is shown to Serena. Serena's card is shown to Serena. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Gregory can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","James","Gregory","Serena"],"index":53952,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9603019357,"difficulty":0.0396980643}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Carlos can now know whether Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Carlos","Daniel"],"index":15185,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9733459949,"difficulty":0.0266540051}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia knows whether Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Albert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sylvia","Matthew","Alicia","Albert"],"index":37009,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982845187,"difficulty":0.0017154813}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kim's forehead is muddy. It is publicly announced that Damian does not know whether Damian's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kim can now know whether Damian can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Damian","Kim"],"index":39171,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994451404,"difficulty":0.0005548596}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Toni does not know whether Toni's forehead is muddy. It is publicly announced that Casey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Toni can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Toni","Bruce","Casey","Lelia"],"index":63507,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9837133884,"difficulty":0.0162866116}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Margaret can now know that Kenneth can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Kenneth","Karen"],"index":14914,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952687621,"difficulty":0.0047312379}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence does not know whether Lawrence's forehead is muddy. It is publicly announced that Lawrence does not know whether Lawrence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lawrence can now know that Luann's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Luann","Lawrence","Andrea","Mckinley"],"index":36355,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9811390042,"difficulty":0.0188609958}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Valerie's forehead is muddy. It is publicly announced that Valerie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Thomas can now know whether Valerie can know whether Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Thomas","Valerie"],"index":65474,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99969697,"difficulty":0.00030303}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. Betty's card is shown to Steven. Steven's card is shown to Aurelia. Aurelia's card is shown to Aurelia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know that Betty can know that Betty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Steven","Aurelia"],"index":21423,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9808005691,"difficulty":0.0191994309}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Michael can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dana","Barbara","William","Michael"],"index":47887,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984169006,"difficulty":0.0015830994}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Joseph can now know whether Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["April","Joseph","Margaret"],"index":12263,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948016405,"difficulty":0.0051983595}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Diane. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Margaret does not know whether Diane picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Margaret can now know that Diane can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Diane","Margaret"],"index":35728,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998188436,"difficulty":0.001811564}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Alphonso can know that Alphonso's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alphonso","Susan","Robert"],"index":40696,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984558821,"difficulty":0.0015441179}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to William. Laura's card is shown to Laura. Jennifer's card is shown to Laura. William's card is shown to Hubert. Hubert's card is shown to Hubert. William's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Laura","Hubert","Jennifer"],"index":55336,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy. It is publicly announced that Diane knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mary can now know that Diane can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Diane"],"index":14750,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.995398581,"difficulty":0.004601419}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tamatha does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Ailene can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","Ailene","Mike","Tamatha"],"index":46421,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6274424195,"difficulty":1.6274424195}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jon knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jesse can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jon","Charles","Jesse"],"index":35964,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Joshua can now know that Wanda can know that Joshua's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Buford","Wanda"],"index":58274,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973222613,"difficulty":0.0026777387}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Eva. Catherine's card is shown to Eva. Eva's card is shown to Mark. Mark's card is shown to Mark. Catherine's card is shown to Mark. Eva's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Mark knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mark can now know that Eva can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eva","Mark","Catherine"],"index":51766,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Walter can now know that Jose can know that Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Beverly","Anna","Walter"],"index":33830,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979709983,"difficulty":0.0020290017}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Moses knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Edward can now know that Garry can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Debra","Garry","Moses"],"index":10960,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99834764,"difficulty":0.00165236}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kiana does not know whether Kiana's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Joe can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deborah","Kiana","Joe"],"index":58905,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986572266,"difficulty":0.0013427734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deborah can now know that Frances can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Derek","Deborah","Jessie","Frances"],"index":18600,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997602105,"difficulty":0.0002397895}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Martin can now know that Robert can know that Lois's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Lois","Martin"],"index":43762,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9733100533,"difficulty":0.0266899467}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kathleen can now know that Pamela can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Robert","Kenneth","Kathleen"],"index":59697,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984075427,"difficulty":0.0015924573}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Keith knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Gary can now know that John can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","George","Gary","John"],"index":57586,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983968139,"difficulty":0.0016031861}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gretchen's card is shown to Gretchen. Bethany's card is shown to Gretchen. Janice's card is shown to Gretchen. Shawn's card is shown to Bethany. Shawn's card is shown to Janice. Janice's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shawn can now know whether Janice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gretchen","Bethany","Shawn","Janice"],"index":34693,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6734692454,"difficulty":0.3265307546}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pam knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Scotty can now know whether Pam is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Pam","Florence","Michael","Scotty"],"index":16977,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9511287212,"difficulty":0.0488712788}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly is thirsty. It is publicly announced that Kimberly knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Kimberly can now know that Brandon can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brandon","Kimberly"],"index":3123,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997839332,"difficulty":0.0002160668}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Morris's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Donald can now know that Morris can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Morris","Rodney","Donald"],"index":45951,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9932929277,"difficulty":0.0067070723}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice's forehead is muddy. It is publicly announced that Jerry knows whether or not everyone's forehead is muddy. It is publicly announced that Angela knows whether Alice's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Angela can now know whether Jerry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jerry","Angela","Alice"],"index":59393,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993565679,"difficulty":0.0006434321}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronni knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Ronni can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronni","Donald","Joseph"],"index":30594,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9867318273,"difficulty":0.0132681727}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Matthew knows whether Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Matthew can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Matthew","Roberta"],"index":15088,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nick's card is shown to Nick. Chad's card is shown to Chad. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tina can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tina","Nicholas","Nick","Chad"],"index":24446,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983434677,"difficulty":0.0016565323}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to George. Matthew's card is shown to George. George's card is shown to Jonathan. Jonathan's card is shown to Jonathan. George's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Matthew knows whether Matthew picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] [ ! (1&2&3) ] (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] [ ! (1&2&3) ] 0","hypothesis":"Jonathan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Jonathan","Matthew"],"index":28407,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Eric","Christopher"],"index":30451,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983219504,"difficulty":0.0016780496}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Carla. Carla's card is shown to Carla. Carla's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Karen picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Carla can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Carla","Karen"],"index":30783,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998287499,"difficulty":0.001712501}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Alice. Juan's card is shown to Mary. Gary's card is shown to Juan. Juan's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Juan does not know whether or not everyone picked a red card. It is publicly announced that Alice does not know whether Alice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Juan can now know whether Mary can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Mary","Juan","Gary"],"index":52122,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to James. Cassandra's card is shown to Cassandra. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","James","Cassandra","Vickie"],"index":56852,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7002394199,"difficulty":1.7002394199}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Charles. Charles's card is shown to Virginia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that Maryanne can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Maryanne","Virginia"],"index":471,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997687936,"difficulty":0.0002312064}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elaine does not know whether Elaine's forehead is muddy. It is publicly announced that Matthew's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] 0","hypothesis":"Trey can now know that Matthew can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chuck","Elaine","Trey","Matthew"],"index":10575,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8656076193,"difficulty":1.8656076193}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Lisa. Willie's card is shown to Willie. Lisa's card is shown to Doris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Doris can now know whether Willie can know that Willie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","Willie","Doris"],"index":11683,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7409775853,"difficulty":1.7409775853}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether Sharonda is thirsty. It is publicly announced that Michael is thirsty. It is publicly announced that Sharonda knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Michael can now know that Paul can know whether Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Michael","Sharonda"],"index":770,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986798167,"difficulty":0.0013201833}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luis does not know whether Henrietta is thirsty. It is publicly announced that Dennis does not know whether Beverly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Dennis can now know that Luis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Luis","Beverly","Dennis","Henrietta"],"index":42626,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997258544,"difficulty":0.002741456}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy. It is publicly announced that Paula knows whether Paula's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kevin can now know that Daniel can know that Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eugene","Daniel","Paula","Kevin"],"index":52492,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9961704612,"difficulty":0.0038295388}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Verna does not know whether Verna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Verna can now know that Jeannie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeannie","Verna","Wilfredo"],"index":56081,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9699534178,"difficulty":0.0300465822}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danny does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steve knows whether Rodrigo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Danny can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Darci","Steve","Rodrigo","Danny"],"index":28588,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997252822,"difficulty":0.0002747178}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Nadia. Frances's card is shown to Frances. Frances's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Nadia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Frances can now know whether Melissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nadia","Frances","Melissa"],"index":47752,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5314434171,"difficulty":1.5314434171}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Margaret. Margaret's card is shown to Maria. Stephanie's card is shown to Maria. Maria's card is shown to Stephanie. Margaret's card is shown to Betty. Stephanie's card is shown to Betty. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stephanie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margaret","Maria","Stephanie","Betty"],"index":48616,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Marjory's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jennifer can now know that Julian can know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julian","Marjory","Jennifer"],"index":60089,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970772266,"difficulty":0.0029227734}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Mary. Elena's card is shown to Mary. Steven's card is shown to Steven. Elena's card is shown to Steven. Trey's card is shown to Steven. Steven's card is shown to Elena. Trey's card is shown to Trey. It is publicly announced that someone picked a red card. It is publicly announced that Steven knows whether Trey picked a red card. It is publicly announced that Trey does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Elena can now know whether Elena picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Steven","Elena","Trey"],"index":2531,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8124821186,"difficulty":1.8124821186}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether Donald can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Concetta","Donald","Jennifer","Tara"],"index":24055,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997699857,"difficulty":0.0002300143}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen does not know whether Stephen's forehead is muddy. It is publicly announced that Margaret's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Margaret can now know that Joe can know that Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephen","Margaret","Joe"],"index":32768,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9758448005,"difficulty":0.0241551995}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Juli's forehead is muddy. It is publicly announced that Juli does not know whether Juli's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Johnny can now know whether David can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnny","David","Juli"],"index":17186,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9975419044,"difficulty":0.0024580956}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew knows whether or not nobody is thirsty. It is publicly announced that Andrew does not know whether Donald is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Chris can now know that Andrew is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrew","Donald","Chris"],"index":11476,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953081012,"difficulty":0.0046918988}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know that Jason can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jason","James"],"index":11781,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Julia can now know whether Lance can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lance","Charlotte","Stanley","Julia"],"index":56190,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995849729,"difficulty":0.0004150271}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy. It is publicly announced that Pamela's forehead is muddy. It is publicly announced that Eric knows whether Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Pamela can now know whether Eric can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pamela","Charles","Eric","James"],"index":32949,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Opal does not know whether Barry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Opal can now know whether Sol is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernard","Barry","Opal","Sol"],"index":51763,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965811372,"difficulty":0.0034188628}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joshua's card is shown to Lorraine. Joy's card is shown to Lorraine. Joshua's card is shown to Betty. Joy's card is shown to Betty. Joy's card is shown to Joshua. Lorraine's card is shown to Joy. It is publicly announced that someone picked a red card. It is publicly announced that Betty knows whether Joshua picked a red card. It is publicly announced that Betty knows whether someone picked a red card. It is publicly announced that Betty picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Betty can now know that Joy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lorraine","Betty","Joshua","Joy"],"index":53602,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997836947,"difficulty":0.0002163053}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. Ida's card is shown to Paul. Paul's card is shown to Ida. Paul's card is shown to Ruben. It is publicly announced that someone picked a red card. It is publicly announced that Ruben knows whether Paul picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Paul can now know that Ida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Ida","Ruben","Laurie"],"index":54880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966456294,"difficulty":0.0033543706}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tommy knows whether Benjamin's forehead is muddy. It is publicly announced that Tommy knows whether Tommy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Eddie can now know that Marcus can know that Eddie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Benjamin","Marcus","Eddie","Tommy"],"index":14864,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978731871,"difficulty":0.0021268129}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stephen can now know that Jimmy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jimmy","Leola","Winifred","Stephen"],"index":39769,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985846281,"difficulty":0.0014153719}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sadie knows whether Sadie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Albert can now know that Sadie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sadie","John","Michele","Albert"],"index":395,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997412562,"difficulty":0.0002587438}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys knows whether Michale's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Michale can now know that Benito can know that Gladys's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Benito","Michale","Gladys"],"index":43018,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974696636,"difficulty":0.0025303364}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Michael. Michael's card is shown to Jerry. Jerry's card is shown to Jerry. Jerry's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Jerry","Joseph"],"index":44612,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985386133,"difficulty":0.0014613867}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesusita's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesusita's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Mario can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jesusita","Mario","Mary"],"index":58627,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9522354603,"difficulty":0.0477645397}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Roseann. Roseann's card is shown to Gloria. Fred's card is shown to Gloria. Benjamin's card is shown to Fred. Roseann's card is shown to Benjamin. Gloria's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Roseann does not know whether Benjamin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Fred can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roseann","Gloria","Fred","Benjamin"],"index":46987,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997242093,"difficulty":0.0002757907}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad's forehead is not muddy. It is publicly announced that Chad's forehead is not muddy. It is publicly announced that Chad's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Chad can now know that Henrietta can know whether Henrietta's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lazaro","Chad","Henrietta","Earl"],"index":25020,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996198416,"difficulty":0.0003801584}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Cherryl can now know whether Cherryl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Linda","Larry","Cherryl"],"index":52214,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.985219121,"difficulty":1.985219121}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1&2&3) ] 0","hypothesis":"Janet can now know whether James can know whether Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Janet","Derrick"],"index":27742,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997078776,"difficulty":0.0002921224}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nellie knows whether or not nobody's forehead is muddy. It is publicly announced that Philip knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jennifer can now know that Philip's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Philip","Nellie"],"index":62028,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980043769,"difficulty":0.0019956231}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"John can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Steven"],"index":26993,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997414947,"difficulty":0.0002585053}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] 0","hypothesis":"Wesley can now know whether Jennifer can know that Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Wesley"],"index":36016,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996984005,"difficulty":0.0003015995}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether Anne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Anne can now know whether Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anne","Kenneth","Travis"],"index":20798,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997299314,"difficulty":0.0002700686}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Maegan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"George can now know that Timothy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Timothy","Maegan"],"index":37584,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997099042,"difficulty":0.0002900958}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Stacia. Stacia's card is shown to Stacia. Elizabeth's card is shown to Stacia. Stacia's card is shown to Floyd. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Stacia can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Stacia","Floyd","Elizabeth"],"index":5748,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995648265,"difficulty":0.0004351735}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Micheal does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Florence can now know that Michael can know that Micheal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Florence","Michael","Micheal","Natalie"],"index":37415,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9792748094,"difficulty":0.0207251906}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Kenneth can now know that Marie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marie","Kristine","Kenneth"],"index":41715,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969429374,"difficulty":0.0030570626}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roger's forehead is not muddy. It is publicly announced that Edwin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Edwin can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edwin","Roger","Esther"],"index":46109,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999778688,"difficulty":0.000221312}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Scott. John's card is shown to Scott. Scott's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Scott picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Scott can now know whether John can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Scott","John"],"index":24905,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997029901,"difficulty":0.0002970099}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Catherine can now know that Fred can know that Catherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Fred","Jorge","Catherine"],"index":44286,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9969462752,"difficulty":0.0030537248}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Rickie can now know whether Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Rickie","Shaunta"],"index":42161,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971843362,"difficulty":0.0028156638}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"William can now know that Richard can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","William"],"index":18055,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997437596,"difficulty":0.0002562404}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Melissa can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Howard","Melissa","Frankie","John"],"index":57504,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970139265,"difficulty":0.0029860735}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Travis's card is shown to Travis. Travis's card is shown to Frankie. Frankie's card is shown to Frankie. Donna's card is shown to Frankie. Travis's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Donna does not know whether Donna picked a red card. It is publicly announced that Travis picked a black card. It is publicly announced that Frankie knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Frankie can now know whether Travis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Travis","Frankie","Donna"],"index":60173,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.675029099,"difficulty":0.324970901}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Anne can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Charles","Anne","Virginia"],"index":10242,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985698462,"difficulty":0.0014301538}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Craig does not know whether or not everyone's forehead is muddy. It is publicly announced that Craig does not know whether Craig's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Ashley can now know whether Craig can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Craig","Ashley"],"index":32583,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996949434,"difficulty":0.0003050566}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie knows whether Robert is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Julie can now know that Julie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Julie"],"index":65865,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9619200826,"difficulty":0.0380799174}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matt knows whether Matt's forehead is muddy. It is publicly announced that Tommie knows whether Syble's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Dennis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Syble","Matt","Dennis","Tommie"],"index":42797,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982670546,"difficulty":0.0017329454}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Jesse. Gerald's card is shown to Joseph. Gerald's card is shown to Gerald. Darren's card is shown to Gerald. Gerald's card is shown to Darren. Darren's card is shown to Darren. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know whether Darren can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesse","Joseph","Gerald","Darren"],"index":21321,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997742772,"difficulty":0.0002257228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Tiffany's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Tiffany can now know that Virginia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Tiffany","John","Virginia"],"index":1301,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9913873076,"difficulty":0.0086126924}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew knows whether someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jason can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Matthew","Albert","Josephine","Jason"],"index":57737,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy. It is publicly announced that Charlotte knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know whether Leola can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","James","Leola","Charlotte"],"index":36024,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997188449,"difficulty":0.0002811551}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Eric. Eric's card is shown to Jason. Rose's card is shown to Jason. Jason's card is shown to Rose. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jason can now know that Rose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eric","Jason","Rose"],"index":23694,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7696608901,"difficulty":1.7696608901}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittany's card is shown to Brittany. Timothy's card is shown to Brittany. Eric's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Eric picked a red card. It is publicly announced that Diane does not know whether or not everyone picked a red card. It is publicly announced that Timothy picked a red card. It is publicly announced that Brittany does not know whether Diane picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Diane can now know that Diane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brittany","Diane","Eric","Timothy"],"index":28749,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5180197954,"difficulty":1.5180197954}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Steven can now know that Eugene can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steven","Eugene","Linda"],"index":18934,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983479977,"difficulty":0.0016520023}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wayne does not know whether or not everyone is thirsty. It is publicly announced that Wayne does not know whether Lydia is thirsty. It is publicly announced that Lydia does not know whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Sharron can now know that Lydia can know whether Lydia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","Lydia","Sharron","Christopher"],"index":16662,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990172386,"difficulty":0.0009827614}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. Paul's card is shown to Elsa. Elsa's card is shown to Elsa. Nancy's card is shown to Elsa. Mitchell's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paul can now know whether Elsa can know that Mitchell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Elsa","Mitchell","Nancy"],"index":34893,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9041082263,"difficulty":1.9041082263}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Thomas does not know whether Thomas picked a red card. It is publicly announced that Jackson picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Thomas can now know that Jackson can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jackson","Thomas","Dorothy","Jenifer"],"index":38354,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997832179,"difficulty":0.0002167821}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Steven knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Marion can now know whether Steven can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Marion"],"index":47637,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996963739,"difficulty":0.0003036261}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that David is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"David can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Mario"],"index":64774,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999785006,"difficulty":0.000214994}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Tiffany. Tiffany's card is shown to Lacy. Craig's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tiffany can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tiffany","Craig","Lacy","Laura"],"index":7198,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955726862,"difficulty":0.0044273138}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Dorothy can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dorothy","Robert"],"index":44537,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983813763,"difficulty":0.0016186237}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas knows whether or not nobody is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Sally","Antonio"],"index":43898,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991864562,"difficulty":0.0008135438}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy. It is publicly announced that Nicole knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Nicole can now know whether Richard can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Nicole","Rodney"],"index":37336,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997848868,"difficulty":0.0002151132}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessie knows whether Jessie's forehead is muddy. It is publicly announced that Hugh knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Samatha can now know whether Jessie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessie","Samatha","Hugh","Melissa"],"index":56890,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997345805,"difficulty":0.0002654195}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Janette can now know whether Benjamin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jason","Janette","Benjamin"],"index":12322,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997329116,"difficulty":0.0002670884}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Maria's card is shown to Jennifer. Kimberly's card is shown to Jennifer. Kimberly's card is shown to Kimberly. Saul's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Kimberly can know that Kimberly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Jennifer","Kimberly","Saul"],"index":47291,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917969704,"difficulty":0.0082030296}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether someone's forehead is muddy. It is publicly announced that Frank knows whether or not everyone's forehead is muddy. It is publicly announced that Antonia's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Peter can now know that Erin can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antonia","Peter","Frank","Erin"],"index":4139,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997992754,"difficulty":0.002007246}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margarita knows whether Laura's forehead is muddy. It is publicly announced that Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Laura can now know that Esther can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Esther","Margarita","Laura"],"index":6416,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996061921,"difficulty":0.0003938079}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samuel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Samuel can now know that Melissa can know whether Melissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Samuel","Melissa"],"index":56354,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999599278,"difficulty":0.000400722}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brittany knows whether someone is thirsty. It is publicly announced that Milton does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Brittany can now know whether Milton is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Brittany","Milton","Alexandria"],"index":40490,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6062580347,"difficulty":0.3937419653}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Kathy can now know that Kathy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathy","Cynthia","Charles","Nancy"],"index":24641,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9587807655,"difficulty":0.0412192345}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Leslie. Ted's card is shown to Leslie. Michelle's card is shown to Leslie. Michelle's card is shown to Ted. Ted's card is shown to Michelle. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Leslie picked a red card. It is publicly announced that Linda does not know whether or not everyone picked a red card. It is publicly announced that Leslie knows whether Michelle picked a red card. It is publicly announced that Ted does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Linda can now know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leslie","Linda","Ted","Michelle"],"index":34266,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8324131966,"difficulty":0.1675868034}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Stephanie can now know whether Reid can know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Benjamin","Jack","Reid","Stephanie"],"index":16323,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6627268195,"difficulty":0.3372731805}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Timothy. Timothy's card is shown to Patricia. George's card is shown to Patricia. Timothy's card is shown to George. Patricia's card is shown to George. George's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"George can now know whether Patricia can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Patricia","George"],"index":63352,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott does not know whether Cleo is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Scott can now know whether Cleo can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Scott","Cleo"],"index":2415,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9963405728,"difficulty":0.0036594272}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jackie's card is shown to Jackie. Janis's card is shown to Janis. It is publicly announced that someone picked a red card. It is publicly announced that Jackie does not know whether Pedro picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jackie can now know whether Pedro can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","Pedro","Janis"],"index":21997,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9958843589,"difficulty":0.0041156411}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jimmy can now know that Richard can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Demetrius","Jimmy","Richard"],"index":25921,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978166819,"difficulty":0.0021833181}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alvin's card is shown to Mae. Mae's card is shown to Mae. Mae's card is shown to Mona. It is publicly announced that someone picked a red card. It is publicly announced that Alvin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mae can now know whether Alvin can know whether Mona picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alvin","Mae","Mona"],"index":38835,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99766469,"difficulty":0.00233531}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Daniel. John's card is shown to Thomas. Daniel's card is shown to Anne. Anne's card is shown to Anne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that John can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Thomas","John","Anne"],"index":55372,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sandra can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lon","Tamatha","William","Sandra"],"index":53495,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986409545,"difficulty":0.0013590455}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raleigh knows whether Margaret's forehead is muddy. It is publicly announced that Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Margaret can now know that Danielle can know that Raleigh's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Danielle","Raleigh","Margaret"],"index":1963,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8792033195,"difficulty":0.1207966805}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric knows whether someone is thirsty. It is publicly announced that Janice does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Eric can now know that Melissa can know whether Eric is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Eric","Melissa","Janice"],"index":38379,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6969147921,"difficulty":1.6969147921}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kevin can now know that Frank can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Florence","Kevin","Frank","Michelle"],"index":67055,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997437596,"difficulty":0.0002562404}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Kim's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Kim can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kim","Todd"],"index":35596,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. Gregory's card is shown to Paul. Michael's card is shown to Paul. Gregory's card is shown to Gregory. Gregory's card is shown to Michael. Paul's card is shown to Cheryl. It is publicly announced that someone picked a red card. It is publicly announced that Paul picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Paul can now know that Michael can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Gregory","Michael","Cheryl"],"index":43388,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963012934,"difficulty":0.0036987066}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Carolyn can now know that Clark can know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martha","Carolyn","Clark"],"index":9418,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6150510907,"difficulty":0.3849489093}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pauline knows whether Jan's forehead is muddy. It is publicly announced that Pauline's forehead is not muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know that Pauline can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Jan","Janet","Pauline"],"index":32815,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Margie can now know that Burt can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Burt","Margie"],"index":63471,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984163046,"difficulty":0.0015836954}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether or not everyone is thirsty. It is publicly announced that Jennifer does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Richard can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Richard","Jennifer"],"index":44370,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6778706312,"difficulty":0.3221293688}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Diane. Diane's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Diane can now know that Francis can know whether Heather picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Francis","Diane","Heather"],"index":15209,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8325568438,"difficulty":1.8325568438}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antonio knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Teresa can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heidi","Teresa","William","Antonio"],"index":16605,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997383952,"difficulty":0.0002616048}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that Katherine knows whether Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Pamela can now know that James can know that Pamela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Katherine","James"],"index":47832,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947838187,"difficulty":0.0052161813}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Daphine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Daphine can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daphine","Karen","John"],"index":65396,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984124899,"difficulty":0.0015875101}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alan knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Maria can now know whether Alan can know that Alan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Maria","Alan"],"index":60993,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6281287074,"difficulty":1.6281287074}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether or not everyone's forehead is muddy. It is publicly announced that Helen knows whether someone's forehead is muddy. It is publicly announced that Helen knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Helen can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Helen","Regina"],"index":42994,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982280135,"difficulty":0.0017719865}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Bertha's forehead is muddy. It is publicly announced that Paul knows whether Bertha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Bertha can now know whether Justin can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Bertha","Justin","Adam"],"index":30174,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997691512,"difficulty":0.0002308488}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emma's card is shown to Albert. Erwin's card is shown to Albert. Albert's card is shown to Mark. Erwin's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Albert does not know whether Albert picked a red card. It is publicly announced that Albert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Albert can now know that Albert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Albert","Emma","Erwin","Mark"],"index":37881,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8283738494,"difficulty":1.8283738494}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephanie's card is shown to Brenda. Brenda's card is shown to Janice. Stephanie's card is shown to Stephanie. Janice's card is shown to Keith. Stephanie's card is shown to Keith. Keith's card is shown to Keith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janice can now know whether Brenda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brenda","Janice","Stephanie","Keith"],"index":64056,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6476959586,"difficulty":1.6476959586}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Lynne knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Richard can now know that Lynne can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lynne","Fred","Enid","Richard"],"index":15261,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Eric. Ginger's card is shown to Eric. Eric's card is shown to Sheila. Sheila's card is shown to Sheila. Ginger's card is shown to Ginger. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ginger can now know whether Eric can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Sheila","Ginger"],"index":14773,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999582231,"difficulty":0.000417769}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"James can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Allan","James","John","Salvador"],"index":58764,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959661961,"difficulty":0.0040338039}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos knows whether Carlos's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Shirley can now know that Martha can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Shirley","Carlos","Craig"],"index":81,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985212684,"difficulty":0.0014787316}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cora knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Lida can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carolyn","Lida","Cora"],"index":4612,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984945059,"difficulty":0.0015054941}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Mitchell can now know that Mitchell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Mitchell","Cindy","Lorraine"],"index":65872,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9742490649,"difficulty":0.0257509351}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Michael's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy. It is publicly announced that Gary knows whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gary","Michael"],"index":19236,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986133575,"difficulty":0.0013866425}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary's forehead is not muddy. It is publicly announced that Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 1 ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Lawrence can now know whether Patricia can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Gary","Lawrence"],"index":41605,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9946422577,"difficulty":0.0053577423}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Angela can now know whether Michael can know whether Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Angela","Carolyn","Brian"],"index":49487,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994024038,"difficulty":0.0005975962}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Harry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Robert can now know that Jose can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jose","Harry","Robert"],"index":9125,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997499585,"difficulty":0.0002500415}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Steven can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Steven","Wesley","Lupita"],"index":45243,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999610126,"difficulty":0.000389874}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Joseph can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Joseph"],"index":64879,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9938981533,"difficulty":0.0061018467}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Terry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terry","Michael","Jeremy"],"index":28315,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9740961194,"difficulty":0.0259038806}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Dale can now know whether Willie can know that Dale is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Susan","Dale","Willie"],"index":22841,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.984596312,"difficulty":0.015403688}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Carolyn can now know that Samuel can know whether Carolyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carolyn","Samuel"],"index":22550,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996857643,"difficulty":0.0003142357}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Dorothy. Jennifer's card is shown to Harry. Jennifer's card is shown to Jennifer. Peter's card is shown to Peter. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harry can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dorothy","Harry","Jennifer","Peter"],"index":40022,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997715354,"difficulty":0.0002284646}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mattie does not know whether Darin is thirsty. It is publicly announced that Joshua does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Darin can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mattie","Fran","Joshua","Darin"],"index":50948,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether someone's forehead is muddy. It is publicly announced that Claire knows whether or not nobody's forehead is muddy. It is publicly announced that Claire knows whether Karen's forehead is muddy. It is publicly announced that Janine knows whether Janine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Janine can now know whether Claire can know that Janine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Janine","Claire"],"index":21800,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999584496,"difficulty":0.000415504}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Stanley. Ronald's card is shown to Stanley. Beverly's card is shown to Beverly. Dorothy's card is shown to Beverly. Ronald's card is shown to Dorothy. Dorothy's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Ronald does not know whether Beverly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Beverly can now know whether Stanley can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stanley","Beverly","Dorothy","Ronald"],"index":26883,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999778688,"difficulty":0.000221312}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lewis knows whether Lewis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"William can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lila","William","Lewis"],"index":65912,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982694387,"difficulty":0.0017305613}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Sheila. Sharon's card is shown to Sharon. Debra's card is shown to Sharon. Sharon's card is shown to Debra. Debra's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Sheila does not know whether Sharon picked a red card. It is publicly announced that Debra knows whether Sharon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Sheila can now know whether Debra can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sheila","Sharon","Debra"],"index":10992,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Judith. Robert's card is shown to Judith. Judith's card is shown to Christopher. Christopher's card is shown to Christopher. Judith's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether Judith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Judith","Christopher","Robert"],"index":31552,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5399266481,"difficulty":1.5399266481}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Karen can now know that Jeff can know whether Sara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sara","Jeff","Michael","Karen"],"index":30678,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9814916849,"difficulty":0.0185083151}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie does not know whether Marjorie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lee can now know whether David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lee","Marjorie","Teresa","David"],"index":41728,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.917617321,"difficulty":0.082382679}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah does not know whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Alfonso can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deborah","Alfonso","Tanya"],"index":46796,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997474551,"difficulty":0.0002525449}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emmanuel's card is shown to Clara. William's card is shown to Clara. Clara's card is shown to Kimberly. William's card is shown to Emmanuel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberly can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clara","Kimberly","Emmanuel","William"],"index":57805,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985387325,"difficulty":0.0014612675}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clifford knows whether Clifford's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Clifford can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ann","Clifford"],"index":22604,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985513091,"difficulty":0.0014486909}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Albert can now know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Scott","Albert","Paul","James"],"index":19966,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974061847,"difficulty":0.0025938153}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Laverne can now know that David can know whether Laverne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Laverne","Jonathan"],"index":26657,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992955923,"difficulty":0.0007044077}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clifford does not know whether or not everyone is thirsty. It is publicly announced that Kathy is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Marcus can now know that James can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clifford","Marcus","James","Kathy"],"index":31838,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984380603,"difficulty":0.0015619397}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Christopher can now know that Susan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Susan","Robert"],"index":50892,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959586263,"difficulty":0.0040413737}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Robert. Juanita's card is shown to Robert. Robert's card is shown to Juanita. Juanita's card is shown to Juanita. Dennis's card is shown to Juanita. Nancy's card is shown to Dennis. Dennis's card is shown to Dennis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nancy can now know that Nancy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Robert","Juanita","Dennis"],"index":1393,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959642887,"difficulty":0.0040357113}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Henry. Christopher's card is shown to Randy. Randy's card is shown to Randy. Harold's card is shown to Randy. Harold's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Harold picked a red card. It is publicly announced that Christopher knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Randy can now know whether Henry can know whether Henry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Henry","Randy","Harold"],"index":13706,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9925185442,"difficulty":0.0074814558}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerrell does not know whether Carol is thirsty. It is publicly announced that Jerrell does not know whether Wendi is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Jerrell can now know whether Jerrell is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Carol","Jerrell","Wendi"],"index":21058,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984164238,"difficulty":0.0015835762}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Kevin can now know whether Madeline can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Madeline","Mike"],"index":51591,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9964499474,"difficulty":0.0035500526}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Larry can now know whether Laura can know that Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Laura","Catherine"],"index":36447,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998065412,"difficulty":0.001934588}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Rebecca can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Doris","Rebecca"],"index":53149,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984402061,"difficulty":0.0015597939}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Edith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Edith can now know that Edith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Scott","Edith","Michael"],"index":47158,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973381162,"difficulty":0.0026618838}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Harvey is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Audrey can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Audrey","Joseph","Michelle","Harvey"],"index":15004,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986900687,"difficulty":0.0013099313}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandi's card is shown to Brandi. Beverly's card is shown to Megan. Phyllis's card is shown to Megan. Brandi's card is shown to Beverly. Brandi's card is shown to Phyllis. It is publicly announced that someone picked a red card. It is publicly announced that Phyllis does not know whether Phyllis picked a red card. It is publicly announced that Beverly knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Phyllis can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brandi","Megan","Beverly","Phyllis"],"index":2961,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997238517,"difficulty":0.0002761483}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Erika can now know whether Martha is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Judy","Erika","Martha"],"index":35169,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942563176,"difficulty":0.0057436824}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Joshua knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Joshua can now know whether Teressa can know whether Teressa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joshua","Teressa"],"index":13195,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996666908,"difficulty":0.0003333092}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bud knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Bobbi can now know that Connie can know that Connie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bud","Bobbi","Connie","Jacquelyn"],"index":55878,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7367302179,"difficulty":0.2632697821}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neal does not know whether or not everyone's forehead is muddy. It is publicly announced that Chong knows whether Neal's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] Agentc knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mercedes can now know whether Michael can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Neal","Chong","Mercedes","Michael"],"index":63054,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.746702075,"difficulty":0.253297925}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that Larry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Larry","Houston","Gabriel"],"index":8290,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9922079444,"difficulty":0.0077920556}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Aaron. Debra's card is shown to Debra. Beatrice's card is shown to Debra. Debra's card is shown to Beatrice. Beatrice's card is shown to Beatrice. It is publicly announced that someone picked a red card. It is publicly announced that Beatrice does not know whether or not everyone picked a red card. It is publicly announced that Aaron does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Beatrice can now know that Aaron can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Aaron","Debra","Beatrice"],"index":16627,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9554393888,"difficulty":0.0445606112}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether someone's forehead is muddy. It is publicly announced that Donald's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] 0","hypothesis":"James can now know that Donald can know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Mark","Donald"],"index":66374,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9922839999,"difficulty":0.0077160001}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Christopher can now know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Robert","Christopher"],"index":39349,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983881712,"difficulty":0.0016118288}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bob's card is shown to Bob. Edith's card is shown to Bob. Edith's card is shown to Glen. Bob's card is shown to Andrea. Andrea's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Andrea does not know whether Edith picked a red card. It is publicly announced that Glen does not know whether Andrea picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Glen can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bob","Glen","Andrea","Edith"],"index":46225,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985622764,"difficulty":0.0014377236}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vickie's card is shown to Vickie. Inell's card is shown to Vickie. John's card is shown to Vickie. Vickie's card is shown to Inell. Inell's card is shown to Inell. Vickie's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Inell can now know whether John can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vickie","Inell","John"],"index":37056,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997749925,"difficulty":0.0002250075}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether or not everyone is thirsty. It is publicly announced that Ronald does not know whether Timothy is thirsty. It is publicly announced that Earl does not know whether Timothy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Timothy can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earl","Timothy","Bob","Ronald"],"index":51797,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.79125458,"difficulty":0.20874542}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Brian. Ricardo's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know that Michael can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Michael","Ricardo"],"index":25528,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9483143687,"difficulty":0.0516856313}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna's forehead is muddy. It is publicly announced that Anna knows whether Tracy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"James can now know whether Anna can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anna","Tracy","James"],"index":10188,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983456135,"difficulty":0.0016543865}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ladawn does not know whether Ladawn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Casey can now know that Louis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ladawn","Casey","Louis"],"index":18438,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997333169,"difficulty":0.002666831}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] 0","hypothesis":"Gretchen can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Denise","Gretchen","Andrew","Vada"],"index":59852,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997305274,"difficulty":0.0002694726}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelby's card is shown to Jeffrey. Brandon's card is shown to Jeffrey. Jeffrey's card is shown to Brandon. Jeffrey's card is shown to Ryan. Shelby's card is shown to Ryan. Brandon's card is shown to Ryan. Ryan's card is shown to Ryan. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Shelby can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffrey","Shelby","Brandon","Ryan"],"index":39170,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999769032,"difficulty":0.000230968}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Earl does not know whether Arlie is thirsty. It is publicly announced that Arlie does not know whether Earl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Andrea can now know whether Ty can know that Arlie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arlie","Andrea","Earl","Ty"],"index":53870,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9909957051,"difficulty":0.0090042949}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Glen can now know whether Jocelyn can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Frank","Glen","Jocelyn"],"index":33317,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997659326,"difficulty":0.0002340674}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie knows whether Virgil's forehead is muddy. It is publicly announced that Jane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Shirley can now know whether Leslie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shirley","Jane","Leslie","Virgil"],"index":60321,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997240901,"difficulty":0.0002759099}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Susan is thirsty. It is publicly announced that Amy does not know whether Charles is thirsty. It is publicly announced that Amy does not know whether Susan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Amy can now know that Charles can know that Susan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Charles","Amy"],"index":46792,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.988327086,"difficulty":0.011672914}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shane's card is shown to Margaret. Shane's card is shown to Norman. Jesus's card is shown to Shane. Norman's card is shown to Shane. Shane's card is shown to Shane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know whether Norman can know that Norman picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jesus","Margaret","Norman","Shane"],"index":21095,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7951841354,"difficulty":1.7951841354}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether Ashley's forehead is muddy. It is publicly announced that Nancy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Nancy can now know that Michael can know that Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ashley","Michael","Nancy"],"index":16313,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7942575812,"difficulty":0.2057424188}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Jimmy can now know whether Debra can know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Timothy","Debra","Jimmy"],"index":17259,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995304346,"difficulty":0.0004695654}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Bruce can now know that Virginia can know that Bruce's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bruce","Virginia","Susan"],"index":2546,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9385703802,"difficulty":0.0614296198}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel's forehead is not muddy. It is publicly announced that Jeffrey's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Rachel can now know that Jeffrey can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Jeffrey","Rachel","Jack"],"index":2390,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982489347,"difficulty":0.0017510653}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy. It is publicly announced that Consuelo does not know whether Consuelo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Carmela can now know that Consuelo can know whether Carmela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","Consuelo","Carmela"],"index":43433,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987210631,"difficulty":0.0012789369}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce knows whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Henry can now know that Joyce can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Zachary","Henry","Everett","Joyce"],"index":42598,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997474551,"difficulty":0.0002525449}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"April can now know that Summer can know whether Summer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lorraine","April","Garrett","Summer"],"index":62308,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996665716,"difficulty":0.0003334284}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katherine does not know whether Wilson is thirsty. It is publicly announced that Judy is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] Agenta knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Katherine can now know that John can know that Katherine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katherine","Judy","Wilson","John"],"index":34775,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9910797477,"difficulty":0.0089202523}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michel knows whether someone's forehead is muddy. It is publicly announced that Michael's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] 0","hypothesis":"Michel can now know that Michael can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michel","Michael"],"index":21106,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997842908,"difficulty":0.0002157092}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Nancy. Jennifer's card is shown to Jennifer. Shelton's card is shown to Jennifer. Jennifer's card is shown to Shelton. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shelton can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Jennifer","Shelton"],"index":57330,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kim knows whether Marlyn's forehead is muddy. It is publicly announced that Pedro does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Marlyn can now know that Pedro's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marlyn","Kim","Pedro","Paul"],"index":64956,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.749199748,"difficulty":0.250800252}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Erick can now know that Roberto can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Erick","Roberto","Barbara","William"],"index":38816,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984744191,"difficulty":0.0015255809}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Frank can now know whether Lakenya can know that Lakenya's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Margaret","Bonnie","Lakenya"],"index":52875,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9710202217,"difficulty":1.9710202217}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Enedina can now know whether Patricia can know that Gwendolyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gwendolyn","Ruth","Enedina","Patricia"],"index":61021,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9901208878,"difficulty":0.0098791122}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucille's card is shown to Sonia. Sonia's card is shown to Gary. Lucille's card is shown to Courtney. It is publicly announced that someone picked a red card. It is publicly announced that Sonia picked a red card. It is publicly announced that Sonia does not know whether Gary picked a red card. It is publicly announced that Gary does not know whether Courtney picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Sonia can now know that Lucille can know whether Lucille picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucille","Sonia","Gary","Courtney"],"index":34722,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9859316349,"difficulty":0.0140683651}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. James's card is shown to William. William's card is shown to William. James's card is shown to Stephanie. William's card is shown to Stephanie. Stephanie's card is shown to Stephanie. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Stephanie can now know whether Stephanie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","William","Stephanie"],"index":15725,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9756778479,"difficulty":0.0243221521}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether Brian's forehead is muddy. It is publicly announced that Ana knows whether someone's forehead is muddy. It is publicly announced that Ana knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Brian can now know whether David can know whether Ana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Ana","David"],"index":56043,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993950129,"difficulty":0.0006049871}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Susan can now know that Susan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Susan","Charles"],"index":53022,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9803905487,"difficulty":0.0196094513}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecelia's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Heather can now know that Cecelia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Heather","Cecelia"],"index":4589,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983952641,"difficulty":0.0016047359}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chase knows whether or not nobody's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy. It is publicly announced that Chase does not know whether Chase's forehead is muddy. It is publicly announced that Enrique knows whether Enrique's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Chase can now know that Enrique's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Enrique","Chase","Barbara"],"index":24326,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9809025526,"difficulty":1.9809025526}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Edith can now know that Kelli can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edith","Brian","Kelli","Rita"],"index":14459,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9945096374,"difficulty":0.0054903626}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to John. John's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Amanda can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Amanda"],"index":61956,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976154566,"difficulty":0.0023845434}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathan's forehead is muddy. It is publicly announced that Nathan's forehead is muddy. It is publicly announced that Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Bert can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carolyn","Michael","Nathan","Bert"],"index":54311,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995206594,"difficulty":0.0004793406}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know whether Nell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathleen","Nell","Karen"],"index":35317,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997258782,"difficulty":0.0002741218}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Donna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Donna can now know whether Jessica can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cindy","Robert","Donna","Jessica"],"index":17305,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Hillary is thirsty. It is publicly announced that Michele is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Michele can now know that Wesley can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wesley","Michele","John","Hillary"],"index":54565,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980849028,"difficulty":0.0019150972}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly does not know whether or not everyone's forehead is muddy. It is publicly announced that Rosa knows whether or not nobody's forehead is muddy. It is publicly announced that Beverly does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Edwin can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edwin","Beverly","Rosa"],"index":11637,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9865575433,"difficulty":0.0134424567}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether Walter's forehead is muddy. It is publicly announced that Walter knows whether Walter's forehead is muddy. It is publicly announced that Jessica knows whether Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jessica can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jessica","Walter"],"index":20409,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997666478,"difficulty":0.0002333522}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgia's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Georgia can now know whether Earl can know whether Mildred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earl","Judy","Georgia","Mildred"],"index":6025,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996912479,"difficulty":0.0003087521}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher does not know whether Patty is thirsty. It is publicly announced that Christopher does not know whether Jacqueline is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Natalie can now know whether Natalie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Natalie","Patty","Christopher","Jacqueline"],"index":25380,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9953505993,"difficulty":0.0046494007}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deanna knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kevin can now know that Joyce can know that Deanna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Joyce","Deanna"],"index":51561,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8944473863,"difficulty":0.1055526137}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Randy does not know whether Shameka is thirsty. It is publicly announced that Shameka does not know whether Randy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Dennis can now know that Shameka can know whether Shameka is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dennis","Randy","Shameka"],"index":45464,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986361861,"difficulty":0.0013638139}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. Betty's card is shown to Gregory. Gregory's card is shown to Irene. Betty's card is shown to Irene. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Gregory knows whether or not nobody picked a red card. It is publicly announced that Betty knows whether Irene picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Gregory can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gregory","Betty","Irene"],"index":53639,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9917308688,"difficulty":0.0082691312}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor knows whether Jill's forehead is muddy. It is publicly announced that Eleanor knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Samuel can now know that Eleanor can know whether Jill's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jill","Eleanor","Samuel"],"index":62852,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999748528,"difficulty":0.000251472}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth is thirsty. It is publicly announced that Elizabeth knows whether or not nobody is thirsty. It is publicly announced that Elizabeth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Elizabeth can now know whether Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Terri","Martha","Patricia"],"index":63168,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999032259,"difficulty":0.000967741}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Paula. Paula's card is shown to Maria. Gussie's card is shown to Maria. Gussie's card is shown to Neil. Paula's card is shown to Gussie. Maria's card is shown to Gussie. Neil's card is shown to Gussie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gussie can now know that Paula can know that Paula picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paula","Maria","Neil","Gussie"],"index":39991,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9927499294,"difficulty":0.0072500706}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Mercedes knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jana can now know that Mercedes can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mercedes","Jana"],"index":46945,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959100485,"difficulty":0.0040899515}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Georgia knows whether someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Heidi can now know whether Vickie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heidi","Georgia","Vickie","Robert"],"index":47519,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9510550499,"difficulty":1.9510550499}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether Charlene's forehead is muddy. It is publicly announced that Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Charlene can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlene","Larry","Raymond","Rita"],"index":57432,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984104633,"difficulty":0.0015895367}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ed knows whether or not everyone's forehead is muddy. It is publicly announced that Paige's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Ed can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ann","Tamra","Paige","Ed"],"index":51389,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997140765,"difficulty":0.0002859235}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Rebecca. Diane's card is shown to Diane. Diane's card is shown to Lonna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rebecca can now know that Lonna can know that Lonna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebecca","Diane","Lonna"],"index":34830,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976900816,"difficulty":0.0023099184}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"George can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Robert","George"],"index":24716,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982415438,"difficulty":0.0017584562}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Amanda knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Amanda can now know that Gregorio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregorio","Amanda","Robert","Virginia"],"index":34280,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996587038,"difficulty":0.003412962}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clifton does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Bonnie can now know that Michelle can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bonnie","Michelle","Matthew","Clifton"],"index":50775,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9806563258,"difficulty":0.0193436742}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy. It is publicly announced that Joan knows whether or not nobody's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Joan can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christina","William","Joan"],"index":1129,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9648580551,"difficulty":0.0351419449}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that John knows whether Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Geraldine can now know whether Nancy can know whether Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Rodney","Geraldine","Nancy"],"index":1095,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996545315,"difficulty":0.0003454685}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Audrey knows whether Audrey is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Joseph can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joseph","Audrey"],"index":38445,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9926630259,"difficulty":0.0073369741}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel is thirsty. It is publicly announced that Jessica knows whether Jessica is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Jessica can now know that Daniel can know that Jessica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jessica","Daniel"],"index":2510,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.819852829,"difficulty":0.180147171}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Essie. Gloria's card is shown to Essie. Essie's card is shown to Eugene. Essie's card is shown to Gloria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eugene can now know whether Essie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronald","Essie","Eugene","Gloria"],"index":34529,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7360391617,"difficulty":0.2639608383}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Ricky's card is shown to Robert. Robert's card is shown to Ricky. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ricky can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Robert","Ricky"],"index":56553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983363748,"difficulty":0.0016636252}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Scott can now know that Gregory can know that Henry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Scott","Gregory","Lester"],"index":58197,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959432483,"difficulty":0.0040567517}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agenta knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Veronica can now know that Bruce can know that Veronica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Veronica","Michael","Frank","Bruce"],"index":26677,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9791337252,"difficulty":0.0208662748}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Louise can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Teresa","Louise"],"index":55466,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982656837,"difficulty":0.0017343163}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Katherine can now know that Vivian can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Vivian","Martha","Katherine"],"index":3407,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997670054,"difficulty":0.0002329946}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Andrea can now know whether Vernie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeremy","Andrea","Vernie","Sherry"],"index":38186,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999751389,"difficulty":0.000248611}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether someone's forehead is muddy. It is publicly announced that Hal does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Eric can now know whether Hal can know that Hal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hal","Eric"],"index":38701,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9346632361,"difficulty":0.0653367639}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Daniel can now know whether Dorothy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Ryan","Charles","Dorothy"],"index":45961,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995663762,"difficulty":0.0004336238}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Virginia can now know that Virginia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Paula","Virginia","Curtis"],"index":25619,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9785259962,"difficulty":0.0214740038}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Casey's card is shown to Casey. Kristen's card is shown to Kristen. Kristen's card is shown to Marian. It is publicly announced that someone picked a red card. It is publicly announced that Casey does not know whether Lien picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lien can now know that Kristen can know that Marian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Casey","Kristen","Lien","Marian"],"index":34091,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960173965,"difficulty":0.0039826035}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda's forehead is muddy. It is publicly announced that Brenda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Brenda can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brenda","Michael"],"index":8710,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997817874,"difficulty":0.0002182126}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marc does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Francis can now know that Jack can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Francis","Jack","Marc"],"index":12921,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942088127,"difficulty":0.0057911873}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Saundra's card is shown to Rosie. Rosie's card is shown to Saundra. It is publicly announced that someone picked a red card. It is publicly announced that Saundra does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Saundra can now know whether Rosie can know that Rosie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rosie","Saundra"],"index":18009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9103563428,"difficulty":0.0896436572}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tara does not know whether or not everyone is thirsty. It is publicly announced that Homer knows whether Homer is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Tara can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tara","Homer"],"index":5006,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7438854575,"difficulty":0.2561145425}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jennifer can now know that Charles can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jennifer","Charles"],"index":62539,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9235162139,"difficulty":0.0764837861}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Nettie. Jeanna's card is shown to Jeanna. Carolyn's card is shown to Jeanna. Carolyn's card is shown to Carolyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nettie can now know that Jeanna can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nettie","Jeanna","Carolyn"],"index":60674,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997209907,"difficulty":0.0002790093}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lincoln does not know whether Robert is thirsty. It is publicly announced that Pamela knows whether or not everyone is thirsty. It is publicly announced that Pamela knows whether Pamela is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"David can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pamela","David","Lincoln","Robert"],"index":18991,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982349873,"difficulty":0.0017650127}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Billy can now know whether James can know that Lois's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Billy","Lois","Raymond","James"],"index":51827,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983036518,"difficulty":0.0016963482}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Kimberly can now know that David can know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Kimberly","Dennis"],"index":32299,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979377389,"difficulty":0.0020622611}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Bruce knows whether Bruce's forehead is muddy. It is publicly announced that Janet knows whether Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Bruce can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janet","Bruce","Nathan"],"index":63202,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.698344171,"difficulty":0.301655829}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Micheal's card is shown to Mary. Mary's card is shown to Micheal. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Micheal can now know that Mary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Micheal"],"index":64838,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983124733,"difficulty":0.0016875267}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Patrick can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patrick","Kenneth"],"index":62867,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996943474,"difficulty":0.0003056526}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Tyler can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terrence","Rochell","Brandon","Tyler"],"index":22161,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981682301,"difficulty":0.0018317699}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hannah does not know whether or not everyone is thirsty. It is publicly announced that Jonathan knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Desirae can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonathan","Hannah","Desirae"],"index":23303,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997757077,"difficulty":0.0002242923}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter does not know whether David is thirsty. It is publicly announced that Elizabeth does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Elizabeth can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Peter","Elizabeth","David"],"index":59616,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983724952,"difficulty":0.0016275048}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether Michelle can know whether Andrew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Michelle","Andrew"],"index":41950,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992154837,"difficulty":0.0007845163}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy does not know whether Tammy's forehead is muddy. It is publicly announced that Earl knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Tammy can now know whether Earl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tammy","Earl"],"index":39780,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992115498,"difficulty":0.0007884502}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelique knows whether someone's forehead is muddy. It is publicly announced that June's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Angelique can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Angelique","Dorothy","Michael","June"],"index":36883,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997715354,"difficulty":0.0002284646}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Nancy can now know that Josephine can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josephine","Tisha","Pamela","Nancy"],"index":10273,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Cynthia can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martha","Clotilde","Cynthia","Wilma"],"index":2965,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999727428,"difficulty":0.000272572}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Taylor's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Taylor can now know that Louise can know that Louise's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Taylor","Louise"],"index":57369,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9903805256,"difficulty":1.9903805256}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Freddie knows whether Freddie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Julie can now know whether Julie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julie","Freddie","Matt","Carroll"],"index":61323,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999563992,"difficulty":0.000436008}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1&2&3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1&2&3) ] 0","hypothesis":"Dennis can now know that Margret can know whether Dennis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margret","Dennis","Patricia"],"index":57554,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997342229,"difficulty":0.0002657771}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether or not everyone's forehead is muddy. It is publicly announced that Jonathan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Julie can now know that Jonathan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Matthew","Joyce","Jonathan"],"index":13157,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983496666,"difficulty":0.0016503334}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie knows whether Marvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Adam can now know that Marvin can know that Adam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marvin","Stephanie","Adam"],"index":38032,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984474778,"difficulty":0.0015525222}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Georgia can now know that Georgia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Georgia","Sandra"],"index":40164,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997887671,"difficulty":0.002112329}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brooke does not know whether Rebecca is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Brooke can now know that Brooke is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebecca","Brooke","James","Virginia"],"index":58712,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9174262285,"difficulty":0.0825737715}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Addie can now know whether Etta can know whether Addie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rich","John","Etta","Addie"],"index":41830,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9970229268,"difficulty":0.0029770732}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jorge knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Teresa can now know that Jorge can know that Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Doris","Teresa","Jorge"],"index":36918,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7389541864,"difficulty":0.2610458136}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sue does not know whether Sue's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Benita can now know that Sue can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Benita","Leonardo","Phillip","Sue"],"index":34122,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999702394,"difficulty":0.000297606}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackie knows whether Jackie's forehead is muddy. It is publicly announced that Peter knows whether Jerome's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Peter can now know that Jackie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerome","Jackie","Bobby","Peter"],"index":2956,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997035861,"difficulty":0.002964139}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Nilda is thirsty. It is publicly announced that Charise does not know whether Ronald is thirsty. It is publicly announced that Nilda does not know whether Charise is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Ronald can now know that Ronald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Charise","Nilda"],"index":24193,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8811534047,"difficulty":0.1188465953}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Ruth. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Clarence does not know whether or not everyone picked a red card. It is publicly announced that Ruth knows whether Clarence picked a red card. It is publicly announced that Clarence does not know whether Ruth picked a red card. It is publicly announced that Clarence knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Clarence can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ruth","Clarence"],"index":56781,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether Carolyn's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Edwin does not know whether Edwin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"David can now know whether Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carolyn","Edwin","David","Melissa"],"index":7016,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995743632,"difficulty":0.0004256368}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Joseph. Karen's card is shown to Joseph. Xavier's card is shown to Xavier. Karen's card is shown to Xavier. Joseph's card is shown to Eric. Xavier's card is shown to Karen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Karen can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Xavier","Eric","Karen"],"index":52152,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9749364853,"difficulty":0.0250635147}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Christopher can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Aaron","Christopher","Carolyn"],"index":29012,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985120893,"difficulty":0.0014879107}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether or not nobody's forehead is muddy. It is publicly announced that Abigail's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Peter can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Abigail","Peter"],"index":43340,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986269474,"difficulty":0.0013730526}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Alice. Nicholas's card is shown to Alice. Michael's card is shown to Nicholas. Alice's card is shown to Michael. Nicholas's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether Robbie picked a red card. It is publicly announced that Nicholas knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robbie can now know that Nicholas can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Nicholas","Robbie","Michael"],"index":27084,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5585314035,"difficulty":0.4414685965}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond does not know whether Patricia is thirsty. It is publicly announced that Raymond does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Miguel can now know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Miguel","Patricia"],"index":54977,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5418677926,"difficulty":0.4581322074}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karla's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Dominic can now know that Armando can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karla","Dominic","Armando","Carole"],"index":16974,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985092282,"difficulty":0.0014907718}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alfredo does not know whether John is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know that David can know whether Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","John","Maria","Alfredo"],"index":46830,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9917055368,"difficulty":0.0082944632}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicky's card is shown to Darlena. Kenneth's card is shown to Kenneth. Nicky's card is shown to Nicky. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Nicky picked a red card. It is publicly announced that Darlena does not know whether Darlena picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Darlena","Kenneth","Nicky"],"index":1220,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9244576097,"difficulty":0.0755423903}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether Alfred is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Richard can now know whether Alfred can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfred","Barbara","Isabel","Richard"],"index":64159,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997490406,"difficulty":0.002509594}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela's forehead is not muddy. It is publicly announced that Sherry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] Agenta knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Maynard can now know whether Genoveva can know that Genoveva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maynard","Sherry","Angela","Genoveva"],"index":22848,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996637106,"difficulty":0.0003362894}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathleen's card is shown to Joseph. Harold's card is shown to Joseph. Cathleen's card is shown to Cathleen. Harold's card is shown to Harold. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cathleen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Cathleen","Harold"],"index":14535,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984880686,"difficulty":0.0015119314}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen knows whether or not everyone is thirsty. It is publicly announced that Olive knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Olive can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rose","Lillian","Olive","Karen"],"index":46819,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978252649,"difficulty":0.0021747351}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Stacey. Mary's card is shown to Mary. Stacey's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether Stacey picked a red card. It is publicly announced that Mary does not know whether Stacey picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Stacey can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stacey","Mary","David"],"index":52224,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9061954021,"difficulty":0.0938045979}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to John. Rosemary's card is shown to Rosemary. Curtis's card is shown to Lillian. Curtis's card is shown to Curtis. It is publicly announced that someone picked a red card. It is publicly announced that Lillian does not know whether Lillian picked a red card. It is publicly announced that Rosemary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] 0","hypothesis":"John can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Rosemary","Lillian","Curtis"],"index":15006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982104301,"difficulty":0.0017895699}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Angelina. Preston's card is shown to Preston. Shannon's card is shown to Preston. George's card is shown to Preston. Preston's card is shown to Shannon. Shannon's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that George does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Shannon can now know that George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angelina","Preston","Shannon","George"],"index":13993,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6083693504,"difficulty":0.3916306496}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Beverly is thirsty. It is publicly announced that Alicia does not know whether David is thirsty. It is publicly announced that Felicia knows whether or not nobody is thirsty. It is publicly announced that Felicia is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agenta knows that (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"David can now know that Felicia can know that Felicia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Alicia","Felicia","Beverly"],"index":47224,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8554920554,"difficulty":1.8554920554}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myra's card is shown to Myra. Myra's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know that Myra can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Myra","Patricia"],"index":2715,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985237718,"difficulty":0.0014762282}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille knows whether or not nobody's forehead is muddy. It is publicly announced that Joyce knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Joyce can now know whether Joyce's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lucille","Joyce"],"index":20331,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.974645853,"difficulty":0.025354147}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth is not thirsty. It is publicly announced that Paul is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"Paul can now know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Teresa","Diego","Elizabeth","Paul"],"index":41066,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.966094017,"difficulty":0.033905983}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Gloria can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Cynthia","Gloria","David"],"index":5987,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983397722,"difficulty":0.0016602278}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Odette's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Kathy can now know that Cynthia can know whether Odette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Odette","Kathy","Cynthia"],"index":27198,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99973768,"difficulty":0.00026232}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Betty knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Hollis can now know whether William can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Hollis","William","John"],"index":38414,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997726083,"difficulty":0.0002273917}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gina knows whether Gina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Gina can now know that Linda can know whether Linda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bobby","Gina","Linda"],"index":42716,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9749831557,"difficulty":0.0250168443}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"James can now know whether David can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","David"],"index":15272,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997397065,"difficulty":0.0002602935}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Enrique does not know whether Beverly is thirsty. It is publicly announced that Enrique knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Enrique can now know that Tia can know that Enrique is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Beverly","Enrique","Tia"],"index":58001,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9051575065,"difficulty":1.9051575065}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Howard","Brian","Daniel"],"index":48122,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9242963791,"difficulty":0.0757036209}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kim does not know whether Kim's forehead is muddy. It is publicly announced that Deb does not know whether or not everyone's forehead is muddy. It is publicly announced that Christen knows whether Deb's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Kim can now know that Deb's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kim","Deb","Jorge","Christen"],"index":2259,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5353388786,"difficulty":1.5353388786}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bertha knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Bertha can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bertha","Erica","John"],"index":18143,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997521043,"difficulty":0.0002478957}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Herbert can now know whether Doris can know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herbert","Dorothy","Doris"],"index":37818,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996454716,"difficulty":0.0003545284}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lucy can now know that Lucy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amanda","Lucy","Martha"],"index":13142,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998395741,"difficulty":0.001604259}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yvonne does not know whether Juan is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that June does not know whether Juan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Gloria can now know that Juan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Juan","Yvonne","Gloria","June"],"index":42892,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942312241,"difficulty":0.0057687759}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Billy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Margaret can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Billy","Araceli","Margaret"],"index":6845,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kay can now know that Iona can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kay","Vanessa","Iona","Dorothy"],"index":37284,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9533547163,"difficulty":0.0466452837}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Luis knows whether or not nobody's forehead is muddy. It is publicly announced that Luis knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kevin can now know whether Luis can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Luis"],"index":13363,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997809529,"difficulty":0.0002190471}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Aaron can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Jimmie","Aaron","Mary"],"index":5896,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984595776,"difficulty":0.0015404224}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kimberly can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kimberly","Caroline","Scott","Marcia"],"index":27237,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9978058934,"difficulty":0.0021941066}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Hazel can now know that Hazel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Margie","Hazel","Mary","George"],"index":56290,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985038042,"difficulty":0.0014961958}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Patricia can now know whether Wallace can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Patricia","Michelle","Wallace"],"index":9983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9903278947,"difficulty":0.0096721053}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myra knows whether someone's forehead is muddy. It is publicly announced that Myra knows whether Myra's forehead is muddy. It is publicly announced that Paul knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Seth can now know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Myra","Seth","Paul"],"index":42767,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997569263,"difficulty":0.002430737}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Andrea's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] 0","hypothesis":"William can now know that Tim's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tim","William","Andrea","Catherine"],"index":44402,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967108965,"difficulty":0.0032891035}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"John can now know that Lisa can know that Lisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","John","Mark"],"index":60863,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981541038,"difficulty":0.0018458962}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether or not everyone is thirsty. It is publicly announced that Thomas does not know whether Candace is thirsty. It is publicly announced that Thomas knows whether Thomas is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Thomas can now know whether Candace can know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Candace","Thomas"],"index":8878,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982819557,"difficulty":0.0017180443}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Seth. Michele's card is shown to Michele. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card. It is publicly announced that Mary does not know whether Michele picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mary can now know that Seth can know whether Seth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Seth","Michele"],"index":21480,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.944280684,"difficulty":0.055719316}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Trevor can now know that Bessie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Trevor","Bessie","Natasha"],"index":54212,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983385801,"difficulty":0.0016614199}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Ralph's card is shown to Mary. Ralph's card is shown to Ralph. Marilyn's card is shown to Ralph. Dana's card is shown to Marilyn. Ralph's card is shown to Dana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dana can now know whether Ralph can know that Ralph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Ralph","Marilyn","Dana"],"index":47302,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9370186329,"difficulty":0.0629813671}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jana knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Cynthia can now know that Joshua can know that Cynthia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jana","Joshua","Cynthia"],"index":16101,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9005150199,"difficulty":0.0994849801}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Juan. Patricia's card is shown to Juan. Robert's card is shown to Juan. Juan's card is shown to Patricia. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Juan can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juan","Patricia","Robert"],"index":37621,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984531403,"difficulty":0.0015468597}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Noemi's card is shown to Terrance. Noemi's card is shown to Joanne. Terrance's card is shown to Noemi. Noemi's card is shown to Noemi. It is publicly announced that someone picked a red card. It is publicly announced that Noemi picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (1&2&3) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Joanne can now know that Noemi can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Terrance","Joanne","Noemi"],"index":59226,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9877080917,"difficulty":0.0122919083}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alex's card is shown to Cherish. Alex's card is shown to Alex. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Cherish can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cherish","Alex","Virginia"],"index":26110,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919703007,"difficulty":0.0080296993}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosalia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Curtis can now know whether Curtis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Curtis","Rosalia","Roy"],"index":55698,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995440841,"difficulty":0.0004559159}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy. It is publicly announced that Jacqueline knows whether Jacqueline's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jacqueline can now know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jacqueline","Richard"],"index":57672,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959340096,"difficulty":0.0040659904}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Herbert can now know whether Marcene can know whether Herbert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Herbert","Irene","Marcene"],"index":16856,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997151494,"difficulty":0.0002848506}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"George can now know that Amber can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["George","Amber"],"index":47622,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997478127,"difficulty":0.0002521873}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marshall is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Helen can now know whether Michael can know whether Marshall is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Helen","Marshall"],"index":25196,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991044402,"difficulty":0.0008955598}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Laura. Nicholas's card is shown to Jason. Scott's card is shown to Nicholas. Nicholas's card is shown to Scott. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know that Scott can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Jason","Nicholas","Scott"],"index":28150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998374939,"difficulty":0.001625061}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Patricia can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Patricia","John"],"index":43896,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984600544,"difficulty":0.0015399456}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Marvin. Kim's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Marvin knows whether someone picked a red card. It is publicly announced that Marvin does not know whether or not everyone picked a red card. It is publicly announced that Marvin picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(1) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(1) ] 0","hypothesis":"Kim can now know that Kim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marvin","Kim"],"index":38470,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8964804411,"difficulty":0.1035195589}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julia does not know whether Christopher is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Christopher can now know whether Jacob can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Julia","Jacob"],"index":61626,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997162223,"difficulty":0.0002837777}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Van's card is shown to Kimberly. Ruth's card is shown to Kimberly. Van's card is shown to Van. Van's card is shown to Roland. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roland can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kimberly","Van","Roland","Ruth"],"index":49049,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997264743,"difficulty":0.0002735257}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharita does not know whether Brandi is thirsty. It is publicly announced that Sharita does not know whether Brandi is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Brandi can now know that Sharita can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brandi","Sharita"],"index":63039,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997225404,"difficulty":0.0002774596}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwayne's card is shown to Arturo. Arturo's card is shown to Linda. Linda's card is shown to Linda. Dwayne's card is shown to Linda. Maria's card is shown to Dwayne. Arturo's card is shown to Dwayne. Linda's card is shown to Dwayne. Dwayne's card is shown to Dwayne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know that Linda can know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Arturo","Linda","Dwayne"],"index":47166,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8787176609,"difficulty":0.1212823391}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to Rhonda. Cynthia's card is shown to Rhonda. Rhonda's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Rhonda picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Cynthia can now know that Rhonda can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rhonda","Cynthia"],"index":44754,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985075593,"difficulty":0.0014924407}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Terry can now know that Edward can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Terry","Steven","Brittany","Edward"],"index":53042,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977491498,"difficulty":0.0022508502}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Albert. Thelma's card is shown to Donald. Albert's card is shown to Thelma. Albert's card is shown to Richard. Donald's card is shown to Richard. Thelma's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether Donald picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Donald can now know whether Thelma can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Donald","Thelma","Richard"],"index":19774,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997772574,"difficulty":0.0002227426}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mike's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Mike can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Mike"],"index":66392,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8355779648,"difficulty":1.8355779648}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mildred does not know whether Mildred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Henry can now know that Mildred can know that Mildred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Henry","Earl","Ralph"],"index":47668,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9918391109,"difficulty":0.0081608891}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Anthony can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Guadalupe","John"],"index":35972,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99975425,"difficulty":0.00024575}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Dale. Kay's card is shown to Dale. Dale's card is shown to Kay. Dale's card is shown to Leonard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dale can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dale","Kay","Marion","Leonard"],"index":65146,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998357594,"difficulty":0.001642406}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether Leticia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Frances can now know whether William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leticia","Frances","William","Lynne"],"index":56898,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.995459497,"difficulty":0.004540503}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Eric. Madelyn's card is shown to Eric. Faustino's card is shown to Faustino. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Madelyn can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Madelyn","Letitia","Faustino"],"index":1903,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7372769117,"difficulty":0.2627230883}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne knows whether Juan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentc knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Jane can now know whether Pedro can know that Juan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","Pedro","Jane","Juan"],"index":61526,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997175336,"difficulty":0.0002824664}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Anne's forehead is not muddy. It is publicly announced that Irma's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agentb knows that (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Anne can now know that Irma can know whether Irma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Irma","Anne"],"index":19012,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996907711,"difficulty":0.0003092289}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Ralph. Cynthia's card is shown to Sammy. Ralph's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Ralph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Sammy can now know whether Sammy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Sammy","Cynthia"],"index":2883,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6956377029,"difficulty":1.6956377029}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lorie knows whether someone is thirsty. It is publicly announced that Patrick knows whether Lorie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Patrick can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lorie","Patrick"],"index":15018,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998293221,"difficulty":0.001706779}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Elvis can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Matthew","Elvis","Leora","John"],"index":20739,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981923699,"difficulty":0.0018076301}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy. It is publicly announced that Betty knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Betty can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","David","Sarah"],"index":1556,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997608066,"difficulty":0.0002391934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Moises does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Florence can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Moises","Florence","Roma","Eddie"],"index":34476,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997270703,"difficulty":0.0002729297}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juanita knows whether Juanita's forehead is muddy. It is publicly announced that Carolyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Carolyn can now know whether Juanita can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juanita","Cecil","Carolyn","Mark"],"index":10796,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know whether Stanley can know that Stanley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Stanley","Robert","Latoya"],"index":30853,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8969242573,"difficulty":0.1030757427}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Wilma. Catherine's card is shown to Wilma. Raymond's card is shown to Raymond. Raymond's card is shown to Lynn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymond can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wilma","Raymond","Lynn","Catherine"],"index":45603,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932994843,"difficulty":0.0067005157}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether Maria's forehead is muddy. It is publicly announced that Maria's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agentd knows that (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Paul can now know that Maria can know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Helen","John","Paul"],"index":67292,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9916104674,"difficulty":0.0083895326}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harvey's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Mildred can now know that Billy can know that Mildred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Latonya","Harvey","Billy","Mildred"],"index":20389,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947603345,"difficulty":0.0052396655}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Melissa","Irene","Jennifer","Robert"],"index":47434,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9907704592,"difficulty":1.9907704592}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Teresa. Patricia's card is shown to Patricia. Stephen's card is shown to Patricia. Ruby's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Teresa does not know whether or not everyone picked a red card. It is publicly announced that Stephen does not know whether Teresa picked a red card. It is publicly announced that Teresa does not know whether Ruby picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Patricia can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Teresa","Patricia","Stephen","Ruby"],"index":12580,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5783175826,"difficulty":0.4216824174}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chad's card is shown to Alberta. Alberta's card is shown to Linda. Edwin's card is shown to Linda. Chad's card is shown to Edwin. Linda's card is shown to Edwin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alberta can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alberta","Chad","Linda","Edwin"],"index":10621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997227788,"difficulty":0.0002772212}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Chris. Clara's card is shown to Chris. Gregg's card is shown to Gregg. Clara's card is shown to Clara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clara can now know whether Gregg can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chris","Gregg","Clara"],"index":51180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997125268,"difficulty":0.0002874732}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Samantha is thirsty. It is publicly announced that Samantha is not thirsty. It is publicly announced that Samantha does not know whether William is thirsty. It is publicly announced that William knows whether Samantha is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Samantha can now know that William can know that Joy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Samantha","Joy"],"index":40522,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9727838635,"difficulty":0.0272161365}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Mary","Tony","Harry"],"index":32123,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985197186,"difficulty":0.0014802814}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Abigail. Abigail's card is shown to Abigail. Abigail's card is shown to Francis. It is publicly announced that someone picked a red card. It is publicly announced that Francis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Christopher can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adele","Christopher","Abigail","Francis"],"index":35623,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982713461,"difficulty":0.0017286539}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentd knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Mary can now know whether Donna can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donna","Richard","Amy","Mary"],"index":24988,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8866086006,"difficulty":0.1133913994}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mary can now know that Paula can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wanda","Paula","Mary"],"index":56222,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983429909,"difficulty":0.0016570091}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kevin can now know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Margaret","Robert","Kevin","Patricia"],"index":64267,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9593253732,"difficulty":0.0406746268}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Robert","Nicholas"],"index":23729,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997313619,"difficulty":0.0002686381}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jacqueline can now know whether Charles can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Jacqueline","Charles"],"index":51952,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9856690168,"difficulty":0.0143309832}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Daniel. Rosa's card is shown to Raymond. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know whether Raymond picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacob","Daniel","Rosa","Raymond"],"index":7963,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9500477314,"difficulty":0.0499522686}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Ann. Ann's card is shown to Nicole. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ann can now know that Ann picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ann","Nicole","Robert"],"index":9477,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944936037,"difficulty":0.0055063963}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Salvatore can now know whether Janice can know whether Christine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Salvatore","Janice","Christine","Patrick"],"index":2309,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997038245,"difficulty":0.0002961755}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that Neoma knows whether Nicholas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agenta knows that (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Craig can now know that Neoma can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Craig","Mary","Nicholas","Neoma"],"index":40444,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966202974,"difficulty":0.0033797026}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether John can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elizabeth","John"],"index":55650,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9318970442,"difficulty":0.0681029558}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Henry does not know whether Darnell is thirsty. It is publicly announced that Henry does not know whether Charles is thirsty. It is publicly announced that Darnell does not know whether Velma is thirsty. It is publicly announced that Velma is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! 4 ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! 4 ] 0","hypothesis":"Henry can now know that Charles is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Henry","Darnell","Charles","Velma"],"index":32635,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9565755725,"difficulty":0.0434244275}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Allan can now know that Arthur can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Allan","Arthur"],"index":30683,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996194839,"difficulty":0.0003805161}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol does not know whether Virginia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Eric can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Virginia","Eric"],"index":51218,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997199178,"difficulty":0.0002800822}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Evelyn. Johnie's card is shown to Evelyn. German's card is shown to Evelyn. Johnie's card is shown to Johnie. German's card is shown to Johnie. Evelyn's card is shown to German. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Johnie does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Robert can now know whether Johnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Johnie","German","Robert"],"index":57253,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7312379479,"difficulty":0.2687620521}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juan knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Albertha can now know that Juan can know whether Albertha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Albertha","Paula","Juan"],"index":29220,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9813641906,"difficulty":0.0186358094}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan knows whether Fidela's forehead is muddy. It is publicly announced that Cecilia knows whether Cecilia's forehead is muddy. It is publicly announced that Cecilia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Fidela can now know that Cecilia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cecilia","Norma","Alan","Fidela"],"index":44733,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985798597,"difficulty":0.0014201403}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Maritza. Maritza's card is shown to Elida. Elida's card is shown to Elida. Chris's card is shown to Elida. Maritza's card is shown to Chris. Elida's card is shown to Chris. Chris's card is shown to Chris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elida can now know whether Chris can know that Chris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maritza","Elida","Chris"],"index":26268,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9200591445,"difficulty":0.0799408555}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard does not know whether Leonard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Tina can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Leonard","Tina"],"index":43952,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997215867,"difficulty":0.0002784133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Malissa does not know whether or not everyone is thirsty. It is publicly announced that Malissa does not know whether Steven is thirsty. It is publicly announced that Jeffery does not know whether Steven is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Steven can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffery","Malissa","Steven","Daniel"],"index":33091,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brittany knows whether Harvey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Leonard can now know that Ron can know that Harvey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harvey","Leonard","Brittany","Ron"],"index":5100,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974428415,"difficulty":0.0025571585}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Robert's card is shown to Katherine. Katherine's card is shown to Katherine. Gary's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lloyd can now know whether Robert can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Katherine","Lloyd","Gary"],"index":46373,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9841252565,"difficulty":0.0158747435}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Enriqueta. Aaron's card is shown to James. Enriqueta's card is shown to Aaron. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Enriqueta can now know whether James can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Enriqueta","James","Aaron"],"index":43671,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997699857,"difficulty":0.0002300143}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rita does not know whether Fred is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Rita can now know that Rita is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rita","Billy","Fred","Joshua"],"index":40815,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9452050924,"difficulty":0.0547949076}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Ernestina. Ernestina's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether or not everyone picked a red card. It is publicly announced that Cynthia does not know whether Cynthia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ernestina can now know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ernestina","Cynthia"],"index":30258,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9134255648,"difficulty":0.0865744352}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kali knows whether someone's forehead is muddy. It is publicly announced that Kali knows whether someone's forehead is muddy. It is publicly announced that Kali knows whether someone's forehead is muddy. It is publicly announced that Kali knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kali","John","Sara"],"index":34063,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977910519,"difficulty":0.0022089481}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Norma. Dora's card is shown to Norma. Greg's card is shown to George. Norma's card is shown to Dora. Dora's card is shown to Dora. Dora's card is shown to Greg. Greg's card is shown to Greg. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1,3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1,3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Norma can now know whether Greg can know whether George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norma","George","Dora","Greg"],"index":21282,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997969687,"difficulty":0.002030313}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond does not know whether Marlene is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Lisa is thirsty. It is publicly announced that Lisa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Raymond can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Marlene","Guadalupe","Raymond"],"index":67093,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997258782,"difficulty":0.0002741218}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Norma can now know that Alice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Norma","Craig","Alice"],"index":35165,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9848885536,"difficulty":0.0151114464}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether someone's forehead is muddy. It is publicly announced that Steven knows whether Marie's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Marie can now know that Mellisa can know whether Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mellisa","Jeffrey","Marie","Steven"],"index":51505,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995883107,"difficulty":0.0004116893}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Megan is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Megan can now know whether Michelle can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Annette","Michelle","Megan"],"index":24141,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997214675,"difficulty":0.0002785325}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know that Brandy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Beverly","Annette","Christine","Brandy"],"index":47115,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983341098,"difficulty":0.0016658902}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra is thirsty. It is publicly announced that Lamont knows whether Sandra is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether 3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Lamont can now know that Donald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lamont","Donald","Sandra"],"index":52891,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9730584025,"difficulty":0.0269415975}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shawn does not know whether Deborah is thirsty. It is publicly announced that Deborah does not know whether Paul is thirsty. It is publicly announced that Deborah is thirsty. It is publicly announced that Deborah knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Cynthia can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cynthia","Deborah","Paul","Shawn"],"index":45023,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997848868,"difficulty":0.0002151132}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julia can now know whether Hazel can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julia","Hazel","Henry"],"index":11320,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997124076,"difficulty":0.0002875924}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Raymond can now know that Matt can know that Alberto's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Matt","Alberto","Raymond"],"index":19501,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971219897,"difficulty":0.0028780103}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Martha can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martha","Nelda","Margaret","Theresa"],"index":57101,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997826219,"difficulty":0.0002173781}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Judy. Larry's card is shown to Tyler. Judy's card is shown to Larry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Judy can now know whether Martin can know that Larry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Judy","Martin","Tyler","Larry"],"index":14217,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9022735953,"difficulty":1.9022735953}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elaine knows whether or not everyone's forehead is muddy. It is publicly announced that Elaine does not know whether Elaine's forehead is muddy. It is publicly announced that Curtis knows whether Curtis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Elaine can now know whether Curtis can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elaine","Daniel","Curtis"],"index":31384,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996932745,"difficulty":0.0003067255}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Mary is thirsty. It is publicly announced that Tonya does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Mary can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Robert","Tonya","Jean"],"index":5676,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9919819236,"difficulty":0.0080180764}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia does not know whether or not everyone's forehead is muddy. It is publicly announced that Monica knows whether someone's forehead is muddy. It is publicly announced that Virginia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Theresa can now know whether Aline can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Theresa","Virginia","Monica","Aline"],"index":1445,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9974078536,"difficulty":0.0025921464}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether or not nobody's forehead is muddy. It is publicly announced that Deborah's forehead is muddy. It is publicly announced that Juan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Juan can now know that Deborah's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anita","Deborah","Juan","Catherine"],"index":28475,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5000963807,"difficulty":1.5000963807}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candice's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Candice can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Candice","Bryant","Laura"],"index":50742,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984592199,"difficulty":0.0015407801}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Joann can now know that Cheryl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joann","Cheryl","James"],"index":9959,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.775603354,"difficulty":1.775603354}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Willie. Robert's card is shown to Rebecca. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether Willie picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Rebecca picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Willie can now know whether Rebecca can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Willie","Rebecca","Robert"],"index":55707,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9557442069,"difficulty":0.0442557931}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl knows whether Corey's forehead is muddy. It is publicly announced that Corey's forehead is muddy. It is publicly announced that Douglas does not know whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Corey can now know whether Kenneth can know whether Douglas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","Kenneth","Cheryl","Corey"],"index":11867,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991894364,"difficulty":0.0008105636}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karol's forehead is not muddy. It is publicly announced that June knows whether Karol's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Karol can now know that Christine can know that Karol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karol","June","Christine"],"index":3570,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9737839103,"difficulty":0.0262160897}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Audrey can now know that Joan can know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Audrey","Joan","Ruth","Nicole"],"index":39639,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995768666,"difficulty":0.0004231334}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elsie's forehead is muddy. It is publicly announced that Christopher does not know whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Michael can now know that Christopher can know that Elsie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Elsie","Christopher"],"index":49763,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8389801979,"difficulty":1.8389801979}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Jason knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"David can now know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Milton","Jason"],"index":21503,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972990155,"difficulty":0.0027009845}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherri knows whether Sherri's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Anna can now know whether Sherri can know whether Cole's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Anna","Cole","Sherri"],"index":41224,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993645549,"difficulty":0.0006354451}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Kyle can now know that Merle can know that Kyle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Merle","Kyle","Mary"],"index":50496,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9956620336,"difficulty":0.0043379664}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Leonard can now know whether Elsa can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tiffany","Leonard","Elsa","Julie"],"index":52207,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catherine knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Allen can now know whether Allen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Catherine","Allen","Gregory","Jerry"],"index":46134,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998344183,"difficulty":0.001655817}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jesse can now know that Frank's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesse","Frank","Rebecca","William"],"index":46776,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959214926,"difficulty":0.0040785074}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lee's card is shown to Willie. Lee's card is shown to Crystal. Willie's card is shown to Lee. Crystal's card is shown to Lee. It is publicly announced that someone picked a red card. It is publicly announced that Willie does not know whether Willie picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Lee can now know that Crystal can know whether Lee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Willie","Crystal","Lee"],"index":42262,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5413293242,"difficulty":1.5413293242}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donovan does not know whether George is thirsty. It is publicly announced that George does not know whether or not everyone is thirsty. It is publicly announced that George does not know whether Ramon is thirsty. It is publicly announced that George does not know whether Ramon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"George can now know that Donovan can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donovan","George","Ramon"],"index":17733,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy. It is publicly announced that Mindy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Tamera can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mindy","Raymond","James","Tamera"],"index":12957,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998095572,"difficulty":0.001904428}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. Curtis's card is shown to Sarah. Hazel's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Hazel does not know whether Sarah picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Hazel can now know whether Curtis can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Curtis","Hazel","Sarah"],"index":11104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myrtle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Myrtle can now know that Sylvia can know that Angela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Sylvia","Angela","Myrtle"],"index":5769,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9631307721,"difficulty":0.0368692279}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. James's card is shown to John. John's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arthur","Andrea","John","James"],"index":48891,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982535243,"difficulty":0.0017464757}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Robert's card is shown to Frances. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Frances picked a red card. It is publicly announced that Robert does not know whether Frances picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Frances can now know that Robert can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Frances"],"index":62776,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9946405888,"difficulty":0.0053594112}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Richard can now know that Catherine can know that Catherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Catherine"],"index":11313,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9711712003,"difficulty":0.0288287997}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether or not nobody's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Rebecca does not know whether Rebecca's forehead is muddy. It is publicly announced that Charlotte knows whether Charlotte's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Rebecca can now know whether Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charlotte","Rebecca","John"],"index":40734,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8570752144,"difficulty":0.1429247856}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Gino knows whether Rachel's forehead is muddy. It is publicly announced that Gino knows whether someone's forehead is muddy. It is publicly announced that Gino's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Rachel can now know that Gino can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josephine","Gino","Susan","Rachel"],"index":15434,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997817874,"difficulty":0.0002182126}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julianne is thirsty. It is publicly announced that Donna does not know whether Lisa is thirsty. It is publicly announced that Katherine knows whether or not nobody is thirsty. It is publicly announced that Katherine is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Donna can now know that Julianne can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Donna","Katherine","Julianne"],"index":3437,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984446168,"difficulty":0.0015553832}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cynthia is not thirsty. It is publicly announced that Cynthia does not know whether Daniela is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Daniela can now know that Cynthia can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniela","Patrick","Cynthia"],"index":4144,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977261424,"difficulty":0.0022738576}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debra knows whether Debra is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Christina can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christina","Jamie","Debra","Rose"],"index":65229,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997072816,"difficulty":0.0002927184}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy. It is publicly announced that Shawn knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Michael can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Shawn","Michael"],"index":18102,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981076717,"difficulty":0.0018923283}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Tonya can now know that Mark can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Tonya","Floyd"],"index":64725,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983224273,"difficulty":0.0016775727}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether Carolyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carolyn can now know that Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carolyn","Alan","Jacob","Helen"],"index":32420,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983914495,"difficulty":0.0016085505}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candy's card is shown to Margaret. Erik's card is shown to James. Erik's card is shown to Erik. Margaret's card is shown to Candy. James's card is shown to Candy. It is publicly announced that someone picked a red card. It is publicly announced that Erik does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Margaret can now know that Erik can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","James","Erik","Candy"],"index":12257,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6138776541,"difficulty":0.3861223459}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Heather can now know that John can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Heather","John"],"index":58728,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984442592,"difficulty":0.0015557408}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Betty can now know that Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martha","Betty","Ada","Jeffrey"],"index":6217,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6779097319,"difficulty":0.3220902681}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Forrest does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Forrest can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Steven","William","Forrest"],"index":50931,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997726083,"difficulty":0.0002273917}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Gwendolyn. Steven's card is shown to Steven. Diann's card is shown to Steven. Gwendolyn's card is shown to Kareem. Kareem's card is shown to Kareem. Gwendolyn's card is shown to Diann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Diann can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gwendolyn","Steven","Kareem","Diann"],"index":23850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alice does not know whether or not everyone is thirsty. It is publicly announced that Jennifer does not know whether Deborah is thirsty. It is publicly announced that Jennifer does not know whether Deborah is thirsty. It is publicly announced that Jennifer does not know whether Dora is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Dora can now know that Deborah can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dora","Jennifer","Alice","Deborah"],"index":6036,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7274941802,"difficulty":0.2725058198}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Juanita is thirsty. It is publicly announced that Trina knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Doyle can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Trina","Doyle","Juanita"],"index":13376,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether Jonathan is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Linda can now know whether Jonathan can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Jonathan","Linda"],"index":36144,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997100234,"difficulty":0.0002899766}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Blossom does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Aaron can now know whether Blossom can know that Aaron is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maggie","Aaron","John","Blossom"],"index":13367,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9624426961,"difficulty":0.0375573039}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Hettie. Timothy's card is shown to Harry. Hettie's card is shown to Betty. Harry's card is shown to Betty. Timothy's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Hettie does not know whether Betty picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Timothy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Hettie","Harry","Timothy","Betty"],"index":17086,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Grant does not know whether Grant's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Theresa knows whether or not everyone's forehead is muddy. It is publicly announced that Theresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Theresa can now know whether Thomas can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Theresa","Grant","Dana"],"index":35528,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9960497022,"difficulty":0.0039502978}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale knows whether Daniel's forehead is muddy. It is publicly announced that Martin's forehead is not muddy. It is publicly announced that Dale knows whether Dale's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Daniel can now know that Brian can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dale","Brian","Daniel","Martin"],"index":64426,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984775186,"difficulty":0.0015224814}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Ann's forehead is muddy. It is publicly announced that Paul knows whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Charles can now know that Ann can know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Ann","Paul"],"index":41391,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983295798,"difficulty":0.0016704202}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kirk's card is shown to Roselyn. Roselyn's card is shown to Kirk. It is publicly announced that someone picked a red card. It is publicly announced that Kirk knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Roselyn can now know that Kirk can know whether Kirk picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Roselyn","Kirk"],"index":60816,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9615015984,"difficulty":1.9615015984}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrin knows whether Geoffrey's forehead is muddy. It is publicly announced that Allen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Geoffrey can now know that Allen can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Geoffrey","Darrin","Allen"],"index":17070,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979516864,"difficulty":0.0020483136}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Enrique does not know whether Shanna is thirsty. It is publicly announced that James does not know whether Enrique is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"James can now know whether Enrique can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Enrique","James","Shanna","Carol"],"index":39595,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5035833716,"difficulty":1.5035833716}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ivy's card is shown to Erica. Erica's card is shown to Mary. Mary's card is shown to Mary. Ivy's card is shown to Mary. Erica's card is shown to Ivy. It is publicly announced that someone picked a red card. It is publicly announced that Ivy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Ivy can know whether Ivy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Erica","Mary","Ivy"],"index":26720,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.861341536,"difficulty":1.861341536}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Hollie's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hollie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Lawrence can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Michael","Marcel","Hollie"],"index":32809,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6548870206,"difficulty":0.3451129794}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Richard's card is shown to Maria. Shirley's card is shown to Maria. Carolyn's card is shown to Maria. Maria's card is shown to Richard. Shirley's card is shown to Shirley. Maria's card is shown to Carolyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know that Carolyn can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Richard","Shirley","Carolyn"],"index":31720,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984764457,"difficulty":0.0015235543}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Shauna. Kathleen's card is shown to Shauna. Kathleen's card is shown to Mary. Shauna's card is shown to Kathleen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Shauna can know that Shauna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shauna","Mary","Kathleen"],"index":34460,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919638634,"difficulty":0.0080361366}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cory's forehead is muddy. It is publicly announced that Catherine knows whether Cory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know that Catherine can know whether Cory's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Catherine","Cory","Margaret","Jeffery"],"index":18557,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995744824,"difficulty":0.0004255176}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Shirley. Shirley's card is shown to Ofelia. It is publicly announced that someone picked a red card. It is publicly announced that Shirley does not know whether Ofelia picked a red card. It is publicly announced that Shirley knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Ofelia can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shirley","Ofelia"],"index":35808,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997163415,"difficulty":0.0002836585}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth does not know whether Bridgett is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Kenneth can now know whether Bridgett can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bridgett","John","Kenneth"],"index":8513,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Vera's forehead is muddy. It is publicly announced that Vera does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Vera can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Christopher","Vera"],"index":6833,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947667122,"difficulty":0.0052332878}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Lisa can now know that Lisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Lisa","Kylee","Michael"],"index":16251,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9282750487,"difficulty":0.0717249513}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna does not know whether or not everyone's forehead is muddy. It is publicly announced that Anna knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Thelma can now know whether Thelma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thelma","Anna"],"index":27749,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5689668655,"difficulty":1.5689668655}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Jerry. Lorraine's card is shown to Inez. Inez's card is shown to Inez. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lorraine can now know whether Jerry can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerry","Lorraine","Christopher","Inez"],"index":63966,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9263662696,"difficulty":0.0736337304}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest knows whether someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Alyce can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ernest","Alyce","James"],"index":24316,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997249246,"difficulty":0.0002750754}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eilene's card is shown to Tamara. Elizabeth's card is shown to Eilene. Eilene's card is shown to Mae. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eilene can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Tamara","Eilene","Mae"],"index":16130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997668862,"difficulty":0.0002331138}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jutta is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Darryl can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jutta","Harold","Darryl"],"index":15971,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9478092194,"difficulty":1.9478092194}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Trudie can now know that Shenita can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shenita","Tamara","Joel","Trudie"],"index":12949,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9961750507,"difficulty":0.0038249493}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jaime can now know whether Catherine can know whether Jimmie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Catherine","Jimmie","Jaime"],"index":66899,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997224212,"difficulty":0.0002775788}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether or not everyone is thirsty. It is publicly announced that Kathleen knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Larry can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juana","Larry","Kathleen","James"],"index":27967,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997182488,"difficulty":0.0002817512}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Monica can now know whether Cheryl can know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cheryl","Jennifer","Monica"],"index":52447,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990414977,"difficulty":0.0009585023}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether George's forehead is muddy. It is publicly announced that Ivana knows whether Debra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Debra can now know that Ivana can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Debra","Ivana","Sage","George"],"index":65513,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981333613,"difficulty":0.0018666387}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pearl's card is shown to Pearl. Nettie's card is shown to Pearl. Pearl's card is shown to Nettie. Nettie's card is shown to Nettie. Gary's card is shown to Nettie. Pearl's card is shown to Gary. Gary's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nettie can now know that Pearl can know whether Nettie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pearl","Nettie","Gary"],"index":27860,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6012396812,"difficulty":1.6012396812}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Salvador's card is shown to Jill. Salvador's card is shown to Salvador. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Salvador can now know that Jill can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jill","Salvador","Jo"],"index":42258,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983949065,"difficulty":0.0016050935}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Henry does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Henry can now know whether Maurice can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maurice","Henry"],"index":11125,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978135824,"difficulty":0.0021864176}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Crystal does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Crystal can now know whether Maria can know that Angelia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angelia","Crystal","Maria","Richard"],"index":824,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9866150022,"difficulty":0.0133849978}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason knows whether or not nobody is thirsty. It is publicly announced that Jason does not know whether Mathew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Holly can now know whether Mathew can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Holly","Mark","Mathew","Jason"],"index":30038,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999466002,"difficulty":0.000533998}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keisha's card is shown to Keisha. It is publicly announced that someone picked a red card. It is publicly announced that Gary knows whether Gary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Gary can now know whether Keisha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gary","Keisha"],"index":59360,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7427507043,"difficulty":1.7427507043}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether Anna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Anna can now know whether Jeffrey can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeffrey","Anna"],"index":39720,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996901751,"difficulty":0.0003098249}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"David can now know whether Carl can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Carl","Allan","David"],"index":58107,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997532964,"difficulty":0.0002467036}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol does not know whether Carol's forehead is muddy. It is publicly announced that Laurence's forehead is not muddy. It is publicly announced that Carol's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] 0","hypothesis":"Laurence can now know that Carol can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carol","James","Laurence"],"index":43198,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985314608,"difficulty":0.0014685392}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Michelle can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michelle","Linda"],"index":33191,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether or not nobody's forehead is muddy. It is publicly announced that Aaron's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Aaron can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Aaron","Kenneth"],"index":61481,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997641444,"difficulty":0.0002358556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose does not know whether Thomas is thirsty. It is publicly announced that Thomas does not know whether John is thirsty. It is publicly announced that Jose does not know whether Thomas is thirsty. It is publicly announced that Jose does not know whether Louis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Thomas can now know whether Jose can know whether Louis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Thomas","John","Jose"],"index":35162,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99800843,"difficulty":0.00199157}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall's forehead is not muddy. It is publicly announced that Stella does not know whether Stella's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Stella can now know that Candice can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stella","Randall","Candice"],"index":18658,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985123277,"difficulty":0.0014876723}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Johnathan's forehead is muddy. It is publicly announced that Johnathan knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Charles can now know that Johnathan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Johnathan","Charles"],"index":6158,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943389297,"difficulty":0.0056610703}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Catherine can now know that Amy can know that Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amy","Anita","Catherine","Ann"],"index":861,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.893245399,"difficulty":0.106754601}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirly knows whether Shirly is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Victor can now know that Jefferson can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirly","Jefferson","Victor"],"index":2071,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997600913,"difficulty":0.0002399087}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Eugene's card is shown to Michael. Cheryl's card is shown to Cheryl. It is publicly announced that someone picked a red card. It is publicly announced that Eugene knows whether or not nobody picked a red card. It is publicly announced that Eugene does not know whether Cheryl picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Cheryl can now know whether Eugene can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","Michael","Cheryl"],"index":37832,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997034669,"difficulty":0.0002965331}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Addie does not know whether William is thirsty. It is publicly announced that Margaret does not know whether William is thirsty. It is publicly announced that Margaret is not thirsty. It is publicly announced that Addie is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! ~(3) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! ~(3) ] 0","hypothesis":"Margaret can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Margaret","William","Addie"],"index":61633,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9179549217,"difficulty":1.9179549217}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony knows whether Eric's forehead is muddy. It is publicly announced that Eric does not know whether Eric's forehead is muddy. It is publicly announced that Eric does not know whether Eric's forehead is muddy. It is publicly announced that Eric knows whether Tony's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Tony can now know that Eric can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tony","Eric"],"index":38215,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997078776,"difficulty":0.0002921224}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lorie can now know that Maria can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Maria","Lorie","George"],"index":49536,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985812902,"difficulty":0.0014187098}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Nancy does not know whether Pattie is thirsty. It is publicly announced that Judy does not know whether Christie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Nancy can now know that Judy can know whether Christie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Judy","Nancy","Pattie","Christie"],"index":64570,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957829714,"difficulty":0.0042170286}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marie is not thirsty. It is publicly announced that Marie knows whether or not everyone is thirsty. It is publicly announced that James does not know whether Alan is thirsty. It is publicly announced that Alan knows whether Alan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"James can now know whether Marie can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marie","James","Alan"],"index":40265,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974855185,"difficulty":0.0025144815}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Jackson does not know whether Diane is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Diane can now know whether Jackson can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Jackson","Diane","Alice"],"index":49807,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991588593,"difficulty":0.0008411407}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Tara's card is shown to Christopher. Tara's card is shown to Tara. Christopher's card is shown to Ray. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tara can now know that Tara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Tara","Ray"],"index":63405,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951559305,"difficulty":0.0048440695}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ian does not know whether Vivian is thirsty. It is publicly announced that Ruth does not know whether Ian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] Agentd knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Ruth can now know that William can know that Ian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ian","William","Vivian","Ruth"],"index":11932,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958136678,"difficulty":0.0041863322}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy. It is publicly announced that Geneva knows whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Geneva can now know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sharon","Geneva","Steven","Gregory"],"index":47839,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9825337529,"difficulty":0.0174662471}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Viola. Viola's card is shown to Viola. Carrie's card is shown to Viola. Steven's card is shown to Carrie. Victor's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that Viola does not know whether Viola picked a red card. It is publicly announced that Carrie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Viola can now know that Steven can know whether Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Viola","Carrie","Victor"],"index":658,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5146448016,"difficulty":1.5146448016}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond does not know whether Isabelle is thirsty. It is publicly announced that Frank is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Isabelle can now know whether Charis can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charis","Frank","Raymond","Isabelle"],"index":14138,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997842908,"difficulty":0.0002157092}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie does not know whether Carrie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Carrie can now know whether Mary can know that Carrie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carrie","Mary"],"index":43234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6626418233,"difficulty":0.3373581767}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan does not know whether Alina is thirsty. It is publicly announced that Alina knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Linette can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eboni","Linette","Alina","Susan"],"index":38624,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997357726,"difficulty":0.0002642274}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Russell knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Doris can now know whether Russell can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Angela","Russell"],"index":57800,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975180626,"difficulty":0.0024819374}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Douglas can now know that Xavier can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nu","Melissa","Xavier","Douglas"],"index":24660,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997429252,"difficulty":0.0002570748}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Charles is thirsty. It is publicly announced that Brian does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Gary can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Gary","Charles","Brian"],"index":48767,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981821775,"difficulty":0.0018178225}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rae knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Frances can now know that Frances's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frances","Rae","Gary"],"index":5189,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6904046535,"difficulty":0.3095953465}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl does not know whether Cora is thirsty. It is publicly announced that Tommie does not know whether Cora is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Cora can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carl","Tommie","Cora","Jim"],"index":41727,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Martha. Chris's card is shown to Martha. Alexandra's card is shown to Evelyn. Martha's card is shown to Chris. Chris's card is shown to Chris. Chris's card is shown to Alexandra. Alexandra's card is shown to Alexandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1,3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1,3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alexandra can now know that Evelyn can know whether Chris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Evelyn","Chris","Alexandra"],"index":37816,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5272200704,"difficulty":1.5272200704}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Norman. Loretta's card is shown to Norman. Norman's card is shown to Edward. Edward's card is shown to Loretta. Loretta's card is shown to Loretta. It is publicly announced that someone picked a red card. It is publicly announced that Loretta picked a red card. It is publicly announced that Norman does not know whether or not everyone picked a red card. It is publicly announced that Norman knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Edward can now know that Loretta can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norman","Edward","Loretta"],"index":37334,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9843969941,"difficulty":0.0156030059}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Callie can now know whether Imogene can know that Karyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Callie","Karyn","Imogene"],"index":53996,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996572733,"difficulty":0.0003427267}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen does not know whether Carmen's forehead is muddy. It is publicly announced that Hazel knows whether Hazel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carmen can now know whether Hazel can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hazel","Carmen"],"index":8892,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997001886,"difficulty":0.0002998114}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Andre can now know that Cody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cody","Andre","Birdie","Edward"],"index":49964,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968366623,"difficulty":0.0031633377}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Louis knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Rex can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anita","Rex","Louis"],"index":46618,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998541832,"difficulty":0.001458168}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna's forehead is muddy. It is publicly announced that Sandra knows whether Kim's forehead is muddy. It is publicly announced that Kim does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Anna can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Kim","Alberto","Sandra"],"index":50745,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998257935,"difficulty":0.001742065}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Wayne can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jane","Wayne"],"index":50330,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997816682,"difficulty":0.0002183318}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Rodney. Helen's card is shown to Helen. Rodney's card is shown to Walter. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rodney can now know whether Helen can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rodney","Helen","Walter"],"index":21126,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9233813286,"difficulty":0.0766186714}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy. It is publicly announced that Fred knows whether or not nobody's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that Fred knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Fred"],"index":10301,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7607599497,"difficulty":1.7607599497}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Casey can now know that Brett's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Casey","Ezequiel","Brian","Brett"],"index":49241,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936616421,"difficulty":0.0063383579}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virgina knows whether Roger's forehead is muddy. It is publicly announced that Cathy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Virgina can now know whether Cathy can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cathy","Roger","Virgina"],"index":12726,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997715354,"difficulty":0.0002284646}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gale knows whether Vicki's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Gale can now know that Vicki's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gale","Vicki"],"index":42363,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.992051065,"difficulty":0.007948935}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Gregory can now know that Bruce can know that Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Melody","Gregory","Bruce"],"index":16335,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8658221364,"difficulty":0.1341778636}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Edna. Neil's card is shown to Neil. Edna's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Neil can now know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edna","Neil","James","Carol"],"index":49140,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9934798479,"difficulty":0.0065201521}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Timothy knows whether Timothy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Timothy can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Timothy","Rhonda"],"index":36519,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vernon knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Brian can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Frank","Vernon","Lisa"],"index":14872,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981549382,"difficulty":0.0018450618}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonio's card is shown to Nathan. Robert's card is shown to William. Antonio's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nathan","Antonio","William","Robert"],"index":56208,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980390668,"difficulty":0.0019609332}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jarvis does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Joshua can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jarvis","Joshua"],"index":45783,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9954761863,"difficulty":0.0045238137}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bettie's card is shown to Johnnie. Matt's card is shown to Johnnie. Bettie's card is shown to Matt. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bettie can now know whether Johnnie can know whether Matt picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnnie","Bettie","Matt"],"index":42788,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987776875,"difficulty":0.0012223125}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Larry can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Flora","Larry"],"index":44741,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981611371,"difficulty":0.0018388629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Heather can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","James","Heather","Debra"],"index":66754,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9688563347,"difficulty":0.0311436653}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kazuko knows whether someone's forehead is muddy. It is publicly announced that Kazuko knows whether Pearlie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"John can now know that Teresa can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Teresa","Pearlie","John","Kazuko"],"index":67571,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983311296,"difficulty":0.0016688704}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalia's card is shown to Clara. Rosalia's card is shown to Rosalia. It is publicly announced that someone picked a red card. It is publicly announced that Clara knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Clara can now know whether Rosalia can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Clara","Rosalia"],"index":481,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997730851,"difficulty":0.0002269149}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know that Ronald can know whether Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Justin","Lidia","Ronald","John"],"index":24873,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963647723,"difficulty":0.0036352277}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Randi does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Michael can now know that Randi can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Randi"],"index":56670,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99844414,"difficulty":0.00155586}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie does not know whether Helen is thirsty. It is publicly announced that Helen does not know whether Nancy is thirsty. It is publicly announced that Helen is thirsty. It is publicly announced that Helen knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Helen can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bonita","Helen","Nancy","Julie"],"index":42555,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984642267,"difficulty":0.0015357733}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ginette is thirsty. It is publicly announced that Susan knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Monica can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Monica","Ginette"],"index":10821,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986031651,"difficulty":0.0013968349}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerard knows whether Carmen's forehead is muddy. It is publicly announced that Gerard knows whether or not everyone's forehead is muddy. It is publicly announced that Jose does not know whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Carmen can now know whether Gerard can know whether Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carmen","Jose","Gerard"],"index":42639,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989593029,"difficulty":0.0010406971}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tyler does not know whether Tyler's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Tyler can now know whether Constance can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Constance","Tyler","Peter"],"index":13666,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9949370623,"difficulty":0.0050629377}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marie does not know whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Christopher can now know whether Christopher is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marie","Ashley","Christopher","Jason"],"index":46550,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979268312,"difficulty":0.0020731688}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jacqueline can now know that Evan can know that Evan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jacqueline","Travis","Evan"],"index":1655,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998118937,"difficulty":0.001881063}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geneva knows whether someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] 0","hypothesis":"Geneva can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Geneva","Robert"],"index":57386,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975318909,"difficulty":0.0024681091}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Melissa can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rebecca","Sharron","Melissa"],"index":29791,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998282671,"difficulty":0.001717329}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Bill can know whether Tesha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bill","Yvonne","Mary","Tesha"],"index":2346,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9894590378,"difficulty":0.0105409622}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Gloria can now know whether James can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Gloria","Sandra"],"index":30006,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999763906,"difficulty":0.000236094}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Jermaine does not know whether Edna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jermaine can now know whether Edna can know that Edna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Suzanne","Jermaine","Edna","Diana"],"index":60780,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7932395935,"difficulty":1.7932395935}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paulette's card is shown to Angela. Angela's card is shown to Paulette. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Paulette can now know whether Angela can know whether Paulette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Angela","Paulette"],"index":49460,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977315068,"difficulty":0.0022684932}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodney knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ella can now know whether Kelly can know whether Ella's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rodney","Ella","Kelly","Sara"],"index":10904,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997083545,"difficulty":0.0002916455}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl does not know whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lynn can now know that Frances can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carl","Lynn","Frances"],"index":52897,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998470366,"difficulty":0.001529634}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Timothy can now know whether Bill can know that Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Gayle","Bill","Noel"],"index":43680,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8622888327,"difficulty":0.1377111673}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leta does not know whether Monica is thirsty. It is publicly announced that Daniel does not know whether Leta is thirsty. It is publicly announced that Leta does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Chad can now know whether Leta can know that Daniel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leta","Chad","Monica","Daniel"],"index":58801,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.989043057,"difficulty":0.010956943}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether Peter's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jon can now know that Richard can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jon","Richard","Peter"],"index":17534,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996041656,"difficulty":0.0003958344}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether James is thirsty. It is publicly announced that Mark does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Mark can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alyssa","James","Viola","Mark"],"index":17155,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998426199,"difficulty":0.001573801}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Scott. Shari's card is shown to Scott. Scott's card is shown to Willa. Willa's card is shown to Willa. Shari's card is shown to Shari. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Scott can now know that Willa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Willa","Shari"],"index":53653,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phillip knows whether Lillie's forehead is muddy. It is publicly announced that Lillie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] 0","hypothesis":"Miranda can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Miranda","Lillie","Darryl","Phillip"],"index":54176,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997335076,"difficulty":0.0002664924}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to James. Patrick's card is shown to Patrick. James's card is shown to Myrtle. Patrick's card is shown to Myrtle. Pearl's card is shown to Myrtle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Patrick","Pearl","Myrtle"],"index":52786,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985342026,"difficulty":0.0014657974}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Philip's card is shown to Lynn. Maria's card is shown to Lynn. Maria's card is shown to Philip. Alexis's card is shown to Alexis. Maria's card is shown to Alexis. Philip's card is shown to Maria. Alexis's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:3,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:3,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Philip can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lynn","Philip","Alexis","Maria"],"index":4652,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997754693,"difficulty":0.0002245307}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen knows whether Benjamin's forehead is muddy. It is publicly announced that Ernest's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Kenneth can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kenneth","Ernest","Stephen","Benjamin"],"index":2064,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999773562,"difficulty":0.000226438}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elsie's card is shown to John. John's card is shown to Anna. Elsie's card is shown to Anna. Elsie's card is shown to Elsie. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Anna picked a red card. It is publicly announced that Elsie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Anna can now know that Elsie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Anna","Elsie"],"index":27805,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dewayne knows whether Sandra's forehead is muddy. It is publicly announced that Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Dewayne can now know that Pamela can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pamela","Dewayne","Sandra"],"index":21396,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles knows whether someone is thirsty. It is publicly announced that Cleo does not know whether Clinton is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Cleo can now know that Charles can know whether Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clinton","Charles","Cleo"],"index":58224,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983533621,"difficulty":0.0016466379}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Bryon. John's card is shown to Angela. Angela's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Angela can now know whether John can know whether Bryon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bryon","Angela","John"],"index":4850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979276657,"difficulty":0.0020723343}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Maria. Maria's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Maria can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Maria","Mary"],"index":34992,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997232556,"difficulty":0.0002767444}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Elenora. Elenora's card is shown to Virginia. Wilburn's card is shown to Wilburn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Virginia can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elenora","Virginia","Wilburn"],"index":21086,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983941913,"difficulty":0.0016058087}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juliette knows whether or not nobody's forehead is muddy. It is publicly announced that Eva's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentb knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Eva can now know that Jeanne can know that Juliette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Terry","Eva","Juliette","Jeanne"],"index":41200,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9932410717,"difficulty":0.0067589283}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rose does not know whether Robert is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"Tracy can now know that Robert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Rose","Tracy","Ruth"],"index":4347,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffery's card is shown to Jeffery. Jeffery's card is shown to Tamara. Tamara's card is shown to Tamara. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Tamara can now know that Jeffery can know whether Jeffery picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeffery","Tamara"],"index":30101,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9719654322,"difficulty":0.0280345678}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] 0","hypothesis":"Don can now know that Sarah can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","Sarah","Don","Rachel"],"index":61480,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983514547,"difficulty":0.0016485453}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Sherly knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Sherly can now know whether Sam can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sherly","Sam"],"index":19008,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997139573,"difficulty":0.0002860427}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Jeffrey. Albert's card is shown to Jeffrey. Jeffrey's card is shown to Albert. Jeffrey's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Karen picked a red card. It is publicly announced that Albert does not know whether Albert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Albert can now know whether Albert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffrey","Albert","Karen"],"index":37425,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9246504307,"difficulty":1.9246504307}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luther's card is shown to Clarence. Luther's card is shown to Luther. It is publicly announced that someone picked a red card. It is publicly announced that Luther does not know whether Clarence picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Luther can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Clarence","Luther"],"index":43480,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey knows whether Jeffrey is thirsty. It is publicly announced that Jeffrey is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 3 ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 3 ] 0","hypothesis":"Michael can now know whether Joy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joy","Michael","Jeffrey"],"index":63607,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8965916038,"difficulty":0.1034083962}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Vanessa. Vanessa's card is shown to Billy. Billy's card is shown to Billy. It is publicly announced that someone picked a red card. It is publicly announced that Vanessa knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Vanessa can now know whether Vanessa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vanessa","Billy"],"index":62618,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9863670468,"difficulty":0.0136329532}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terri knows whether or not everyone's forehead is muddy. It is publicly announced that Margery's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Terri can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Terri","Margery"],"index":13588,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982060194,"difficulty":0.0017939806}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"John can now know that Cindy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Cindy","Betty","James"],"index":21251,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9919296503,"difficulty":0.0080703497}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Mary. Mary's card is shown to Mary. John's card is shown to Mary. Mary's card is shown to John. John's card is shown to John. Glen's card is shown to John. Glen's card is shown to Glen. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Charles can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Mary","John","Glen"],"index":17405,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997691512,"difficulty":0.0002308488}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Florencia can now know whether James can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Hazel","Florencia","James"],"index":65237,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9967148304,"difficulty":0.0032851696}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Colin knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Donna can now know that Colin can know that Colin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Colin","Donna"],"index":4489,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980415106,"difficulty":0.0019584894}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Sara. Sara's card is shown to Victoria. Victoria's card is shown to Victoria. It is publicly announced that someone picked a red card. It is publicly announced that Sara knows whether Earl picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Earl can now know whether Sara can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Earl","Sara","Victoria"],"index":67444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997031093,"difficulty":0.0002968907}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. Flora's card is shown to Betty. Elizabeth's card is shown to Betty. Betty's card is shown to Flora. Flora's card is shown to Flora. Elizabeth's card is shown to Flora. Flora's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Flora","Elizabeth"],"index":36026,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9622592926,"difficulty":0.0377407074}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ella's card is shown to Ella. Deborah's card is shown to Deborah. Ella's card is shown to Jacqueline. It is publicly announced that someone picked a red card. It is publicly announced that Jacqueline does not know whether Jacqueline picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jacqueline can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ella","Deborah","Jacqueline"],"index":47848,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774754,"difficulty":0.000225246}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fredrick does not know whether or not everyone is thirsty. It is publicly announced that Fredrick knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Fredrick can now know that Amanda can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Amanda","Fredrick"],"index":18195,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sally knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Ruth can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ruth","Sally","John"],"index":64326,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984843135,"difficulty":0.0015156865}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julia's card is shown to Julia. Jim's card is shown to Jonathan. Katrina's card is shown to Jonathan. Julia's card is shown to Jim. Julia's card is shown to Katrina. It is publicly announced that someone picked a red card. It is publicly announced that Katrina does not know whether Katrina picked a red card. It is publicly announced that Jim knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jonathan can now know that Jim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julia","Jonathan","Jim","Katrina"],"index":8442,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9920619726,"difficulty":0.0079380274}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roger's card is shown to Roger. Roger's card is shown to Robin. Robin's card is shown to Shawn. Shawn's card is shown to Shawn. Roger's card is shown to Louis. Louis's card is shown to Louis. It is publicly announced that someone picked a red card. It is publicly announced that Roger does not know whether or not everyone picked a red card. It is publicly announced that Roger picked a red card. It is publicly announced that Roger does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Roger can now know that Robin can know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Robin","Shawn","Louis"],"index":39305,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9561376572,"difficulty":1.9561376572}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnathon's card is shown to Carolyn. Johnathon's card is shown to Linda. Linda's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Johnathon can now know whether Carolyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carolyn","Johnathon","Linda"],"index":13542,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9220173359,"difficulty":0.0779826641}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Robert can now know whether Debra can know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Debra","Alfreda","Charles"],"index":28398,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991039634,"difficulty":0.0008960366}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryn's card is shown to Kathryn. Kathryn's card is shown to Sharon. Rocky's card is shown to Sharon. Rocky's card is shown to Rocky. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rocky can now know whether Sharon can know whether Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathryn","Sharon","Rocky"],"index":57166,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9892019033,"difficulty":1.9892019033}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy. It is publicly announced that Codi knows whether Codi's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Codi can now know that Codi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Codi","Kenneth"],"index":32867,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9899110198,"difficulty":0.0100889802}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raven's card is shown to Raven. Joseph's card is shown to Joseph. Willie's card is shown to Joseph. Raven's card is shown to Willie. Joseph's card is shown to Willie. Willie's card is shown to Willie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Willie can now know that Raven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raven","Joseph","Willie"],"index":28851,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979060888,"difficulty":0.0020939112}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Timothy can now know that Aleisha can know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aleisha","Charles","Timothy","Kelly"],"index":62211,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995939136,"difficulty":0.0004060864}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Rosanna can now know that Teresa can know that Bennie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rosanna","Bennie","Teresa","Petra"],"index":38715,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983623624,"difficulty":0.0016376376}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earl knows whether Steven's forehead is muddy. It is publicly announced that Julio's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Earl can now know that Steven can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julio","Earl","Steven","George"],"index":56623,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth does not know whether Christine is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Samuel can now know that Ruth can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christine","Samuel","Ruth"],"index":22769,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9858375192,"difficulty":0.0141624808}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Susan. Richard's card is shown to Susan. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether or not everyone picked a red card. It is publicly announced that Richard knows whether Richard picked a red card. It is publicly announced that Susan knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Susan can now know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Susan","Richard"],"index":15383,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9916981459,"difficulty":0.0083018541}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Andrew knows whether Mary's forehead is muddy. It is publicly announced that Carson knows whether Carson's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carson","Mary","Andrew"],"index":29187,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997058511,"difficulty":0.0002941489}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neil knows whether or not everyone's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Neil can now know that Neil's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daisy","Clifton","Thomas","Neil"],"index":26472,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9552093148,"difficulty":0.0447906852}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Johnnie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Johnnie can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Johnnie","Sally"],"index":43019,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968671203,"difficulty":0.0031328797}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Nora can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eric","Herbert","Sarah","Nora"],"index":11849,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know whether Donald can know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donald","John"],"index":1909,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9004619122,"difficulty":0.0995380878}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lamar knows whether Lamar's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lamar can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Lamar","John"],"index":16120,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997425675,"difficulty":0.0002574325}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theodore's forehead is not muddy. It is publicly announced that Dan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Theodore can now know whether Dan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Theodore","Dan","Elizabeth"],"index":1891,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997509122,"difficulty":0.0002490878}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Foster's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Donna can now know that Sachiko's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sachiko","Thomas","Foster","Donna"],"index":45068,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951198101,"difficulty":0.0048801899}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Joe can now know whether Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Keith","Carlos","Joe"],"index":47450,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994705319,"difficulty":0.0005294681}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teri knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Edward can now know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Edward","Teri"],"index":52719,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984904528,"difficulty":0.0015095472}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Karen. Harold's card is shown to Karen. Carol's card is shown to Karen. Karen's card is shown to Jamika. Jamika's card is shown to Jamika. Carol's card is shown to Jamika. Karen's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know that Harold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Harold","Jamika","Carol"],"index":18510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978790283,"difficulty":0.0021209717}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tonya does not know whether or not everyone's forehead is muddy. It is publicly announced that Felicita knows whether or not everyone's forehead is muddy. It is publicly announced that Tonya does not know whether Tonya's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Faustino can now know whether Felicita can know whether Tonya's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Faustino","Felicita","Ruby","Tonya"],"index":27008,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991183877,"difficulty":0.0008816123}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erica does not know whether Helen is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Helen does not know whether Christopher is thirsty. It is publicly announced that Christopher does not know whether Helen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Christopher can now know that Erica can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Erica","Helen"],"index":51477,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997822642,"difficulty":0.0002177358}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Loretta does not know whether or not everyone is thirsty. It is publicly announced that Loretta does not know whether Vincent is thirsty. It is publicly announced that Joe does not know whether Vincent is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Vincent can now know that Mikki is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mikki","Joe","Vincent","Loretta"],"index":53560,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9733716249,"difficulty":0.0266283751}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Betty. Darren's card is shown to Betty. Betty's card is shown to Alberta. Norman's card is shown to Alberta. Norman's card is shown to Norman. Alberta's card is shown to Darren. It is publicly announced that someone picked a red card. It is publicly announced that Darren picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Darren can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Alberta","Norman","Darren"],"index":50567,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985302687,"difficulty":0.0014697313}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terrance's card is shown to Eric. Terrance's card is shown to Terrance. Terrance's card is shown to Cynthia. Cynthia's card is shown to Cynthia. Cynthia's card is shown to Alex. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Terrance","Cynthia","Alex"],"index":1017,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8592564464,"difficulty":0.1407435536}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joan does not know whether Erin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Samuel can now know that Erin can know that Angela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Erin","Joan","Angela","Samuel"],"index":40944,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981139898,"difficulty":0.0018860102}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jodi knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Helen can now know whether Jodi can know that Jodi's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jodi","Jeffrey","Helen"],"index":15486,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7734873295,"difficulty":0.2265126705}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jo can now know whether Faye can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcella","Jo","Faye","Richard"],"index":9330,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roderick's card is shown to Everett. Everett's card is shown to Roderick. It is publicly announced that someone picked a red card. It is publicly announced that Roderick does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Roderick can now know whether Roderick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Everett","Roderick"],"index":52961,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9954144955,"difficulty":1.9954144955}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether Kathleen's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Andrew can now know whether Monique's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Monique","Kathleen","Andrew"],"index":1118,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997201562,"difficulty":0.0002798438}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Steven can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Alma","Jeremy","Thomas"],"index":771,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.978246212,"difficulty":0.021753788}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"William can now know that Robert can know whether Nathan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Billy","Nathan","William","Robert"],"index":18856,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997346997,"difficulty":0.0002653003}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell knows whether Russell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Susan can now know whether Margaret can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Susan","Diane","Russell"],"index":1114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999530673,"difficulty":0.000469327}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Donna can now know that Geraldine can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Sheila","Geraldine","Regina"],"index":46741,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997590184,"difficulty":0.0002409816}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesus knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Laurence can now know that Gloria can know that Jesus's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laurence","Jesus","Gloria","Donald"],"index":62990,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983996749,"difficulty":0.0016003251}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Desiree does not know whether or not everyone's forehead is muddy. It is publicly announced that Shannon knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Shannon can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Desiree","Rowena","Shannon","Muriel"],"index":4459,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947645664,"difficulty":0.0052354336}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jasper's card is shown to James. James's card is shown to Jasper. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether James picked a red card. It is publicly announced that James does not know whether James picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jasper can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Jasper"],"index":30209,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985992312,"difficulty":0.0014007688}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra does not know whether or not everyone's forehead is muddy. It is publicly announced that Debra does not know whether Debra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"William can now know whether Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","William","Angelina","Debra"],"index":40320,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994327426,"difficulty":0.0005672574}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether Gordon is thirsty. It is publicly announced that Rueben does not know whether Hattie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Gordon can now know that Hattie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rueben","Gordon","Hattie","Stephen"],"index":2000,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973978996,"difficulty":0.0026021004}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David knows whether Darren's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Erica can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beverly","David","Darren","Erica"],"index":13010,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986152649,"difficulty":0.0013847351}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Celia is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Celia can now know that Bryan can know that Celia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bryan","Celia"],"index":15382,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8596006632,"difficulty":0.1403993368}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geraldine's card is shown to Mary. Mary's card is shown to Geraldine. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Mary can now know whether Geraldine can know that Geraldine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Geraldine"],"index":26681,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6342986226,"difficulty":0.3657013774}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Jeanine can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pamela","Jeanine","Keith","Alisha"],"index":28484,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982060194,"difficulty":0.0017939806}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Rosa can now know that David can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Violet","Helen","Rosa","David"],"index":27169,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949502945,"difficulty":0.0050497055}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Cheryl. Cheryl's card is shown to Judith. Judith's card is shown to Polly. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cheryl can now know whether Polly can know whether Ronald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Judith","Polly","Ronald"],"index":61691,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988372922,"difficulty":0.0011627078}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Alicia can now know that Josephine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Josephine","Samuel","Jimmie","Alicia"],"index":65290,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982884526,"difficulty":0.0017115474}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether John is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Howard can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Howard"],"index":36232,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999753654,"difficulty":0.000246346}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Earl's card is shown to Jesse. Walter's card is shown to Earl. Walter's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Earl can now know that Jesse can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesse","Earl","Walter"],"index":13699,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Howard knows whether or not nobody is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Howard can now know whether Jewel can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jewel","Howard"],"index":42571,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994675517,"difficulty":0.0005324483}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Anne. Anne's card is shown to David. David's card is shown to David. David's card is shown to Ronny. Ronny's card is shown to Ronny. It is publicly announced that someone picked a red card. It is publicly announced that Ronny does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ronny can now know that Anne can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anne","David","Ronny"],"index":21891,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9910491705,"difficulty":0.0089508295}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Agnes does not know whether Bruce is thirsty. It is publicly announced that Michael does not know whether Bruce is thirsty. It is publicly announced that Bruce knows whether Bruce is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentd knows whether 4) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Michael can now know that Agnes is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Agnes","Alberto","Michael","Bruce"],"index":6078,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9939369559,"difficulty":0.0060630441}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnette's card is shown to Jennifer. Elsie's card is shown to Jennifer. Katrina's card is shown to Arnette. Arnette's card is shown to Arnette. Arnette's card is shown to Elsie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Katrina can know whether Arnette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Katrina","Arnette","Elsie"],"index":21786,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8307029605,"difficulty":0.1692970395}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Kevin. Jean's card is shown to Kevin. Juan's card is shown to Raymond. Kevin's card is shown to Jean. Raymond's card is shown to Juan. Jean's card is shown to Juan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know whether Raymond can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Raymond","Jean","Juan"],"index":16555,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995923638,"difficulty":0.0004076362}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judith does not know whether Roberta is thirsty. It is publicly announced that Roberta knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Roberta can now know that Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Maricela","Roberta","Judith"],"index":7420,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979257584,"difficulty":0.0020742416}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maurice does not know whether Maurice's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Esther can now know that Maurice can know whether Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maurice","Steven","Esther"],"index":41218,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995388985,"difficulty":0.0004611015}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Travis","Robert","Charles"],"index":61343,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985082746,"difficulty":0.0014917254}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Patricia can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Patricia","Lowell"],"index":39584,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983377457,"difficulty":0.0016622543}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know that Robyn can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Robyn","John","Brian"],"index":41856,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996153116,"difficulty":0.0003846884}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Frank can now know that Trina can know that Fanny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dominick","Frank","Trina","Fanny"],"index":53019,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984859824,"difficulty":0.0015140176}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Alicia knows whether Steven is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Alicia can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Steven","Alicia"],"index":53161,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985728264,"difficulty":0.0014271736}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Benjamin can now know whether Annette can know whether Benjamin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laura","Annette","Benjamin"],"index":22062,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985957742,"difficulty":0.0014042258}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fernando is thirsty. It is publicly announced that Fernando does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Fernando can now know that Mark can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Fernando","Chrystal","Mark"],"index":1315,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy does not know whether Nancy's forehead is muddy. It is publicly announced that Celia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Nancy can now know whether Celia can know that Celia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Celia"],"index":55382,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8320016861,"difficulty":0.1679983139}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Michael can now know that Quinton can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Quinton"],"index":26921,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Thomas does not know whether Archie is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Jamie can now know that Jamie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jamie","Thomas","Archie"],"index":11735,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9842199683,"difficulty":0.0157800317}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Rita. Catherine's card is shown to Rita. Rita's card is shown to Donna. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Catherine can now know whether Rita can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rita","Donna","Catherine"],"index":20355,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Caleb. James's card is shown to Caleb. James's card is shown to Eric. Jack's card is shown to Jack. Eric's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Jack knows whether someone picked a red card. It is publicly announced that Caleb picked a red card. It is publicly announced that Eric does not know whether Jack picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Eric can now know whether James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Caleb","Eric","Jack","James"],"index":27593,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999779284,"difficulty":0.000220716}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether Joe's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Joe can now know that Winnie can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Anthony","Richard","Winnie"],"index":32708,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995948672,"difficulty":0.0004051328}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Juan can now know whether Marion can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juan","Marion","Gloria","Dale"],"index":10920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997304082,"difficulty":0.0002695918}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charolette does not know whether Charolette's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Charolette can now know that Asia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charolette","Asia"],"index":11580,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.898667872,"difficulty":1.898667872}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eunice's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Janet can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Janet","Eunice"],"index":12247,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997865558,"difficulty":0.0002134442}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emily's card is shown to Emily. Connie's card is shown to Emily. Emily's card is shown to Stanley. Emily's card is shown to Connie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stanley can now know whether Emily picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emily","Stanley","Connie"],"index":7065,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9623007178,"difficulty":0.0376992822}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald does not know whether Ronald's forehead is muddy. It is publicly announced that Wayne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Ronald can now know whether Beatrice can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronald","Wayne","Beatrice"],"index":4099,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6210408807,"difficulty":1.6210408807}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa knows whether Lisa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Colleen can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jamel","Lisa","Colleen"],"index":45582,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986222982,"difficulty":0.0013777018}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Douglas's forehead is muddy. It is publicly announced that Raquel knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Karen can now know that Raquel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Douglas","Raquel"],"index":1021,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984549284,"difficulty":0.0015450716}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roberto knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Chris can now know whether Joshua can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chris","Joshua","Roberto","Charles"],"index":15744,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997102618,"difficulty":0.0002897382}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Dustin can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","John","Dustin"],"index":8610,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997665286,"difficulty":0.0002334714}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick's forehead is not muddy. It is publicly announced that Frederick's forehead is not muddy. It is publicly announced that Laura knows whether Frederick's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Laura can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","Felecia","Frederick"],"index":13732,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99836272,"difficulty":0.00163728}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shawn can now know that Stephen can know that Stephen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kirsten","Terry","Shawn","Stephen"],"index":26664,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985582232,"difficulty":0.0014417768}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Roy can now know that Tammy can know that Tammy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roy","Lillie","Tammy"],"index":53792,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983003736,"difficulty":0.0016996264}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Billy. Billy's card is shown to Laura. Michael's card is shown to Laura. Laura's card is shown to Michael. Karl's card is shown to Michael. Laura's card is shown to Karl. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Billy knows whether Billy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Laura can now know whether Billy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","Laura","Michael","Karl"],"index":16556,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6232616305,"difficulty":0.3767383695}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Michael's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Patricia can now know that Michael can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Patricia"],"index":45580,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997763038,"difficulty":0.0002236962}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynn does not know whether Lynn's forehead is muddy. It is publicly announced that Lynn does not know whether Lynn's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lynn can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lynn","Jon"],"index":33045,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998473227,"difficulty":0.001526773}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Deborah. Deborah's card is shown to Patricia. Chad's card is shown to Patricia. Chad's card is shown to Kerry. Kerry's card is shown to Chad. Chad's card is shown to Chad. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deborah can now know whether Patricia can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Patricia","Kerry","Chad"],"index":34531,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Demetrius does not know whether Demetrius's forehead is muddy. It is publicly announced that Demetrius does not know whether Demetrius's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Stacey can now know that Demetrius can know that Demetrius's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Demetrius","Stacey"],"index":48591,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9349743724,"difficulty":0.0650256276}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Brenda can now know whether Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ralph","Brenda","Nancy","Gary"],"index":3801,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997395873,"difficulty":0.0002604127}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas does not know whether Douglas's forehead is muddy. It is publicly announced that Robin knows whether or not nobody's forehead is muddy. It is publicly announced that Robin does not know whether Robin's forehead is muddy. It is publicly announced that Rick knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Rick can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Douglas","Robin","Rick"],"index":52736,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984140396,"difficulty":0.0015859604}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy does not know whether Judy's forehead is muddy. It is publicly announced that Debra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Judy can now know that Debra can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Judy","Delmer","Debra"],"index":454,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984974861,"difficulty":0.0015025139}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessie is not thirsty. It is publicly announced that Jessie knows whether Jessie is thirsty. It is publicly announced that Jessie does not know whether Lorri is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Agustin can now know whether Jessie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessie","Lorri","Agustin"],"index":34052,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clara does not know whether or not everyone's forehead is muddy. It is publicly announced that Clara's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Joshua can now know that Clara can know that Clara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joshua","Carolyn","Clara","Joanne"],"index":48983,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8891712427,"difficulty":1.8891712427}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Franklyn's card is shown to Franklyn. Anglea's card is shown to Franklyn. Anglea's card is shown to Anglea. It is publicly announced that someone picked a red card. It is publicly announced that Anglea does not know whether Franklyn picked a red card. It is publicly announced that Anglea does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Anglea can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Franklyn","Anglea"],"index":62225,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977846742,"difficulty":0.0022153258}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Christine can now know whether Christine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nathan","Scott","Christopher","Christine"],"index":35854,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6880894303,"difficulty":0.3119105697}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Heather can now know whether Laurie can know whether Patrick is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patrick","Heather","Laurie"],"index":4064,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992311001,"difficulty":0.0007688999}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie does not know whether Stephanie's forehead is muddy. It is publicly announced that Jayme does not know whether Jayme's forehead is muddy. It is publicly announced that Billi knows whether Billi's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Stephanie can now know whether Jayme can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jayme","Billi","Stephanie"],"index":61473,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9961432815,"difficulty":0.0038567185}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas knows whether someone's forehead is muddy. It is publicly announced that Nicholas knows whether Dong's forehead is muddy. It is publicly announced that Dong's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] Agentc knows that (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"Nicholas can now know that Dong can know whether Nicholas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dong","Gary","Nicholas"],"index":15284,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9975277781,"difficulty":0.0024722219}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juanita does not know whether Solomon is thirsty. It is publicly announced that Juanita does not know whether or not everyone is thirsty. It is publicly announced that Jason knows whether Juanita is thirsty. It is publicly announced that Solomon does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Solomon can now know that Juanita can know whether Juanita is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Juanita","Solomon"],"index":16221,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989020824,"difficulty":0.0010979176}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosetta knows whether Rosetta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Brian can now know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Rosetta","Charles"],"index":52237,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983587861,"difficulty":0.0016412139}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Errol's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Dave can now know that Micheal's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Micheal","Dave","Todd","Errol"],"index":42669,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996340394,"difficulty":0.003659606}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Henry does not know whether Richard is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Richard knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Henry can now know whether Marvin can know that Marvin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Marvin","Henry"],"index":42271,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6887310147,"difficulty":1.6887310147}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zachary's card is shown to Ronald. Eric's card is shown to Ronald. Zachary's card is shown to Eric. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ronald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Zachary","Eric"],"index":52536,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983316064,"difficulty":0.0016683936}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Michael can now know that David can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Michael"],"index":27452,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992710948,"difficulty":0.0007289052}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Patricia's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Robert","Patricia"],"index":60838,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.917822063,"difficulty":0.082177937}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Thomas can now know whether Charles can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Philip","Charles","Melba","Thomas"],"index":55808,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997144341,"difficulty":0.0002855659}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Bonnie can now know that Bonnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Bonnie","Kimberly"],"index":35486,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.996741116,"difficulty":0.003258884}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwight's card is shown to John. Antonette's card is shown to John. William's card is shown to John. William's card is shown to Dwight. John's card is shown to Antonette. Dwight's card is shown to Antonette. Antonette's card is shown to Antonette. John's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Dwight does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1,2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 Agentc:1,2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know whether Antonette can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Dwight","Antonette","William"],"index":45445,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9940828681,"difficulty":1.9940828681}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ricky knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey does not know whether Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jeffrey can now know that Crystal's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffrey","Crystal","Ricky"],"index":6030,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948838353,"difficulty":0.0051161647}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mary can now know that Jennifer can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Mary","David"],"index":26232,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983873367,"difficulty":0.0016126633}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa is not thirsty. It is publicly announced that Joyce knows whether Lisa is thirsty. It is publicly announced that Joyce is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! 1 ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! 1 ] 0","hypothesis":"William can now know that Phillip can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","William","Phillip","Lisa"],"index":43348,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6553952694,"difficulty":1.6553952694}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Lyle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"George can now know whether Todd's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rosie","Todd","Lyle","George"],"index":34081,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994617105,"difficulty":0.0005382895}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dominick's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Dominick can now know whether Brenda can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dominick","Brenda"],"index":66673,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7313465476,"difficulty":0.2686534524}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Elizabeth. Elizabeth's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Gary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Elizabeth can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Elizabeth","Gary"],"index":7573,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985679388,"difficulty":0.0014320612}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mila knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Stephanie can now know that Mila can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stephanie","Mila"],"index":52396,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983332753,"difficulty":0.0016667247}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to Erin. Erin's card is shown to Kathy. It is publicly announced that someone picked a red card. It is publicly announced that Kathy does not know whether Candace picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Erin can now know that Erin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erin","Kathy","Candace"],"index":52784,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9743359685,"difficulty":0.0256640315}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Elizabeth. Elizabeth's card is shown to Charles. Charles's card is shown to Sharon. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Sharon picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Michelle can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michelle","Elizabeth","Charles","Sharon"],"index":58034,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9400036931,"difficulty":0.0599963069}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether or not nobody's forehead is muddy. It is publicly announced that Anthony knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Paul can now know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Paul","Anthony"],"index":27911,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994749427,"difficulty":0.0005250573}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnold's card is shown to Arnold. Arnold's card is shown to Brian. Helen's card is shown to Brian. Arnold's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether Helen picked a red card. It is publicly announced that Brian knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Brian can now know that Arnold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arnold","Brian","Helen"],"index":55180,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9878758192,"difficulty":0.0121241808}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Natalie knows whether Randy's forehead is muddy. It is publicly announced that George's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Natalie can now know that Randy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Natalie","Randy","Thomas"],"index":39452,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985651374,"difficulty":0.0014348626}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karla does not know whether Laura is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Karla can now know that Laura can know whether Esther is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Laura","Esther","Karla"],"index":24345,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981443882,"difficulty":0.0018556118}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louise does not know whether Patricia is thirsty. It is publicly announced that Patricia does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Ellis can now know whether Louise is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lori","Patricia","Louise","Ellis"],"index":61747,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8041302562,"difficulty":1.8041302562}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia knows whether Patricia is thirsty. It is publicly announced that Mary does not know whether Duane is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mary can now know that Patricia can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Patricia","Duane"],"index":54013,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Cindy. Joan's card is shown to Michael. Cindy's card is shown to Joan. Joan's card is shown to Joan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cindy","Michael","Joan"],"index":64606,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925869107,"difficulty":0.0074130893}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandra's card is shown to Sandra. Amber's card is shown to Markus. Markus's card is shown to Markus. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Sandra can now know that Amber can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amber","Sandra","Markus"],"index":63809,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930039048,"difficulty":0.0069960952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barry does not know whether Anne is thirsty. It is publicly announced that Barry does not know whether Latarsha is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Ernestine can now know whether Anne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ernestine","Anne","Barry","Latarsha"],"index":47407,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9930643439,"difficulty":0.0069356561}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Duane knows whether Duane is thirsty. It is publicly announced that Latonya does not know whether Sean is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sean can now know whether Latonya can know that Sean is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Duane","Sean","Latonya"],"index":9518,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9933199883,"difficulty":0.0066800117}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha knows whether someone is thirsty. It is publicly announced that Edith does not know whether Leesa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Martha can now know whether Edith is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Martha","Edith","Leesa"],"index":66636,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9950892329,"difficulty":0.0049107671}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Rose. Jane's card is shown to Matthew. Eleanor's card is shown to Eleanor. Matthew's card is shown to Jane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jane can now know that Rose can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Matthew","Eleanor","Jane"],"index":9235,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983094931,"difficulty":0.0016905069}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Ronald. Charles's card is shown to Ronald. Laura's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Charles picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ronald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Charles","Laura"],"index":27669,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998470366,"difficulty":0.001529634}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlie's card is shown to Kathy. Patricia's card is shown to Shelia. Kathy's card is shown to Patricia. Shelia's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlie can now know that Kathy can know whether Kathy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlie","Kathy","Shelia","Patricia"],"index":29963,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.693003118,"difficulty":1.693003118}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Ernest's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ernest can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ernest","Charles","Louella","Eric"],"index":26559,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997355342,"difficulty":0.0002644658}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anne can now know whether Karina can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karina","Anne","Micheal"],"index":19418,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997516274,"difficulty":0.0002483726}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samuel does not know whether or not everyone is thirsty. It is publicly announced that Tanner does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Tanner can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Tanner","Mary","Samuel"],"index":5729,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8464292884,"difficulty":0.1535707116}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"William can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Betty","William"],"index":66361,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998136282,"difficulty":0.001863718}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samantha knows whether Jessie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jessie can now know that Joshua's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joshua","Jessie","Samantha"],"index":52340,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984139204,"difficulty":0.0015860796}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Diane. William's card is shown to Diane. Shirley's card is shown to Shirley. William's card is shown to Shirley. Dorothy's card is shown to Shirley. Shirley's card is shown to William. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Shirley knows whether Dorothy picked a red card. It is publicly announced that Dorothy does not know whether Diane picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Dorothy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diane","Shirley","William","Dorothy"],"index":774,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985419512,"difficulty":0.0014580488}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Howard. Jason's card is shown to Howard. Jason's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Howard can now know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Howard","Jason","Matthew"],"index":61076,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.863888979,"difficulty":0.136111021}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jason knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Mary can now know that Marlene can know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Marlene","Mary"],"index":59162,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9954161644,"difficulty":0.0045838356}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley does not know whether Elma is thirsty. It is publicly announced that Shirley does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Elma can now know whether Shirley can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Shirley","Michael","Elma"],"index":39095,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997007847,"difficulty":0.0002992153}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harry's card is shown to Harry. Roy's card is shown to Michael. Amber's card is shown to Amber. Michael's card is shown to Roy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amber can now know whether Roy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harry","Michael","Amber","Roy"],"index":38665,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9943776727,"difficulty":0.0056223273}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy. It is publicly announced that William's forehead is muddy. It is publicly announced that Lisa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Lisa can now know that Tennie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","William","Lisa","Tennie"],"index":30482,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8923054338,"difficulty":0.1076945662}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Alvin. Rebecca's card is shown to Alvin. Rebecca's card is shown to Rebecca. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rebecca can now know whether Charles can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Alvin","Rebecca"],"index":21751,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997005463,"difficulty":0.0002994537}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ana knows whether Mary's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Micheal can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Micheal","Ana","Mary"],"index":6195,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8771349192,"difficulty":1.8771349192}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Willie can now know that Esther can know that Rick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Willie","Esther","Annie","Rick"],"index":52563,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9560382962,"difficulty":0.0439617038}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott knows whether someone is thirsty. It is publicly announced that Catherine does not know whether Scott is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Scott can now know whether Catherine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Scott","Maurice","Catherine"],"index":53157,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9946016073,"difficulty":0.0053983927}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michele's card is shown to Patricia. Ralph's card is shown to Ralph. Patricia's card is shown to Jeff. Patricia's card is shown to Michele. Ralph's card is shown to Michele. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michele can now know that Ralph can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Ralph","Jeff","Michele"],"index":64976,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Margaret can now know whether Stacey is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stacey","Margaret","Abbie"],"index":30334,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978583455,"difficulty":0.0021416545}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"James can now know that Jacqueline can know that Jacqueline is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","James","Jacqueline"],"index":52694,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982227683,"difficulty":0.0017772317}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jared knows whether Jared's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Charles can now know that Jared can know whether Jared's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jared","Charles"],"index":48413,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995158911,"difficulty":0.0004841089}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alex is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Alex can now know that Cheryl can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cheryl","Alex","Michael"],"index":2487,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984502792,"difficulty":0.0015497208}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Mary is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Isabel can now know that Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","Isabel"],"index":26954,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8247140646,"difficulty":0.1752859354}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roberta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Roberta can now know that Claude's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Claude","Roberta","Jamal"],"index":53312,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9608706236,"difficulty":0.0391293764}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jill's card is shown to Jill. Jill's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Jill can now know that Matthew can know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jill","Matthew"],"index":55331,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948688745,"difficulty":0.0051311255}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobbie's card is shown to Bobbie. Fawn's card is shown to Bobbie. Fawn's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bobbie can now know whether Brian can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bobbie","Brian","Fawn"],"index":47829,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994033575,"difficulty":0.0005966425}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerome knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Hector can now know whether Philip is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Philip","Kathryn","Hector","Jerome"],"index":30098,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972547889,"difficulty":0.0027452111}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"George can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["George","Arthur"],"index":43868,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988441467,"difficulty":0.0011558533}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeff knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Jeff can now know that Cora can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cora","Christie","Jeff"],"index":54396,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993835688,"difficulty":0.0006164312}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Douglas does not know whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Donna can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Douglas","Daniel"],"index":46399,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989982247,"difficulty":0.0010017753}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Meagan's card is shown to Meagan. Nathaniel's card is shown to Meagan. Lawrence's card is shown to Meagan. Lawrence's card is shown to Nathaniel. Lawrence's card is shown to Lawrence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Meagan can now know whether Nathaniel can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Meagan","Nathaniel","Lawrence"],"index":62116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99925071,"difficulty":0.00074929}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bertha's forehead is muddy. It is publicly announced that Bertha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Bertha can now know that Kenneth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amber","Gail","Bertha","Kenneth"],"index":7037,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.901879847,"difficulty":1.901879847}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittni's card is shown to James. Thomas's card is shown to James. Ashleigh's card is shown to Ashleigh. Thomas's card is shown to Ashleigh. James's card is shown to Brittni. Ashleigh's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Brittni can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Ashleigh","Brittni","Thomas"],"index":12170,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992181063,"difficulty":0.0007818937}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Elaine can now know that John can know that Elaine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","Reginald","Elaine","John"],"index":59679,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984840751,"difficulty":0.0015159249}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shawanda's card is shown to Al. Sophie's card is shown to Sophie. Shawanda's card is shown to Sophie. Shawanda's card is shown to Shawanda. It is publicly announced that someone picked a red card. It is publicly announced that Shawanda does not know whether Sophie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Al can now know whether Shawanda can know that Shawanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Al","Sophie","Shawanda"],"index":13173,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8449754715,"difficulty":0.1550245285}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindie's card is shown to Ashley. Robin's card is shown to Robin. Ashley's card is shown to Cindie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know whether Ashley can know that Ashley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ashley","Robin","Cynthia","Cindie"],"index":2083,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9542936683,"difficulty":0.0457063317}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel's forehead is muddy. It is publicly announced that Laura knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Darcie can now know that Laura can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Darcie","Daniel","Laura"],"index":59137,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990205765,"difficulty":0.0009794235}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Debbie. Harold's card is shown to Micheal. Debbie's card is shown to Micheal. Micheal's card is shown to Micheal. It is publicly announced that someone picked a red card. It is publicly announced that Harold does not know whether Harold picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Debbie can now know that Debbie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harold","Debbie","Thomas","Micheal"],"index":10553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9913411736,"difficulty":0.0086588264}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Naomi can now know that Mable can know that Theodora's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Naomi","Mable","Theodora"],"index":19269,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975179434,"difficulty":0.0024820566}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elise is thirsty. It is publicly announced that Alfred is not thirsty. It is publicly announced that Lowell does not know whether Elizabeth is thirsty. It is publicly announced that Elise does not know whether Lowell is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lowell can now know whether Elise can know that Lowell is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elise","Lowell","Elizabeth","Alfred"],"index":5731,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9264811873,"difficulty":0.0735188127}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether or not everyone is thirsty. It is publicly announced that Joshua does not know whether or not everyone is thirsty. It is publicly announced that Susan knows whether Susan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Susan can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Manuel","Susan","Joshua","Dorothy"],"index":9369,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987989664,"difficulty":0.0012010336}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy does not know whether or not everyone is thirsty. It is publicly announced that Timothy knows whether or not nobody is thirsty. It is publicly announced that James knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Melba can now know whether Timothy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tabitha","James","Melba","Timothy"],"index":25204,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9924778342,"difficulty":0.0075221658}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janie's card is shown to Janie. Jaime's card is shown to Janie. Janie's card is shown to Damon. Susan's card is shown to Damon. Jaime's card is shown to Damon. Susan's card is shown to Susan. Jaime's card is shown to Susan. Janie's card is shown to Jaime. Jaime's card is shown to Jaime. It is publicly announced that someone picked a red card. It is publicly announced that Damon knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 Agentc:3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 Agentc:3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Janie can now know whether Jaime picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janie","Damon","Susan","Jaime"],"index":25371,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7005489469,"difficulty":0.2994510531}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"James can now know that Dwight can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dwight","James","Scott"],"index":17106,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994571805,"difficulty":0.0005428195}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Ernest knows whether Marisol's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Marisol can now know that Kara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sue","Ernest","Marisol","Kara"],"index":25358,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957404137,"difficulty":0.0042595863}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jessica can now know whether Alton can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wanda","Blake","Alton","Jessica"],"index":17970,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992511868,"difficulty":0.0007488132}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phillip knows whether someone is thirsty. It is publicly announced that Phillip knows whether Phillip is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] [ ! (1&2) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Phillip can now know whether Harold is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harold","Phillip"],"index":2335,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9972019196,"difficulty":0.0027980804}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis does not know whether William is thirsty. It is publicly announced that Michele knows whether or not nobody is thirsty. It is publicly announced that William does not know whether Michele is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"William can now know whether Michele can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Michele","Dennis"],"index":39919,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994531274,"difficulty":0.0005468726}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Tina can now know whether Gregory can know whether Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Omer","Donnell","Tina","Gregory"],"index":24299,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994619489,"difficulty":0.0005380511}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Melissa can now know whether Rebecca can know whether Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rebecca","Melissa","Connie"],"index":35079,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999456346,"difficulty":0.000543654}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin does not know whether Floyd is thirsty. It is publicly announced that David knows whether someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Jonna does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Justin can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Justin","Floyd","Jonna","David"],"index":59540,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994704127,"difficulty":0.0005295873}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna knows whether Donna is thirsty. It is publicly announced that Laci does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Donna can now know that Michael can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Laci","Donna","Michael"],"index":12250,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9832444191,"difficulty":0.0167555809}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Christopher does not know whether Mark is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mark can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","Christopher","Curt","Andrea"],"index":18628,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994356036,"difficulty":0.0005643964}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debra knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Michelle can now know that Michelle is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Delia","Debra","Michelle"],"index":36881,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9773538709,"difficulty":0.0226461291}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Jamal can now know that George can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jamal","Jason","George"],"index":19170,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.844162643,"difficulty":1.844162643}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Danny knows whether or not nobody is thirsty. It is publicly announced that Anthony does not know whether Dennis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Dennis can now know whether Anthony can know whether Dennis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Anthony","Dennis","Danny"],"index":38199,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998940289,"difficulty":0.001059711}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alice does not know whether Betty is thirsty. It is publicly announced that Alice does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Norman can now know whether Brittany can know whether Norman is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Betty","Brittany","Norman"],"index":47174,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990007281,"difficulty":0.0009992719}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know whether Barbara can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phillip","Barbara","John"],"index":30918,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994157553,"difficulty":0.0005842447}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Stella can now know that Rosemary can know whether Stella's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Stella","Rosemary"],"index":34518,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992824197,"difficulty":0.0007175803}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosetta's forehead is muddy. It is publicly announced that Rosetta's forehead is muddy. It is publicly announced that Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Consuelo can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Consuelo","Jane","Rosetta"],"index":45407,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985858202,"difficulty":0.0014141798}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mildred's forehead is not muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Mildred can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mildred","David","Mary"],"index":41809,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994884729,"difficulty":0.0005115271}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Louis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Steven can now know that Eva can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steven","Louis","Eva"],"index":11921,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9922093153,"difficulty":0.0077906847}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catalina knows whether or not everyone's forehead is muddy. It is publicly announced that Martha knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Catalina can now know that Frances can know that Catalina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frances","Catalina","Terry","Martha"],"index":51335,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980973601,"difficulty":0.0019026399}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to Stephen. Frank's card is shown to June. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"June can now know that Stephen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephen","June","Frank"],"index":60565,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988155365,"difficulty":0.0011844635}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steve's card is shown to Marvin. Lynne's card is shown to Marvin. Marvin's card is shown to Richard. Steve's card is shown to Richard. Richard's card is shown to Steve. Steve's card is shown to Steve. Lynne's card is shown to Steve. Marvin's card is shown to Lynne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marvin can now know that Richard can know that Steve picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","Richard","Steve","Lynne"],"index":37809,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978197813,"difficulty":0.0021802187}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cheryl knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Allen can now know whether Dick can know whether Allen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Dick","Allen","Alice"],"index":51934,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991018772,"difficulty":0.0008981228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether Richard is thirsty. It is publicly announced that Scott does not know whether or not everyone is thirsty. It is publicly announced that Scott does not know whether Richard is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Eric can now know whether Richard can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Iva","Richard","Eric","Scott"],"index":12830,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9874780178,"difficulty":0.0125219822}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mose can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Charlotte","Mose","Michael"],"index":48852,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9890283346,"difficulty":0.0109716654}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that Joel can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Veronica","Mary","Joel"],"index":40808,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993626475,"difficulty":0.0006373525}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Michael. Matthew's card is shown to Margie. Grace's card is shown to Grace. Margie's card is shown to Matthew. Grace's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Grace does not know whether Margie picked a red card. It is publicly announced that Michael knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Matthew can now know that Michael can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Margie","Grace","Matthew"],"index":63915,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994516969,"difficulty":0.0005483031}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Mary can now know whether Luis can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Kimberly","Luis"],"index":56320,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995185137,"difficulty":0.0004814863}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eunice's card is shown to Kathleen. Danielle's card is shown to Danielle. Eunice's card is shown to Danielle. Eunice's card is shown to Eunice. It is publicly announced that someone picked a red card. It is publicly announced that Eunice does not know whether Danielle picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Kathleen can now know that Eunice can know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathleen","Danielle","Eunice"],"index":50347,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975630045,"difficulty":0.0024369955}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Janice can now know that Troy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janice","Troy"],"index":66485,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993502498,"difficulty":0.0006497502}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Oliver can now know whether Peter can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Esther","Gary","Peter","Oliver"],"index":17791,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994514585,"difficulty":0.0005485415}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Jayna. Kathryn's card is shown to Lisa. Lisa's card is shown to Douglas. Kathryn's card is shown to Douglas. Jayna's card is shown to Kathryn. Lisa's card is shown to Kathryn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know whether Jayna can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jayna","Lisa","Douglas","Kathryn"],"index":46413,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994009733,"difficulty":0.0005990267}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Billy. Alfred's card is shown to Billy. Marion's card is shown to Eddie. Billy's card is shown to Alfred. Alfred's card is shown to Alfred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Billy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","Eddie","Marion","Alfred"],"index":46396,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993754029,"difficulty":0.0006245971}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Gigi can now know whether William can know that Gigi's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Gigi","Alice"],"index":15435,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9897521734,"difficulty":0.0102478266}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kurt can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Olive","Rebecca","Kurt","Michelle"],"index":33173,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994406104,"difficulty":0.0005593896}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Janet can now know that Mary can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lyndsey","Janet","Carlos","Mary"],"index":5964,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9808457494,"difficulty":0.0191542506}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Patricia's card is shown to Patricia. Jeremy's card is shown to Daniel. Jeremy's card is shown to Jeremy. It is publicly announced that someone picked a red card. It is publicly announced that Jeremy does not know whether Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Patricia can now know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Patricia","Daniel","Jeremy"],"index":19225,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9842018485,"difficulty":0.0157981515}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louis knows whether Louis is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Addie can now know whether Louis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terrell","Addie","Louis"],"index":30303,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9542816281,"difficulty":1.9542816281}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lonnie's card is shown to Jo. Jo's card is shown to Lonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Jo can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jo","Lonnie"],"index":12819,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993461967,"difficulty":0.0006538033}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that Troy does not know whether Troy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Marty can now know whether Troy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marty","Charles","Troy"],"index":59331,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999278605,"difficulty":0.000721395}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cassandra knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Cassandra can now know that Cheryl can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cassandra","Cheryl"],"index":44880,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988213181,"difficulty":0.0011786819}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Elizabeth can now know that Frank can know that Fernando is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frank","Elizabeth","Fernando"],"index":22884,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974859953,"difficulty":0.0025140047}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly knows whether or not nobody is thirsty. It is publicly announced that Lavon does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Teri can now know whether Lavon can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Teri","Lavon","Kimberly"],"index":67320,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.994705379,"difficulty":0.005294621}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nina does not know whether Ray is thirsty. It is publicly announced that Helen is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Ray can now know that Ray is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ray","Nina","Helen"],"index":44162,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9877620935,"difficulty":0.0122379065}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonas's card is shown to Deborah. Zachery's card is shown to Deborah. Deborah's card is shown to Mary. Jonas's card is shown to Mary. Mary's card is shown to Jonas. Jonas's card is shown to Jonas. Zachery's card is shown to Jonas. Deborah's card is shown to Zachery. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2,3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Zachery can now know that Mary can know whether Jonas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Mary","Jonas","Zachery"],"index":54860,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5642182231,"difficulty":0.4357817769}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wallace knows whether someone's forehead is muddy. It is publicly announced that Bradley does not know whether or not everyone's forehead is muddy. It is publicly announced that Wallace knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Bradley can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bradley","Wallace"],"index":20707,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996960938,"difficulty":0.003039062}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne knows whether Tammy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Freda can now know that Freda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Yvonne","Stephanie","Tammy","Freda"],"index":34067,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998323977,"difficulty":0.001676023}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Robert can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Juanita","Karen","Deborah"],"index":9509,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984248877,"difficulty":0.0015751123}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Mary's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Mark can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mark","Mary"],"index":54360,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9882277846,"difficulty":0.0117722154}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bill is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Lynn can now know that Sandra can know whether Lynn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Bill","Rose","Lynn"],"index":13290,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5357995629,"difficulty":0.4642004371}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita does not know whether Kathleen is thirsty. It is publicly announced that Patricia does not know whether Kathleen is thirsty. It is publicly announced that Kathleen does not know whether Anita is thirsty. It is publicly announced that Anita is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agenta knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Patricia can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Kathleen","Anita"],"index":49810,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994480014,"difficulty":0.0005519986}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Alfredo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Joseph can now know whether Alfredo can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","James","Alfredo"],"index":45135,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994406104,"difficulty":0.0005593896}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dale can now know that Jose can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dale","Jose","James"],"index":22577,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994803071,"difficulty":0.0005196929}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Daniel can now know whether David can know that Bill's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Kenneth","Bill","David"],"index":51958,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994439483,"difficulty":0.0005560517}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josephine's card is shown to Marian. Kristy's card is shown to Josephine. Kristy's card is shown to Kristy. It is publicly announced that someone picked a red card. It is publicly announced that Kristy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kristy can now know whether Josephine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marian","Josephine","Kristy"],"index":59017,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992873073,"difficulty":0.0007126927}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverlee does not know whether Beverlee's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Frank can now know that Frank's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beverlee","Frank","Gloria","Alicia"],"index":8046,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9919962287,"difficulty":0.0080037713}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosemarie knows whether Rosemarie is thirsty. It is publicly announced that Lynwood does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Megan can now know that Lynwood can know whether Lynwood is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosemarie","Lynwood","Megan"],"index":66797,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9873429537,"difficulty":0.0126570463}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Jonathan can now know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Anthony","Jonathan"],"index":59560,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6108977199,"difficulty":1.6108977199}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gussie knows whether Federico's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Bobbie can now know that Gussie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Federico","Gussie","Candy","Bobbie"],"index":1600,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980199337,"difficulty":0.0019800663}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jon knows whether or not nobody's forehead is muddy. It is publicly announced that Verena does not know whether Verena's forehead is muddy. It is publicly announced that Verena does not know whether Verena's forehead is muddy. It is publicly announced that Verena does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Verena can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marie","Jon","Verena"],"index":58964,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994391799,"difficulty":0.0005608201}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Wesley is thirsty. It is publicly announced that Steven does not know whether Wesley is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Wesley can now know that Steven can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Jeremy","John","Wesley"],"index":21303,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994322658,"difficulty":0.0005677342}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Harvey's card is shown to Robert. Harvey's card is shown to Harvey. It is publicly announced that someone picked a red card. It is publicly announced that Harvey picked a red card. It is publicly announced that Harvey does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Harvey can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Harvey"],"index":26838,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6589302421,"difficulty":0.3410697579}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Jeanne. Adam's card is shown to Donald. Christina's card is shown to Adam. Adam's card is shown to Christina. It is publicly announced that someone picked a red card. It is publicly announced that Adam does not know whether or not everyone picked a red card. It is publicly announced that Jeanne does not know whether Jeanne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Donald can now know whether Christina can know whether Jeanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeanne","Donald","Adam","Christina"],"index":18874,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979193807,"difficulty":0.0020806193}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Lynn can now know whether Sandra can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Lynn","Greg","Francisco"],"index":54520,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994494319,"difficulty":0.0005505681}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Warren knows whether Hazel's forehead is muddy. It is publicly announced that Warren knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Clyde can now know whether Lillian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lillian","Clyde","Hazel","Warren"],"index":37083,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994182587,"difficulty":0.0005817413}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Celia is thirsty. It is publicly announced that Celia does not know whether Amanda is thirsty. It is publicly announced that Celia is thirsty. It is publicly announced that Celia knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Celia can now know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Celia","Amanda","Mary"],"index":14321,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9900892973,"difficulty":0.0099107027}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jennifer can now know whether Daniel can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Daniel"],"index":28103,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993876219,"difficulty":0.0006123781}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristine's card is shown to Roy. Cristine's card is shown to Jared. Cristine's card is shown to Cristine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know that Roy can know whether Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roy","Jared","Ruth","Cristine"],"index":39652,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993827641,"difficulty":0.006172359}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois knows whether someone's forehead is muddy. It is publicly announced that Ruth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lois","Ruth","Mary","Daniel"],"index":6541,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992715716,"difficulty":0.0007284284}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that Ted does not know whether or not everyone's forehead is muddy. It is publicly announced that Thomas knows whether Ted's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Ted can now know that Ted's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Ted","Bernice","Thomas"],"index":17028,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5266287327,"difficulty":0.4733712673}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holly's card is shown to James. Kathryn's card is shown to James. Holly's card is shown to Charles. Kathryn's card is shown to Charles. Charles's card is shown to Kathryn. Kathryn's card is shown to Kathryn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Holly can know that Holly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Charles","Holly","Kathryn"],"index":46017,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8750053644,"difficulty":0.1249946356}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith does not know whether Judith's forehead is muddy. It is publicly announced that Judith's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agenta knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Jeffrey can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Reginald","Judith","Mary"],"index":36382,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980080724,"difficulty":0.0019919276}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Daniel's card is shown to Dorothy. Dorothy's card is shown to Daniel. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy picked a black card. It is publicly announced that Daniel knows whether or not nobody picked a red card. It is publicly announced that Daniel knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Daniel can now know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dorothy","Daniel"],"index":46841,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8283134699,"difficulty":0.1716865301}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bonnie can now know that Mary can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Mary","Jacob","Bonnie"],"index":39151,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979368448,"difficulty":0.0020631552}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Cody does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that James can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cody","Charles","James"],"index":2657,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994674325,"difficulty":0.0005325675}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Helen can now know that Lee can know whether Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lee","Helen"],"index":32320,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994414449,"difficulty":0.0005585551}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathleen can now know whether Carl can know that Kathleen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edward","Kathleen","Carl"],"index":22891,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969160557,"difficulty":0.0030839443}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Jeffrey. Frank's card is shown to Frank. Margaret's card is shown to Rodney. Jeffrey's card is shown to Margaret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know whether Margaret can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Frank","Rodney","Margaret"],"index":59046,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7706487775,"difficulty":0.2293512225}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Angelina. Angelina's card is shown to James. James's card is shown to James. Joseph's card is shown to James. Angelina's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angelina","James","Joseph"],"index":54582,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966307282,"difficulty":0.0033692718}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"John can now know that Pauline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Loretta","Norbert","Pauline"],"index":24583,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.993478179,"difficulty":0.006521821}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geneva knows whether Ryan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Geneva can now know that David can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Ryan","Geneva"],"index":3263,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993268251,"difficulty":0.0006731749}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sean does not know whether or not everyone is thirsty. It is publicly announced that Sean does not know whether Anita is thirsty. It is publicly announced that Troy does not know whether Anita is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Anita can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Troy","Anita","Sean"],"index":57412,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9950915575,"difficulty":0.0049084425}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy does not know whether Roy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Roy can now know that John can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jamie","Keith","John","Roy"],"index":37483,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994295239,"difficulty":0.0005704761}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether Beth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Beth can now know that Gregory can know that Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gregory","Beth","Rose"],"index":33197,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978952408,"difficulty":0.0021047592}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Corina's card is shown to Corina. Corina's card is shown to Judith. Brandon's card is shown to Judith. Judith's card is shown to Brandon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Judith can now know that Corina can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Corina","Judith","Brandon"],"index":40240,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9916732907,"difficulty":0.0083267093}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Walter. Walter's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Robert picked a red card. It is publicly announced that Robert does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Walter can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Walter","Robert"],"index":56474,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990459085,"difficulty":0.0009540915}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Matthew can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Matthew"],"index":51427,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993615746,"difficulty":0.0006384254}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alvin knows whether someone's forehead is muddy. It is publicly announced that Teresa does not know whether or not everyone's forehead is muddy. It is publicly announced that Alvin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Teresa can now know whether Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Teresa","Alvin"],"index":51495,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6517314315,"difficulty":0.3482685685}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorraine does not know whether Lorraine's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Marina knows whether or not everyone's forehead is muddy. It is publicly announced that Marina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] Agentc knows whether (Agentd knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Lorraine can now know whether Thomas can know that Lorraine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Marina","Lorraine","Thomas"],"index":37973,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9658320546,"difficulty":0.0341679454}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Marylou is thirsty. It is publicly announced that Mozella does not know whether or not everyone is thirsty. It is publicly announced that John does not know whether Kevin is thirsty. It is publicly announced that Marylou knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Mozella can now know whether Kevin can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marylou","John","Mozella","Kevin"],"index":63762,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994157553,"difficulty":0.0005842447}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Richard's card is shown to Georgianna. Anthony's card is shown to Nancy. Richard's card is shown to Nancy. Nancy's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Anthony can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Georgianna","Nancy","Richard"],"index":60080,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5027320981,"difficulty":1.5027320981}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tom does not know whether Phyllis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mary can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Phyllis","Tom","Mary"],"index":15453,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993447661,"difficulty":0.0006552339}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Benjamin can now know that John can know whether Benjamin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Benjamin"],"index":15234,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9683125615,"difficulty":0.0316874385}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia does not know whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Cynthia can now know that Charles can know that Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cynthia","Joy","Charles"],"index":27361,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948245287,"difficulty":0.0051754713}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura is thirsty. It is publicly announced that Laura does not know whether Matthew is thirsty. It is publicly announced that Robert does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jesus can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Jesus","Matthew","Laura"],"index":4707,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999008894,"difficulty":0.000991106}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Marco's card is shown to Mark. Raymond's card is shown to Mark. Marco's card is shown to Marco. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marco can now know whether Mark can know that Raymond picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Marco","Raymond"],"index":57729,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8751494884,"difficulty":1.8751494884}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Teresa can now know whether Janet can know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donna","Janet","Teresa"],"index":20635,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993736148,"difficulty":0.0006263852}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Dayle's card is shown to Linda. Douglas's card is shown to Linda. Dayle's card is shown to Dayle. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Douglas can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Linda","Dayle","Douglas"],"index":45120,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994180202,"difficulty":0.0005819798}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise knows whether Gabriel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Amber can now know whether Paul can know that Gabriel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gabriel","Louise","Amber","Paul"],"index":58323,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994615912,"difficulty":0.0005384088}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lola does not know whether Eugene is thirsty. It is publicly announced that Eva does not know whether Eugene is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Sonya can now know that Eugene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eva","Eugene","Lola","Sonya"],"index":44216,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9956572056,"difficulty":0.0043427944}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linwood is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Linwood can now know whether Tanya can know whether Tanya is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linwood","Gilbert","Tanya"],"index":1728,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978215694,"difficulty":0.0021784306}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annette knows whether or not everyone's forehead is muddy. It is publicly announced that Annette knows whether Daniel's forehead is muddy. It is publicly announced that Annette's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Daniel can now know that Annette can know that Annette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Annette","Daniel"],"index":49260,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9599816799,"difficulty":0.0400183201}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice knows whether someone is thirsty. It is publicly announced that Leroy does not know whether Janice is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Ruth can now know that Janice can know that Ruth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruth","Janice","Leroy","Sarah"],"index":21109,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975023866,"difficulty":0.0024976134}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura does not know whether Johnny is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Nohemi can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Patsy","Nohemi","Laura"],"index":14575,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989936948,"difficulty":0.0010063052}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Logan's card is shown to Leo. Holly's card is shown to Logan. Leo's card is shown to Holly. Logan's card is shown to Holly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Holly can now know whether Logan can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leo","Logan","Holly"],"index":28028,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994015694,"difficulty":0.0005984306}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Shane can now know whether Clara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shane","William","Rose","Clara"],"index":10600,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973424077,"difficulty":0.0026575923}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Ollie is thirsty. It is publicly announced that Ollie does not know whether Brian is thirsty. It is publicly announced that Julia does not know whether or not everyone is thirsty. It is publicly announced that Ollie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Ollie can now know that Ollie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ollie","Brian","Julia"],"index":26674,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8469185233,"difficulty":1.8469185233}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly's forehead is not muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jeff can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeff","Angelina","Beverly","Joseph"],"index":44976,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994934797,"difficulty":0.0005065203}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Thelma can now know that Jose can know that Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jose","Virginia","Thelma"],"index":58707,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9471739531,"difficulty":1.9471739531}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bradly's card is shown to Bradly. Kelly's card is shown to Tracy. Kelly's card is shown to Deanna. It is publicly announced that someone picked a red card. It is publicly announced that Tracy does not know whether Bradly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Kelly can now know that Tracy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Bradly","Tracy","Deanna"],"index":37543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9892942905,"difficulty":0.0107057095}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether Guadalupe is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Barbara can now know that Patricia can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Barbara","Guadalupe","Sandra"],"index":5468,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989851117,"difficulty":0.0010148883}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether or not nobody is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Michele can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Armando","Michele"],"index":48831,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9018855691,"difficulty":1.9018855691}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roger does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Pamela can now know that Robert can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roger","Pamela","Robert"],"index":18646,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980022311,"difficulty":0.0019977689}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Matthew can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Matthew","Oscar"],"index":58113,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9929915667,"difficulty":0.0070084333}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Edward. Edward's card is shown to Tommy. It is publicly announced that someone picked a red card. It is publicly announced that Edward knows whether someone picked a red card. It is publicly announced that Tommy knows whether Tommy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Edward can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edward","Tommy"],"index":61746,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.95588696,"difficulty":1.95588696}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Boyd can now know whether Boyd's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hazel","Boyd","Denise"],"index":66865,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994227886,"difficulty":0.0005772114}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Sharon. Larry's card is shown to Sharon. Sharon's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Sharon can now know whether Larry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sharon","Larry"],"index":64162,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9045239687,"difficulty":1.9045239687}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Matthew can now know whether Amy can know whether Diana is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Amy","Clara","Diana"],"index":21153,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991868138,"difficulty":0.0008131862}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether Alice's forehead is muddy. It is publicly announced that Laura's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Alice can now know whether Alice's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alice","Laura"],"index":13200,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7883610725,"difficulty":1.7883610725}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rudolph's card is shown to Ronald. Rudolph's card is shown to Bryan. Rudolph's card is shown to Rudolph. It is publicly announced that someone picked a red card. It is publicly announced that Bryan does not know whether Ronald picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Bryan picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Ronald can now know that Bryan can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Bryan","Rudolph"],"index":64018,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988019466,"difficulty":0.0011980534}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myrtle does not know whether Cody is thirsty. It is publicly announced that Myrtle does not know whether Cole is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Cody can now know that Dawn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cody","Myrtle","Dawn","Cole"],"index":46457,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982604384,"difficulty":0.0017395616}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Dennis. Antoinette's card is shown to Dennis. Frank's card is shown to Dennis. Dennis's card is shown to Antoinette. Dennis's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Frank can now know whether Antoinette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Antoinette","Frank"],"index":4058,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5173355341,"difficulty":0.4826644659}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda knows whether someone is thirsty. It is publicly announced that Abraham does not know whether Clarence is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Linda knows whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Abraham can now know that Tommie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clarence","Tommie","Linda","Abraham"],"index":51487,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999337256,"difficulty":0.000662744}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Chang can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nathan","Chang","Stephanie"],"index":3196,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9879084229,"difficulty":0.0120915771}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether someone's forehead is muddy. It is publicly announced that Willie knows whether Eugene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Ruth can now know whether Eugene can know whether Eugene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Eugene","Michael","Willie"],"index":53319,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994276166,"difficulty":0.0005723834}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dianne knows whether someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Christopher can now know that Dianne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dianne","Christopher","Angelica","Irma"],"index":37178,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9954906106,"difficulty":0.0045093894}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Owen's card is shown to Marissa. John's card is shown to Owen. Marissa's card is shown to John. Owen's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Owen knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"John can now know that Marissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marissa","Owen","John"],"index":22224,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997535944,"difficulty":0.002464056}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vincent knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Vincent can now know whether Pat can know whether Pat's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vincent","Pat"],"index":67497,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993853569,"difficulty":0.0006146431}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Viola does not know whether Patrick is thirsty. It is publicly announced that Viola does not know whether Jeffrey is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Patrick can now know that Viola can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patrick","Jeffrey","Viola"],"index":64882,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994139671,"difficulty":0.0005860329}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Gladys. Kenneth's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know whether Gladys can know whether Ray picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Gladys","Charles","Ray"],"index":44496,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990112782,"difficulty":0.0009887218}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vernon's card is shown to Sandra. Audrey's card is shown to Audrey. Vernon's card is shown to Vernon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vernon can now know that Audrey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Audrey","Vernon"],"index":18996,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978052974,"difficulty":0.0021947026}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Samuel. Ted's card is shown to Ted. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Samuel does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Samuel can now know that Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Samuel","Ted","Jerry","Mark"],"index":29116,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7118496299,"difficulty":1.7118496299}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Adam. Adam's card is shown to Nelson. Nelson's card is shown to Nelson. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Adam can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Adam","Nelson"],"index":51735,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9905754328,"difficulty":0.0094245672}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fidel's card is shown to Fidel. Jose's card is shown to Jose. Barbara's card is shown to Jose. Jose's card is shown to Barbara. Jose's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that Fidel does not know whether Jose picked a red card. It is publicly announced that Jose picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Annie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Fidel","Jose","Barbara","Annie"],"index":64382,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994646907,"difficulty":0.0005353093}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Anthony's card is shown to Lester. Mike's card is shown to Lester. Anthony's card is shown to Donnie. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether Mike picked a red card. It is publicly announced that Donnie knows whether or not everyone picked a red card. It is publicly announced that Anthony does not know whether Lester picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lester can now know whether Anthony can know whether Donnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Lester","Donnie","Mike"],"index":29648,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997961998,"difficulty":0.002038002}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peggy knows whether Eugene's forehead is muddy. It is publicly announced that Peggy's forehead is not muddy. It is publicly announced that Luisa knows whether Peggy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Peggy can now know whether Luisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Peggy","Eugene","Luisa"],"index":11517,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994576573,"difficulty":0.0005423427}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to John. Jillian's card is shown to Jillian. Jillian's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jillian can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Jillian","Jeffrey"],"index":2960,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9918704033,"difficulty":0.0081295967}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Bruce. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Thomas can now know whether Bruce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bruce","Thomas"],"index":3920,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.880617857,"difficulty":0.119382143}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin does not know whether or not everyone's forehead is muddy. It is publicly announced that Robin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Robin can now know whether Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Pamela","Robin","Loyd","Leann"],"index":48741,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992591739,"difficulty":0.0007408261}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Claude does not know whether Debby is thirsty. It is publicly announced that Genevieve does not know whether Claude is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Genevieve can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Genevieve","Frank","Claude","Debby"],"index":63812,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980871677,"difficulty":0.0019128323}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether James is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"James can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Terri","James"],"index":50162,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989331365,"difficulty":0.0010668635}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Eddie. Gloria's card is shown to Eddie. Gloria's card is shown to Helen. Eddie's card is shown to Carol. Helen's card is shown to Gloria. Carol's card is shown to Gloria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Eddie can know that Eddie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eddie","Helen","Carol","Gloria"],"index":7540,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982335567,"difficulty":0.0017664433}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond's forehead is not muddy. It is publicly announced that Richard knows whether Roberto's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Roberto can now know that Richard can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roberto","Richard","Raymond"],"index":54939,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993056059,"difficulty":0.0006943941}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ezequiel knows whether or not everyone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Frederick can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Ezequiel","Frederick"],"index":78,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994900227,"difficulty":0.0005099773}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. Deborah's card is shown to Jessica. Freddie's card is shown to Jessica. Jessica's card is shown to Deborah. William's card is shown to William. Jessica's card is shown to Freddie. William's card is shown to Freddie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deborah can now know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Deborah","William","Freddie"],"index":25303,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9405893087,"difficulty":0.0594106913}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne knows whether or not everyone's forehead is muddy. It is publicly announced that Wanda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Wanda can now know that Ross can know that Ross's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ross","Anne","Jean","Wanda"],"index":24171,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976656437,"difficulty":0.0023343563}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anabel knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Paul can now know that Suzanne can know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anabel","Paul","Suzanne"],"index":11403,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997900486,"difficulty":0.002099514}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Lee can now know that Michael can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Lee","Mary"],"index":37691,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9905728698,"difficulty":0.0094271302}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elbert's forehead is not muddy. It is publicly announced that Thomas's forehead is muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Thomas can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Thomas","Elbert"],"index":21483,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989432693,"difficulty":0.0010567307}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carmen does not know whether Nancy is thirsty. It is publicly announced that Carmen does not know whether Katherine is thirsty. It is publicly announced that Katherine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] Agentc knows that (Agentd knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] 0","hypothesis":"Carmen can now know that Katherine can know whether Adela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Adela","Nancy","Carmen","Katherine"],"index":47990,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9948790073,"difficulty":0.0051209927}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gail's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Gail can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gail","Robert","Mindy","Jennifer"],"index":45819,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988942742,"difficulty":0.0011057258}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Beverly can now know that Dortha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beverly","Cherie","Debra","Dortha"],"index":33068,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9893395305,"difficulty":0.0106604695}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judith is not thirsty. It is publicly announced that Kara does not know whether Darrin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] Agentd knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Judith can now know that Kara can know that Judith is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darcy","Darrin","Kara","Judith"],"index":18433,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949102998,"difficulty":0.0050897002}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gabrielle can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gabrielle","Lisa","John"],"index":36593,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989614487,"difficulty":0.0010385513}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Brett can now know that Kevin can know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Toi","Brett","Kevin"],"index":60594,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983560443,"difficulty":0.0016439557}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Walter. James's card is shown to Walter. Walter's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Walter can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Walter","James"],"index":48611,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949126244,"difficulty":0.0050873756}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mamie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mamie can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mamie","Margaret","Bruce"],"index":67614,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988307357,"difficulty":0.0011692643}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Retta. Eugene's card is shown to Eugene. Doris's card is shown to Eugene. Eugene's card is shown to Doris. Doris's card is shown to Doris. It is publicly announced that someone picked a red card. It is publicly announced that Doris picked a red card. It is publicly announced that Doris does not know whether Retta picked a red card. It is publicly announced that Doris knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Doris can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Retta","Eugene","Doris"],"index":45282,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986996651,"difficulty":0.0013003349}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia is thirsty. It is publicly announced that Martha knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Martha can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jane","Rebecca","Martha","Virginia"],"index":53069,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995017052,"difficulty":0.0004982948}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Joseph knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Margaret can now know that Joseph can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Margaret"],"index":17792,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994493127,"difficulty":0.0005506873}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Henry can now know whether Carey can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Margaret","Carey","Henry"],"index":57108,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9921756387,"difficulty":0.0078243613}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Mamie's card is shown to James. James's card is shown to Mamie. James's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Mamie","Michael","John"],"index":15235,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982364178,"difficulty":0.0017635822}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marian knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Carolyn can now know that Marian can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Felix","Marian","Sharon","Carolyn"],"index":47251,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987704158,"difficulty":0.0012295842}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Douglas can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Douglas","Robert","Margaret"],"index":48973,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994798303,"difficulty":0.0005201697}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwayne's card is shown to Dwayne. Dwayne's card is shown to Bridget. Matt's card is shown to Matt. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bridget can now know that Matt picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dwayne","Judy","Bridget","Matt"],"index":60427,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966484904,"difficulty":0.0033515096}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosa does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Manuel can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rosa","Michael","Manuel"],"index":24196,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995063543,"difficulty":0.0004936457}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether Gerald's forehead is muddy. It is publicly announced that Ashley's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Ashley can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gerald","Ashley"],"index":15904,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981104136,"difficulty":0.0018895864}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Lucille can now know that Rose can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Donald","Lucille","Paul"],"index":63748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982734919,"difficulty":0.0017265081}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Howard does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Howard can now know that Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Howard","Erica"],"index":60944,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9938321114,"difficulty":0.0061678886}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Douglas can now know that Salvatore can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Salvatore","Douglas","Patricia"],"index":64525,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988220334,"difficulty":0.0011779666}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jerry can now know whether James can know whether Jerry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Jerry","Betty"],"index":26740,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9478775263,"difficulty":0.0521224737}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Inez's card is shown to Lakisha. Michael's card is shown to Inez. Inez's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Lakisha knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Michael can now know that Inez can know whether Inez picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lakisha","Inez","Michael"],"index":22405,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.777705133,"difficulty":1.777705133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether Gary's forehead is muddy. It is publicly announced that Timothy does not know whether Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Fredrick can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gary","Sean","Timothy","Fredrick"],"index":21274,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999427557,"difficulty":0.000572443}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rutha's card is shown to Rutha. Judith's card is shown to Rutha. Judith's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that Judith knows whether or not nobody picked a red card. It is publicly announced that Judith does not know whether Rutha picked a red card. It is publicly announced that Rutha picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Judith can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rutha","Judith"],"index":24708,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984478951,"difficulty":0.0015521049}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Miguel can now know that Miguel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Miguel","Aldo","Matthew"],"index":58333,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982296824,"difficulty":0.0017703176}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lavern knows whether Joseph's forehead is muddy. It is publicly announced that Todd's forehead is not muddy. It is publicly announced that Todd knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know whether Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lavern","Todd","Joseph"],"index":15783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994804263,"difficulty":0.0005195737}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maggie knows whether Benjamin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Rebecca can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebecca","Maggie","Sean","Benjamin"],"index":32504,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990008473,"difficulty":0.0009991527}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda does not know whether or not everyone is thirsty. It is publicly announced that Donna is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] Agentd knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Donna can now know that Danny can know that Donna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amanda","Elnora","Danny","Donna"],"index":17723,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9814872742,"difficulty":0.0185127258}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. Charles's card is shown to Charles. Charles's card is shown to Willie. Willie's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Willie can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Charles","Willie"],"index":44360,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.818497479,"difficulty":0.181502521}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to William. Maureen's card is shown to Steven. William's card is shown to Andrew. William's card is shown to Maureen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Steven","Andrew","Maureen"],"index":30503,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968485236,"difficulty":0.0031514764}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie does not know whether Seth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Julie can now know that Evelyn can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Evelyn","Seth","Julie"],"index":27686,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989824891,"difficulty":0.0010175109}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chad's card is shown to Zaida. Zaida's card is shown to Zaida. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Hunter can now know that Zaida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hunter","Carolyn","Chad","Zaida"],"index":4676,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9890322089,"difficulty":0.0109677911}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruben does not know whether Ruben's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Fumiko can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Annie","Frank","Fumiko","Ruben"],"index":2442,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.981400609,"difficulty":0.018599391}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Adrian can now know that Monte can know whether Monte's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Adrian","Monte","Terrance","Jose"],"index":34666,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999445498,"difficulty":0.000554502}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether or not everyone's forehead is muddy. It is publicly announced that Jean knows whether someone's forehead is muddy. It is publicly announced that Jean's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] Agentb knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Harold can now know that Jean can know that Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marie","Harold","Jean"],"index":24469,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7121785879,"difficulty":0.2878214121}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether or not everyone is thirsty. It is publicly announced that Ben is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] Agentc knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Ralph can now know whether Ben can know that Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Nancy","Ralph","Ben"],"index":698,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9911912084,"difficulty":0.0088087916}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gayla does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Russell can now know whether Chelsea can know whether Chelsea's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chelsea","Gayla","Herman","Russell"],"index":42760,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8241086006,"difficulty":0.1758913994}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rick does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rick can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Benjamin","Rick","John"],"index":4035,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994727969,"difficulty":0.0005272031}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Eugene can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eugene","Paul"],"index":9764,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988629818,"difficulty":0.0011370182}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Mattie. Mattie's card is shown to Michele. Virginia's card is shown to Michele. William's card is shown to William. Virginia's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mattie can now know whether Michele can know whether Mattie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mattie","Michele","William","Virginia"],"index":65359,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985331297,"difficulty":0.0014668703}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"George can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathy","George","William","Nerissa"],"index":7819,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984342456,"difficulty":0.0015657544}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Charlotte can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Charlotte"],"index":56060,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948595762,"difficulty":0.0051404238}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Andrew can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andrew","Andy"],"index":37995,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985864162,"difficulty":0.0014135838}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Donald's card is shown to Cecil. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Cecil can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Donald","Cecil"],"index":35085,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993802309,"difficulty":0.0006197691}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vito does not know whether Viola is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Viola can now know that Gary can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Viola","Andrew","Vito"],"index":67242,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989053011,"difficulty":0.0010946989}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether Scott's forehead is muddy. It is publicly announced that Natalie knows whether Darrell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Darrell can now know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darrell","Scott","Natalie","Winnie"],"index":2351,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997033,"difficulty":0.002967}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myron's card is shown to Donald. Myron's card is shown to Myron. Samuel's card is shown to Myron. Freddy's card is shown to Myron. Myron's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether Samuel picked a red card. It is publicly announced that Myron picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Myron can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Myron","Samuel","Freddy"],"index":53869,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985547662,"difficulty":0.0014452338}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rupert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Loretta can now know that Rupert can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Loretta","Rupert","Edward"],"index":41158,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993904829,"difficulty":0.0006095171}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Brian. John's card is shown to Brian. Brian's card is shown to Daniel. Daniel's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether Brian picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Daniel can now know that Brian can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Daniel","John"],"index":18673,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960120916,"difficulty":0.0039879084}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Tonya knows whether Gretchen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Raymond can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gretchen","Tonya","Raymond"],"index":6836,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989672899,"difficulty":0.0010327101}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander knows whether Kristine's forehead is muddy. It is publicly announced that Alexis knows whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Alexander can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jerry","Alexander","Kristine","Alexis"],"index":4472,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993707538,"difficulty":0.0006292462}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Ronald. Ronald's card is shown to Craig. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Mattie can now know whether Mattie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Mattie","Craig"],"index":29132,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9156314731,"difficulty":0.0843685269}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Kristi. Kristi's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Kristi knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Maria can now know whether Kristi can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kristi","Maria"],"index":64513,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9938752055,"difficulty":0.0061247945}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Margaret's card is shown to James. James's card is shown to Marion. Charles's card is shown to Marion. Margaret's card is shown to Marion. Charles's card is shown to Charles. Margaret's card is shown to Charles. James's card is shown to Margaret. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Marion knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 Agentc:3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 Agentc:3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Margaret can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Marion","Charles","Margaret"],"index":26158,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993342757,"difficulty":0.0006657243}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harriet's card is shown to Harriet. Dennis's card is shown to Clyde. Clyde's card is shown to Darlene. Dennis's card is shown to Darlene. Darlene's card is shown to Darlene. It is publicly announced that someone picked a red card. It is publicly announced that Harriet picked a red card. It is publicly announced that Dennis picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 3 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Dennis can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harriet","Clyde","Dennis","Darlene"],"index":41239,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990469813,"difficulty":0.0009530187}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Robert can now know whether Joshua can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Joshua"],"index":36870,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993659854,"difficulty":0.0006340146}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Rebecca. Reggie's card is shown to Reggie. Jose's card is shown to Reggie. Reggie's card is shown to Brittany. Brittany's card is shown to Jose. Jose's card is shown to Jose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jose can now know that Reggie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebecca","Reggie","Brittany","Jose"],"index":59888,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973348975,"difficulty":0.0026651025}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wallace's card is shown to Norma. Kevin's card is shown to Norma. Kevin's card is shown to Wallace. Norma's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Norma can now know that Wallace can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Norma","Wallace","Kevin"],"index":22665,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993484616,"difficulty":0.0006515384}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Richard can now know whether Devora can know whether Devora's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Devora"],"index":2427,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9580442905,"difficulty":1.9580442905}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Nannie's card is shown to Nannie. Shelby's card is shown to Nannie. Dorothy's card is shown to Shelby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nannie can now know whether Dorothy can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Nannie","Shelby"],"index":6175,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992744327,"difficulty":0.0007255673}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patrick does not know whether Jennifer is thirsty. It is publicly announced that Mattie is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Mattie can now know that Jennifer can know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patrick","Mattie","Jennifer","Elaine"],"index":47058,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9942270517,"difficulty":0.0057729483}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aaron's card is shown to Rex. Aaron's card is shown to Aaron. Rex's card is shown to Peggy. Elizabeth's card is shown to Peggy. It is publicly announced that someone picked a red card. It is publicly announced that Aaron does not know whether Elizabeth picked a red card. It is publicly announced that Aaron knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Aaron can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rex","Aaron","Peggy","Elizabeth"],"index":10640,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9934660792,"difficulty":0.0065339208}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tricia's card is shown to Tricia. Eric's card is shown to Tricia. Tricia's card is shown to Helen. Tricia's card is shown to Eric. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eric can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tricia","Helen","Eric"],"index":42205,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8720653653,"difficulty":0.1279346347}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tianna knows whether Karen's forehead is muddy. It is publicly announced that Tianna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Tianna can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Karen","Tianna"],"index":50838,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990154505,"difficulty":0.0009845495}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. Jack's card is shown to Betty. Betty's card is shown to Jack. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Jack can now know whether Betty can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Betty","Jack"],"index":48828,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994385839,"difficulty":0.0005614161}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether or not everyone's forehead is muddy. It is publicly announced that Tony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Santos can now know whether Jose can know that Carol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Santos","Carol","Jose","Tony"],"index":801,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994674325,"difficulty":0.0005325675}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeanne knows whether Jeanne is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Stacey can now know that Jeanne can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeanne","Stacey"],"index":42444,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8896322846,"difficulty":0.1103677154}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Nicole can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lucy","Kay","Nicole","Francisco"],"index":13810,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993268251,"difficulty":0.0006731749}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Maria can now know whether Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maria","Malik","Nichole","Rebecca"],"index":51701,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9867103696,"difficulty":0.0132896304}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Ginette can now know whether Erik can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erik","Vonnie","Ginette"],"index":7424,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994074106,"difficulty":0.0005925894}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Catherine. Catherine's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether Deborah picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Catherine can now know whether Deborah can know that Deborah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Deborah"],"index":1557,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8723253012,"difficulty":0.1276746988}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan knows whether Juan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Elda can now know whether Nicholas can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicholas","Elda","Juan","David"],"index":42984,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993803501,"difficulty":0.0006196499}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Norma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Norma can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brandon","Paul","Norma","John"],"index":23849,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994605184,"difficulty":0.0005394816}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Ruth does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] Agentb knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Gayle can now know that Ruth can know whether Ruth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Gayle","Roy","Ruth"],"index":47593,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99650985,"difficulty":0.00349015}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francis does not know whether India is thirsty. It is publicly announced that India does not know whether Philip is thirsty. It is publicly announced that Philip does not know whether Francis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Francis can now know whether India can know whether India is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Francis","Philip","India"],"index":27264,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984989166,"difficulty":0.0015010834}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Lillian can now know that Gloria can know that Gloria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Daniel","Lillian"],"index":26901,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981841445,"difficulty":0.0018158555}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fred does not know whether Kim is thirsty. It is publicly announced that Kim knows whether or not everyone is thirsty. It is publicly announced that Kendra knows whether or not everyone is thirsty. It is publicly announced that Kendra does not know whether Fred is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Kim can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kendra","Fred","Kim"],"index":7027,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994909763,"difficulty":0.0005090237}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melvin does not know whether Lyle is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Melvin can now know that Lyle can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lyle","Melvin"],"index":33745,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9923037887,"difficulty":0.0076962113}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Frank can now know that Mark can know that Mark is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","Laura","Mark"],"index":19292,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9926828742,"difficulty":0.0073171258}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gustavo does not know whether Trina is thirsty. It is publicly announced that Gary does not know whether Trina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Gustavo can now know whether Trina can know whether Gary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Trina","Gustavo","Gary"],"index":28813,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990907907,"difficulty":0.0009092093}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christene knows whether Erika's forehead is muddy. It is publicly announced that Justin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Rose can now know that Christene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Rose","Christene","Erika"],"index":48996,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972981811,"difficulty":0.0027018189}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty. It is publicly announced that Randall knows whether someone is thirsty. It is publicly announced that Randall is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"David can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Oren","Randall","David","Dave"],"index":17634,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977351427,"difficulty":0.0022648573}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. Dana's card is shown to Andrea. Dana's card is shown to Dana. It is publicly announced that someone picked a red card. It is publicly announced that Eleanor picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Eleanor can now know whether Eleanor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andrea","Eleanor","Dana"],"index":14251,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7666087151,"difficulty":0.2333912849}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman knows whether Judith's forehead is muddy. It is publicly announced that Anna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Anna can now know that Norman can know that Priscilla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anna","Norman","Judith","Priscilla"],"index":44698,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977068901,"difficulty":0.0022931099}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Julie. Rosa's card is shown to Philip. Rosa's card is shown to Rosa. Michael's card is shown to Rosa. Philip's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Rosa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Julie can now know that Rosa can know that Philip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Philip","Rosa","Michael"],"index":54068,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975939393,"difficulty":0.0024060607}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chasity does not know whether Marcus is thirsty. It is publicly announced that Marcus is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Marcus can now know that Franklin can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Olin","Franklin","Marcus","Chasity"],"index":27425,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982872605,"difficulty":0.0017127395}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurice's card is shown to Elsie. Maurice's card is shown to Maurice. Twila's card is shown to Maurice. It is publicly announced that someone picked a red card. It is publicly announced that Elsie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Maurice can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elsie","Maurice","Russ","Twila"],"index":45914,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994458556,"difficulty":0.0005541444}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know that Sylvia can know whether Larry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Kathleen","Sylvia","Steven"],"index":24084,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9797734618,"difficulty":0.0202265382}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abbie knows whether Meaghan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Dennis can now know that Meaghan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Abbie","Dennis","Meaghan","Lionel"],"index":24136,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989045858,"difficulty":0.0010954142}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that Kim can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kim","Jennefer","David","Eric"],"index":7358,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993947744,"difficulty":0.0006052256}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime knows whether Johnny's forehead is muddy. It is publicly announced that Bonnie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Jaime can now know whether Jaime's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jodi","Bonnie","Jaime","Johnny"],"index":37695,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994445443,"difficulty":0.0005554557}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Omar","Ronald","James","Robert"],"index":57389,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7505317926,"difficulty":1.7505317926}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynn knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Lynn can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Wanda","Scott","Lynn"],"index":15919,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993165731,"difficulty":0.0006834269}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether or not nobody's forehead is muddy. It is publicly announced that Shirlee's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Carol can now know whether Carol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Kyong","Shirlee"],"index":28190,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994139671,"difficulty":0.0005860329}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephanie is thirsty. It is publicly announced that Alice does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Alice can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alice","Stephanie","Ian"],"index":54533,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9087539911,"difficulty":0.0912460089}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Wendy can now know that Anita can know that Anita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wendy","Florence","Anita","Jesse"],"index":24676,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5607432723,"difficulty":0.4392567277}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arthur does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Arthur knows whether someone is thirsty. It is publicly announced that Arthur knows whether Arthur is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kyle can now know that Arthur can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arthur","Kyle"],"index":35507,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994401336,"difficulty":0.0005598664}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Anita. Mildred's card is shown to Sharon. Anita's card is shown to Robert. Sharon's card is shown to Robert. Sharon's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Sharon can now know whether Anita can know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anita","Sharon","Robert","Mildred"],"index":14014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8750885725,"difficulty":0.1249114275}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brenda can now know that Ronald can know whether Brenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lynne","Ronald","Brenda"],"index":48083,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993584752,"difficulty":0.0006415248}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Louis knows whether or not nobody's forehead is muddy. It is publicly announced that Louis knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Louis can now know that Anthony can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anthony","Louis"],"index":65851,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9955452681,"difficulty":0.0044547319}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Cyndy. Cyndy's card is shown to Julie. Cyndy's card is shown to Luis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Cyndy can know whether Julie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cyndy","John","Julie","Luis"],"index":50653,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9529048204,"difficulty":1.9529048204}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Michael can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Michael","Richard","Alice"],"index":5552,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9593044519,"difficulty":0.0406955481}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Theodore is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Theodore can now know that John can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Theodore","Mary","John"],"index":2669,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954012632,"difficulty":0.0045987368}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy. It is publicly announced that Krystle knows whether Krystle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Susan can now know whether Sean can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Krystle","Sean","Susan"],"index":20011,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9807495475,"difficulty":1.9807495475}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy. It is publicly announced that Joseph's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Marion can now know that Madison can know that Marion's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marion","Linda","Madison","Joseph"],"index":54023,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979673028,"difficulty":0.0020326972}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Betty can now know that George can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Janet","Betty"],"index":14370,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989176989,"difficulty":0.0010823011}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Henry can now know that Jody can know whether Roberta's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jody","Henry","Roberta"],"index":14766,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994328618,"difficulty":0.0005671382}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Donna's card is shown to Donna. Jonathon's card is shown to Jonathon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donna can now know whether Valerie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Valerie","Donna","Jonathon"],"index":59249,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9236021042,"difficulty":0.0763978958}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mohammad knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Mark can now know that Mohammad can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ricardo","Mark","Joyce","Mohammad"],"index":33347,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994020462,"difficulty":0.0005979538}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby does not know whether Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Franklin can now know whether Garry can know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bobby","Patricia","Franklin","Garry"],"index":49875,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999253571,"difficulty":0.000746429}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Jean can now know that Julia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julia","Derrick","Jean"],"index":64132,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9874316454,"difficulty":0.0125683546}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Steve. Tabitha's card is shown to Lucy. Dorothy's card is shown to Lucy. Tabitha's card is shown to Tabitha. Dorothy's card is shown to Tabitha. Lucy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Tabitha does not know whether Lucy picked a red card. It is publicly announced that Tabitha does not know whether Lucy picked a red card. It is publicly announced that Dorothy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Lucy can now know whether Dorothy can know that Lucy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steve","Lucy","Tabitha","Dorothy"],"index":49360,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9082512856,"difficulty":0.0917487144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shannon does not know whether Beulah is thirsty. It is publicly announced that Shannon does not know whether Michael is thirsty. It is publicly announced that Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] Agentd knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] 0","hypothesis":"Michael can now know that Beulah can know that Shannon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Max","Beulah","Shannon","Michael"],"index":51230,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9675040841,"difficulty":0.0324959159}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Von knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Anthony can now know that Von can know that Von's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Von","Linda"],"index":53223,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979050159,"difficulty":0.0020949841}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Florence","Sharon","Bernice","William"],"index":52362,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989889264,"difficulty":0.0010110736}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois knows whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Marilyn can now know that Lois can know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lois","Jennifer","Marilyn"],"index":48863,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992972612,"difficulty":0.0007027388}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Katrina knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Scott can now know that Katrina can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chris","Scott","John","Katrina"],"index":39300,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998908639,"difficulty":0.001091361}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Helen can now know that Roberto can know that Helen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Roberto","Helen"],"index":61899,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.994797051,"difficulty":0.005202949}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Beverly can now know that Betty can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harold","Beverly","Betty"],"index":13355,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977042079,"difficulty":0.0022957921}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua does not know whether or not everyone is thirsty. It is publicly announced that Joshua knows whether Joshua is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joshua can now know that Barbara can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barbara","Joshua"],"index":2325,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990116358,"difficulty":0.0009883642}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jody does not know whether Jody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jody can now know that Donna can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jody","Jackie","Donna"],"index":50288,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990031123,"difficulty":0.0009968877}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether David is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether Alfred can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Charles","Alfred","Emmett"],"index":40545,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955881834,"difficulty":0.0044118166}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy. It is publicly announced that Charles's forehead is not muddy. It is publicly announced that Leslie knows whether William's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leslie","Mary","William","Charles"],"index":26385,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9897123575,"difficulty":0.0102876425}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Joey can now know that Dorothy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Enoch","Dorothy","Joey"],"index":42255,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9304432273,"difficulty":0.0695567727}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Rita can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josefina","Justin","George","Rita"],"index":25694,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992597699,"difficulty":0.0007402301}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqueline's card is shown to Jacqueline. Jacqueline's card is shown to Dennis. Alan's card is shown to Dennis. Duncan's card is shown to Duncan. Dennis's card is shown to Alan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dennis can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacqueline","Dennis","Duncan","Alan"],"index":28009,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957398176,"difficulty":0.0042601824}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Randy. Randy's card is shown to Victor. Richard's card is shown to Victor. Randy's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Victor can now know that Richard can know that Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Randy","Victor","Richard"],"index":30821,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9904452562,"difficulty":0.0095547438}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Blanca's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Eva can now know that Clarice can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Blanca","Clarice","Eva"],"index":56938,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989777803,"difficulty":0.0010222197}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Courtney does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Audrey can now know whether Jennell can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Courtney","Joseph","Audrey","Jennell"],"index":60296,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8745191693,"difficulty":0.1254808307}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah does not know whether George is thirsty. It is publicly announced that Deborah does not know whether Katie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Katie can now know whether George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Deborah","Katie"],"index":10486,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972633123,"difficulty":0.0027366877}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vicki's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Vicki can now know that William can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Vicki","William"],"index":27154,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989669323,"difficulty":0.0010330677}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy does not know whether Tammy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Naomi","John","Tammy"],"index":27377,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9862315059,"difficulty":0.0137684941}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to Ricardo. Erin's card is shown to Erin. Erin's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Erin can now know whether Richard can know that Ricardo picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Ricardo","Erin","James"],"index":36217,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9412826896,"difficulty":0.0587173104}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Brett can now know that Warren can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Brett","Warren","Alicia"],"index":36301,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994266033,"difficulty":0.0005733967}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Cliff can now know that Cliff's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Jeffrey","Cliff"],"index":22046,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963415265,"difficulty":0.0036584735}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lawrence can now know that Elwood can know whether Norma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Lawrence","Norma","Elwood"],"index":1897,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993572831,"difficulty":0.0006427169}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristine knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"David can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kristine","Deborah","David"],"index":49962,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994484782,"difficulty":0.0005515218}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jessie can now know whether Philip can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earl","Philip","Arthur","Jessie"],"index":20353,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994996786,"difficulty":0.0005003214}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether or not everyone's forehead is muddy. It is publicly announced that Larry's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Dorothy can now know that Larry can know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Larry"],"index":41360,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9970550537,"difficulty":1.9970550537}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mattie does not know whether James is thirsty. It is publicly announced that Mattie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know whether James can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mattie","James","Robert"],"index":5522,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9950988889,"difficulty":0.0049011111}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynda knows whether Felicia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Dionne can now know whether Felicia can know whether Felicia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dionne","Jennifer","Lynda","Felicia"],"index":50564,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8244357109,"difficulty":0.1755642891}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eleanor does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Maria can now know whether Eleanor can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Dena","Eleanor"],"index":31285,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994906187,"difficulty":0.0005093813}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman's forehead is not muddy. It is publicly announced that Brigette knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Brigette can now know whether Brigette's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Faye","Norman","Brigette","Ignacio"],"index":16843,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9805940986,"difficulty":0.0194059014}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Teresa can now know that Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Teresa","Alice"],"index":31780,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9927996397,"difficulty":0.0072003603}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know whether William can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phil","John","William","Frank"],"index":57895,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994644523,"difficulty":0.0005355477}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michele's card is shown to Mark. Mark's card is shown to Mary. Michele's card is shown to Mary. Mary's card is shown to Michele. Michele's card is shown to Michele. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Mary","Michele"],"index":46073,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5992802978,"difficulty":0.4007197022}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Robert can now know whether Richard can know that Melvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Elizabeth","Melvin","Robert"],"index":28146,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994623065,"difficulty":0.0005376935}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Anne can now know that Linda can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Anne"],"index":30537,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993004799,"difficulty":0.0006995201}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alberto is thirsty. It is publicly announced that Glenn knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Alberto can now know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Joseph","Glenn","Alberto"],"index":16588,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976270795,"difficulty":0.0023729205}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Brian can now know whether Arthur can know whether Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Samuel","Arthur"],"index":30093,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9974139929,"difficulty":0.0025860071}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Dorothy can now know that Jason's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Dorothy","Nicole","Henry"],"index":59906,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976516366,"difficulty":0.0023483634}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen does not know whether Helen's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3&4) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3&4) ] 0","hypothesis":"Michael can now know whether Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elva","Helen","Evelyn","Michael"],"index":6174,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990816116,"difficulty":0.0009183884}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Phyllis can now know that Gerald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Phyllis","Gregory","Gerald"],"index":45790,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9871284962,"difficulty":0.0128715038}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tanya's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Lee can now know that Tanya's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tanya","Lee","Catherine"],"index":32353,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6523046494,"difficulty":0.3476953506}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Amy can now know that Larry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amy","Kent","Larry"],"index":22840,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990124702,"difficulty":0.0009875298}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Del. James's card is shown to Sallie. Karen's card is shown to Karen. Sallie's card is shown to James. Karen's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Sallie picked a red card. It is publicly announced that Del knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Karen can now know that James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Del","Sallie","Karen","James"],"index":52640,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8746550083,"difficulty":0.1253449917}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Levi's card is shown to Levi. Penny's card is shown to Penny. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Levi does not know whether Penny picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Levi can now know whether Penny can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Levi","Penny"],"index":58716,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994395375,"difficulty":0.0005604625}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose's forehead is muddy. It is publicly announced that Jose knows whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jose can now know that Jennifer can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Robert","Jose"],"index":8232,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994226694,"difficulty":0.0005773306}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robbie can now know whether Virginia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverly","Robbie","Virginia","Bobby"],"index":31987,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992966652,"difficulty":0.0007033348}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ciara can now know whether Vicki can know that Ciara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Ciara","Vicki","Clarence"],"index":46298,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958567023,"difficulty":0.0041432977}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty. It is publicly announced that Michael does not know whether Mark is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Rachel can now know that Pierre can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Mark","Rachel","Pierre"],"index":48706,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7274909019,"difficulty":0.2725090981}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tara's card is shown to Tara. Tara's card is shown to Juan. Juan's card is shown to Juan. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Tara can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tara","Juan"],"index":59126,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989748001,"difficulty":0.0010251999}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Michael can now know whether Ann can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ann","Michael"],"index":41335,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9901204109,"difficulty":0.0098795891}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy. It is publicly announced that Glenn knows whether Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Glenn can now know that Martha can know that Glenn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martha","Glenn","Mary"],"index":45384,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984880686,"difficulty":0.0015119314}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Agnes. Agnes's card is shown to Agnes. Paul's card is shown to Agnes. Joseph's card is shown to Agnes. Paul's card is shown to Paul. Joseph's card is shown to Paul. Agnes's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Steven can now know that Agnes can know that Agnes picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Agnes","Paul","Joseph"],"index":64358,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9931898713,"difficulty":0.0068101287}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Melvin. Laurene's card is shown to Melvin. Laurene's card is shown to Miguel. Melvin's card is shown to Laurene. Melvin's card is shown to Dexter. It is publicly announced that someone picked a red card. It is publicly announced that Dexter does not know whether Miguel picked a red card. It is publicly announced that Dexter does not know whether Dexter picked a red card. It is publicly announced that Miguel does not know whether Dexter picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Melvin can now know that Dexter can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melvin","Miguel","Laurene","Dexter"],"index":35943,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994039536,"difficulty":0.0005960464}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon knows whether Patricia's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jeanette can now know that Patricia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cody","Patricia","Jeanette","Brandon"],"index":63921,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994232655,"difficulty":0.0005767345}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy. It is publicly announced that Vance's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] 0","hypothesis":"William can now know whether Vance can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","William","Vance"],"index":15239,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999484539,"difficulty":0.000515461}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffani's card is shown to Tiffani. Tiffani's card is shown to Milton. Milton's card is shown to Milton. It is publicly announced that someone picked a red card. It is publicly announced that Milton knows whether Milton picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Tiffani can now know whether Milton can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tiffani","Milton"],"index":38064,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9781832695,"difficulty":1.9781832695}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether Latoya's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Latoya can now know that Latoya's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Latoya","Bobby","Deborah"],"index":39216,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.991322279,"difficulty":0.008677721}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Richard. Robert's card is shown to Richard. Jessica's card is shown to Jessica. Robert's card is shown to Jessica. Robert's card is shown to Robert. Nakita's card is shown to Robert. Nakita's card is shown to Nakita. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jessica can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Jessica","Robert","Nakita"],"index":30964,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9905418754,"difficulty":0.0094581246}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edith knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Edith can now know that Corina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kimberly","Edith","Corina","Joseph"],"index":53209,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984977245,"difficulty":0.0015022755}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether Christy's forehead is muddy. It is publicly announced that Willie's forehead is not muddy. It is publicly announced that Timothy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Willie can now know that Nancy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Christy","Nancy","Willie"],"index":62375,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987609386,"difficulty":0.0012390614}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Helen's forehead is muddy. It is publicly announced that Linda knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Helen can now know that Ruth can know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Helen","Ruth","Maria"],"index":492,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977232814,"difficulty":0.0022767186}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Thomas can now know that Florence can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Thomas","Florence"],"index":61102,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984310269,"difficulty":0.0015689731}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis does not know whether Dennis's forehead is muddy. It is publicly announced that Dennis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Dennis can now know that Patti can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Raymond","Nelson","Dennis","Patti"],"index":8901,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989612103,"difficulty":0.0010387897}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Andrew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Andrew can now know whether William can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","Maria","James","William"],"index":54682,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.996057272,"difficulty":0.003942728}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether someone's forehead is muddy. It is publicly announced that Donald knows whether or not everyone's forehead is muddy. It is publicly announced that Kurt's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kurt can now know whether Frank can know whether Frank's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kurt","Rose","Donald","Frank"],"index":11620,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9505963922,"difficulty":1.9505963922}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Floyd's card is shown to Floyd. Jeffrey's card is shown to Floyd. Floyd's card is shown to Jeffrey. Ha's card is shown to Arnold. Jeffrey's card is shown to Arnold. Arnold's card is shown to Arnold. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ha can now know that Jeffrey can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ha","Floyd","Jeffrey","Arnold"],"index":44353,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993846416,"difficulty":0.0006153584}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Christopher is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Hilda can now know whether Hilda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Hilda","Christopher"],"index":4906,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9971579313,"difficulty":0.0028420687}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Austin's card is shown to Sharon. Austin's card is shown to Steven. Steven's card is shown to Steven. Mary's card is shown to Steven. Sharon's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Steven picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Steven can now know whether Sharon can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Austin","Sharon","Steven","Mary"],"index":35711,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994391799,"difficulty":0.0005608201}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jeffery can now know that Thomas can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Jeffery","Bertha","Charles"],"index":9907,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990531802,"difficulty":0.0009468198}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mike can now know that Sharon can know whether Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Susan","Mike"],"index":19310,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.968937993,"difficulty":0.031062007}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Gregory can now know whether Ophelia can know whether Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gregory","Ophelia","Donna"],"index":15757,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994428754,"difficulty":0.0005571246}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann does not know whether Ann's forehead is muddy. It is publicly announced that Alana knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ann can now know that Beatrice's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ann","Beatrice","Alana","Celia"],"index":2897,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973070621,"difficulty":0.0026929379}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eula's card is shown to Craig. Craig's card is shown to Eula. Matthew's card is shown to Eula. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Matthew can now know whether Craig can know whether Craig picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Craig","Matthew","Eula"],"index":15804,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9856993556,"difficulty":0.0143006444}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lonnie can now know that Jose can know that Victoria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Victoria","Lonnie","Jose"],"index":54076,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9903780222,"difficulty":0.0096219778}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rena knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Barbara can now know whether Rena's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Barbara","Rena"],"index":26619,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991162419,"difficulty":0.0008837581}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynne does not know whether Victor is thirsty. It is publicly announced that Elaine does not know whether Lynne is thirsty. It is publicly announced that Victor does not know whether Elaine is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Elaine can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynne","Elaine","Victor"],"index":67407,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965832829,"difficulty":0.0034167171}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Jason. Jason's card is shown to Edward. Leo's card is shown to Leo. It is publicly announced that someone picked a red card. It is publicly announced that Leo picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jason can now know that Lori can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jason","Lori","Edward","Leo"],"index":31216,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990104437,"difficulty":0.0009895563}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Shirley can now know that Curtis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","Curtis","Dale","Hazel"],"index":48810,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9927681684,"difficulty":0.0072318316}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carrie's card is shown to Carrie. Robert's card is shown to Robert. Patti's card is shown to Robert. Patti's card is shown to Patti. Carrie's card is shown to Sandy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Carrie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carrie","Robert","Patti","Sandy"],"index":24335,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.979539156,"difficulty":1.979539156}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Claudia's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Roger's card is shown to Carolyn. Claudia's card is shown to Roger. Carolyn's card is shown to Roger. Roger's card is shown to Roger. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Claudia can now know that Carolyn can know that Roger picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Claudia","Carolyn","Roger"],"index":45507,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973466396,"difficulty":0.0026533604}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earline knows whether Earline's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"David can now know that Claire's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Claire","Earline","Ryan"],"index":39968,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979189038,"difficulty":0.0020810962}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether Antwan can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Antwan","Mary","Troy"],"index":38222,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9475513697,"difficulty":0.0524486303}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know that Bill can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Scott","Jennifer","Bill"],"index":60465,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988397956,"difficulty":0.0011602044}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jean is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Jean","Bessie"],"index":56571,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995232821,"difficulty":0.0004767179}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darryl's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Max can now know that Darryl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harold","Megan","Darryl","Max"],"index":1786,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939774275,"difficulty":0.0060225725}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shane's card is shown to Shane. Ann's card is shown to Daniel. Luis's card is shown to Ann. Shane's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Shane knows whether Shane picked a red card. It is publicly announced that Shane does not know whether or not everyone picked a red card. It is publicly announced that Daniel does not know whether Daniel picked a red card. It is publicly announced that Ann does not know whether Daniel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Daniel can now know that Luis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shane","Daniel","Ann","Luis"],"index":65813,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9312731624,"difficulty":0.0687268376}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Jason can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Betty","Jason","Paul"],"index":64038,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988030195,"difficulty":0.0011969805}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Pat can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pat","Linda","Roderick"],"index":32173,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7684646249,"difficulty":0.2315353751}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Catherine. Catherine's card is shown to Antone. Antone's card is shown to Antone. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Catherine can now know whether Zachary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Catherine","Cynthia","Antone","Zachary"],"index":54638,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981377125,"difficulty":0.0018622875}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Noelle does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Eleanor can now know whether Natasha can know that Timothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Noelle","Natasha","Eleanor","Timothy"],"index":42736,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.996157825,"difficulty":0.003842175}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy is thirsty. It is publicly announced that Carlton knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Dorothy can now know whether Gwen can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gwen","Carlton","Dorothy"],"index":43535,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994894266,"difficulty":0.0005105734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Brenda can now know that Kevin can know that Wiley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Brenda","Wiley","Kevin"],"index":52690,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975298047,"difficulty":0.0024701953}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eliz knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kyle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nina","Eliz","Kyle","Robert"],"index":50936,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987648726,"difficulty":0.0012351274}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Kimberly's card is shown to Mary. Gary's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gary","Mary","Norma","Kimberly"],"index":41641,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994020462,"difficulty":0.0005979538}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jame's forehead is muddy. It is publicly announced that Angela knows whether or not nobody's forehead is muddy. It is publicly announced that Jame knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jame can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffrey","Angela","Jame"],"index":58154,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9962701797,"difficulty":0.0037298203}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monique's card is shown to Monique. Monroe's card is shown to Monroe. Joshua's card is shown to Monroe. Joshua's card is shown to Joshua. Monique's card is shown to Cory. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joshua can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Monique","Monroe","Joshua","Cory"],"index":66463,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993724227,"difficulty":0.0006275773}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly knows whether Kelly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kelly can now know whether Linda can know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Linda","Kelly"],"index":9230,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9677744508,"difficulty":1.9677744508}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christoper does not know whether Christoper's forehead is muddy. It is publicly announced that Christoper does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Michael can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christoper","Michael"],"index":9413,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988842607,"difficulty":0.0011157393}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether or not everyone's forehead is muddy. It is publicly announced that Madeline's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Madeline can now know whether Kathleen can know whether Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathleen","Madeline"],"index":18682,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993931055,"difficulty":0.0006068945}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jamal does not know whether Charles is thirsty. It is publicly announced that Jamal does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jamal can now know that Jamal is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clyde","Charles","Jamal"],"index":32573,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6554293036,"difficulty":1.6554293036}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Enrique's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Alma can now know that Tracy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roberta","Alma","Enrique","Tracy"],"index":28364,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993390441,"difficulty":0.0006609559}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether Lynn is thirsty. It is publicly announced that Lula is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agenta knows that (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Thomas can now know that Lynn can know whether Frances is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Lula","Frances","Lynn"],"index":61785,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9889516234,"difficulty":0.0110483766}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Albert. Albert's card is shown to Sharon. Thea's card is shown to Sharon. Duane's card is shown to Duane. Thea's card is shown to Duane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sharon can now know that Duane can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Albert","Sharon","Duane","Thea"],"index":32945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988617897,"difficulty":0.0011382103}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Doris is thirsty. It is publicly announced that Daniel does not know whether Adalberto is thirsty. It is publicly announced that Doris knows whether Doris is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Doris can now know that Daniel can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adalberto","Daniel","Doris"],"index":19430,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999440372,"difficulty":0.000559628}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin does not know whether Robin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jerry can now know whether Robin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Jerry","Robin"],"index":56381,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987394214,"difficulty":0.0012605786}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] 0","hypothesis":"Mary can now know whether Bruce's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ryan","Mary","Bruce"],"index":7666,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988648891,"difficulty":0.0011351109}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph does not know whether or not everyone's forehead is muddy. It is publicly announced that Ralph does not know whether Ralph's forehead is muddy. It is publicly announced that Misty's forehead is muddy. It is publicly announced that Misty knows whether Ralph's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ralph can now know whether Ralph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ralph","Misty"],"index":6013,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5559831262,"difficulty":1.5559831262}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Katherine. Deanna's card is shown to Katherine. Katherine's card is shown to Lisa. Katherine's card is shown to Deanna. Lisa's card is shown to Deanna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deanna can now know that Lisa can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Katherine","Lisa","Deanna"],"index":20427,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981049299,"difficulty":0.0018950701}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Tracy can now know that Micheal's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Tracy","Micheal"],"index":21488,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978523254,"difficulty":0.0021476746}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arthur does not know whether or not everyone is thirsty. It is publicly announced that Arthur does not know whether Ricardo is thirsty. It is publicly announced that Stephen does not know whether Ricardo is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ricardo can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carlos","Stephen","Ricardo","Arthur"],"index":47906,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990121126,"difficulty":0.0009878874}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Ida. Ida's card is shown to Charles. Richard's card is shown to Charles. Ida's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that Charles can know that Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ida","Charles","Richard"],"index":20551,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971504807,"difficulty":0.0028495193}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Marie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Marie can now know whether David can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Marie"],"index":7529,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994327426,"difficulty":0.0005672574}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Brooke. Sue's card is shown to Sue. Brooke's card is shown to Ashley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brooke can now know that Sue can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brooke","Sue","Ashley"],"index":41671,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990216494,"difficulty":0.0009783506}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Amy's card is shown to Pedro. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Pedro can now know that Amy can know that Pedro picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Amy","Pedro"],"index":54464,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996943295,"difficulty":0.003056705}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lloyd is thirsty. It is publicly announced that Jerry does not know whether Lemuel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lemuel can now know whether Lloyd can know that Lemuel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Ronald","Lemuel","Lloyd"],"index":39844,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8963222504,"difficulty":0.1036777496}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dean knows whether or not nobody is thirsty. It is publicly announced that Dean does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Melissa can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dean","Melissa","Walter"],"index":4503,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994626641,"difficulty":0.0005373359}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theresa does not know whether Deborah is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Deborah can now know that Theresa can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Theresa","Marie","Deborah"],"index":66561,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990130663,"difficulty":0.0009869337}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether Nicholas is thirsty. It is publicly announced that Laverna does not know whether Paul is thirsty. It is publicly announced that Nicholas does not know whether Laverna is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Laverna can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Laverna","Nicholas"],"index":58726,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999014616,"difficulty":0.000985384}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Ola. Ola's card is shown to Sara. It is publicly announced that someone picked a red card. It is publicly announced that Ola picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Ola can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ola","Sara"],"index":65677,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994683862,"difficulty":0.0005316138}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Clara can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clara","Mary","George","Mark"],"index":8558,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986863732,"difficulty":0.0013136268}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Laura can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Melody","Willie","Mary"],"index":42481,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985311031,"difficulty":0.0014688969}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernestine's card is shown to Ernestine. Angeline's card is shown to Angeline. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Ernestine can now know whether Angeline can know that Angeline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ernestine","Angeline"],"index":23789,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8530878425,"difficulty":1.8530878425}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that Eleanor knows whether Eleanor's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Eleanor"],"index":24922,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993021488,"difficulty":0.0006978512}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Salley knows whether or not everyone's forehead is muddy. It is publicly announced that Salley knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Devin can now know that Salley can know that Devin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Devin","Salley"],"index":38857,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9777184129,"difficulty":0.0222815871}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mallory's card is shown to Mallory. Justin's card is shown to Mallory. Joanne's card is shown to Mallory. Justin's card is shown to Justin. Justin's card is shown to Joanne. Mallory's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Mallory picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Mallory can now know whether Joanne can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mallory","Justin","Joanne","Fred"],"index":47714,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999132812,"difficulty":0.000867188}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Gloria can now know whether William can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Anthony","Gloria","George"],"index":56947,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999380827,"difficulty":0.000619173}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Chastity can now know whether Ralph can know that Chastity's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ralph","Chastity"],"index":7337,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7813766599,"difficulty":0.2186233401}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathan's card is shown to Nathan. John's card is shown to Nathan. Nathan's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Mark knows whether or not everyone picked a red card. It is publicly announced that Nathan knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Nathan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Nathan","John"],"index":2281,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994662404,"difficulty":0.0005337596}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beau's card is shown to Mildred. Sean's card is shown to Alice. Alice's card is shown to Alice. Sean's card is shown to Beau. Mildred's card is shown to Beau. Beau's card is shown to Beau. It is publicly announced that someone picked a red card. It is publicly announced that Mildred knows whether Alice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Alice can now know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sean","Mildred","Alice","Beau"],"index":63673,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9527548552,"difficulty":1.9527548552}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Jason's card is shown to William. Steven's card is shown to Jason. Leland's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Steven picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Steven","Leland","Jason"],"index":14324,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996981442,"difficulty":0.003018558}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwain's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Dwain can now know that Nathan can know that Nathan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nathan","Sherry","Dwain"],"index":58830,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979844093,"difficulty":0.0020155907}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Michael. Mikel's card is shown to Ruth. Ruth's card is shown to Mikel. It is publicly announced that someone picked a red card. It is publicly announced that Mikel does not know whether Mikel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mikel can now know that Ruth can know that Mikel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Ruth","Mikel","Jack"],"index":39112,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9915286303,"difficulty":0.0084713697}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard knows whether Tony's forehead is muddy. It is publicly announced that Howard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Tony can now know that Howard can know whether Howard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tony","Howard"],"index":16682,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994630218,"difficulty":0.0005369782}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"George can now know that Anita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anita","John","George"],"index":61789,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977422953,"difficulty":0.0022577047}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Floyd's card is shown to Floyd. Peter's card is shown to Floyd. James's card is shown to Floyd. Floyd's card is shown to Richard. Richard's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Floyd can now know that Peter can know that Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Floyd","Richard","Peter","James"],"index":67008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982308745,"difficulty":0.0017691255}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beau's card is shown to Marilyn. John's card is shown to Beau. Beau's card is shown to Beau. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Marilyn can know that Marilyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Marilyn","Beau"],"index":7489,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972658157,"difficulty":0.0027341843}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Claire's forehead is muddy. It is publicly announced that Claire's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Claire can now know that Donald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donald","Claire"],"index":66460,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984714389,"difficulty":0.0015285611}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Eva. It is publicly announced that someone picked a red card. It is publicly announced that Eva knows whether someone picked a red card. It is publicly announced that Eva does not know whether Eva picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Eva can now know that Charles can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Eva","Leslie"],"index":38621,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9550372362,"difficulty":0.0449627638}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilma knows whether Wilma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Carolyn can now know that Charles can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Charles","Carolyn","Wilma"],"index":30846,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940561056,"difficulty":0.0059438944}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Shirley. Rose's card is shown to Justin. Silvia's card is shown to Justin. Shirley's card is shown to Rose. Justin's card is shown to Rose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know that Rose can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirley","Justin","Rose","Silvia"],"index":40971,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990327358,"difficulty":0.0009672642}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosemary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Rosemary can now know that Mary can know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosemary","Chris","Mary"],"index":14923,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993491769,"difficulty":0.0006508231}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Mark is thirsty. It is publicly announced that Alta does not know whether Mark is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"James can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","James","Alta","Mark"],"index":29127,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9773287177,"difficulty":0.0226712823}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"John can now know whether Patricia can know whether Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Patricia","John","Johnny"],"index":2405,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994578958,"difficulty":0.0005421042}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Louis can now know that Suzanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Suzanne","Louis"],"index":4560,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982313514,"difficulty":0.0017686486}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Carol can now know that Danny can know that Danny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Estelle","Danny","Manuel","Carol"],"index":61477,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9941053391,"difficulty":0.0058946609}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marguerite does not know whether Gail is thirsty. It is publicly announced that Joseph does not know whether Marguerite is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Marguerite can now know whether Joseph can know whether Gail is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Marguerite","Gail"],"index":20686,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990757704,"difficulty":0.0009242296}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eugene can now know whether Clint can know whether Stephanie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Eugene","Clint","Stephanie"],"index":45952,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990861416,"difficulty":0.0009138584}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Amy can now know that Linda can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amy","Linda","Katharine"],"index":50171,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993801117,"difficulty":0.0006198883}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ken is not thirsty. It is publicly announced that Michael does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Rita can now know whether Ken can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rita","Mary","Michael","Ken"],"index":9082,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9965909719,"difficulty":0.0034090281}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert knows whether or not nobody is thirsty. It is publicly announced that Robert does not know whether James is thirsty. It is publicly announced that Andrea knows whether or not everyone is thirsty. It is publicly announced that James knows whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Andrea","James"],"index":46031,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990381002,"difficulty":0.0009618998}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jason can now know whether Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jason","Amanda","Richard","Maurice"],"index":38380,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993082285,"difficulty":0.0006917715}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Juan can now know that Mario can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irma","Shirley","Mario","Juan"],"index":22265,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989809394,"difficulty":0.0010190606}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Tony can now know whether David can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Tony","Elvia"],"index":44163,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992908239,"difficulty":0.0007091761}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Michael. Michael's card is shown to Michael. David's card is shown to Michael. Matthew's card is shown to David. Martha's card is shown to David. Martha's card is shown to Martha. It is publicly announced that someone picked a red card. It is publicly announced that Martha picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Matthew can now know whether David can know whether Martha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Michael","David","Martha"],"index":39134,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989314675,"difficulty":0.0010685325}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether Jean's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jean can now know that Willie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Willie","Jean"],"index":33469,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989500642,"difficulty":0.0010499358}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Soila's card is shown to Ronnie. Soila's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ronnie can now know that Ronnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronnie","Joseph","Soila"],"index":13144,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9914242625,"difficulty":0.0085757375}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aaron knows whether someone's forehead is muddy. It is publicly announced that Young's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Young can now know that Terrance's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terrance","Young","Aaron"],"index":32388,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9552783966,"difficulty":0.0447216034}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to George. Paul's card is shown to George. George's card is shown to Kristina. Paul's card is shown to Kristina. Kristina's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Paul does not know whether George picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"George can now know whether Paul can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Kristina","Paul"],"index":21020,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977059364,"difficulty":0.0022940636}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Albert can now know that Bettina can know that Ana is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Albert","Christopher","Bettina","Ana"],"index":29982,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965879917,"difficulty":0.0034120083}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacy does not know whether Stacy's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Stacy","Albert"],"index":54583,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5903241038,"difficulty":1.5903241038}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judy does not know whether Virginia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Charles can now know that Joel can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Judy","Joel","Virginia"],"index":48218,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988822341,"difficulty":0.0011177659}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Julia. Marie's card is shown to Julia. Julia's card is shown to Marie. Thelma's card is shown to Marie. Kenneth's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth picked a red card. It is publicly announced that Thelma does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thelma can now know that Thelma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julia","Thelma","Kenneth","Marie"],"index":41884,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7828445435,"difficulty":1.7828445435}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy. It is publicly announced that Betty's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Betty can now know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Betty"],"index":50976,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994174242,"difficulty":0.0005825758}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christina knows whether someone is thirsty. It is publicly announced that Christina does not know whether Paul is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Christina can now know whether Paul can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Christina"],"index":21076,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9885593057,"difficulty":1.9885593057}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pauline does not know whether Pauline's forehead is muddy. It is publicly announced that Pauline does not know whether Pauline's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Alexander can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","Emma","Rose","Alexander"],"index":12339,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989904761,"difficulty":0.0010095239}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susanna's card is shown to Mary. Virgina's card is shown to Virgina. Lisa's card is shown to Virgina. Virgina's card is shown to Lisa. Susanna's card is shown to Susanna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susanna can now know whether Mary can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Virgina","Lisa","Susanna"],"index":63550,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991606474,"difficulty":0.0008393526}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather does not know whether Laura is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Laura can now know that Heather can know that Heather is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Heather","Laura","Lucio"],"index":63788,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9822177291,"difficulty":0.0177822709}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louis knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know whether Louis can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lorraine","Louis","Timothy"],"index":55634,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999491334,"difficulty":0.000508666}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Larry can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeremy","Larry","Sonia"],"index":6200,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9922661185,"difficulty":0.0077338815}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Benjamin can now know that Marcus can know whether Marcus's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dwight","Paul","Marcus","Benjamin"],"index":3161,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999412179,"difficulty":0.000587821}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Alexander is thirsty. It is publicly announced that Alexander does not know whether John is thirsty. It is publicly announced that John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Alexander can now know whether Scott is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Scott","Alexander","John","Brian"],"index":51038,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979739785,"difficulty":0.0020260215}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Katherine can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Katherine","James"],"index":37243,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986922145,"difficulty":0.0013077855}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nga does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jimmy can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Nga","Jimmy","Susan"],"index":27695,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968808889,"difficulty":0.0031191111}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilma's card is shown to Wilma. Natalia's card is shown to Natalia. Donald's card is shown to Natalia. Lloyd's card is shown to Lloyd. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilma can now know whether Wilma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wilma","Natalia","Lloyd","Donald"],"index":9385,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5755204558,"difficulty":0.4244795442}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Antonio. Antonio's card is shown to Larry. Larry's card is shown to Jessica. Larry's card is shown to Joe. It is publicly announced that someone picked a red card. It is publicly announced that Jessica knows whether or not everyone picked a red card. It is publicly announced that Joe does not know whether Jessica picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Larry can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Antonio","Larry","Jessica","Joe"],"index":25460,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994714856,"difficulty":0.0005285144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Natalie does not know whether Natalie's forehead is muddy. It is publicly announced that Rod's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Natalie can now know whether Tony can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tony","Natalie","Nanci","Rod"],"index":45728,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9876313806,"difficulty":0.0123686194}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether Elizabeth is thirsty. It is publicly announced that William knows whether or not everyone is thirsty. It is publicly announced that William does not know whether Mark is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mark can now know that Elizabeth can know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","Mark","William"],"index":44345,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9629180431,"difficulty":0.0370819569}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Edward can now know whether Ward can know whether Ward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Ward","Edward"],"index":2505,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994511008,"difficulty":0.0005488992}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Terrie. Terrie's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"David can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terrie","David","Robert"],"index":3348,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9269023538,"difficulty":1.9269023538}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abbie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Natasha can now know that Virginia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Natasha","Abbie","Virginia"],"index":42425,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979900122,"difficulty":0.0020099878}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregorio's forehead is muddy. It is publicly announced that Bruce does not know whether Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Margaret can now know whether Gregorio can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bruce","Margaret","Gregorio"],"index":16462,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992961884,"difficulty":0.0007038116}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Joyce. Anthony's card is shown to Joyce. Carol's card is shown to Anthony. Joyce's card is shown to Anthony. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Jose","Joyce","Anthony"],"index":40717,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966611862,"difficulty":0.0033388138}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Laura can now know whether Anne can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laura","Anne","Kelly"],"index":21705,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999368608,"difficulty":0.000631392}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Barbara. Leo's card is shown to Leo. Amy's card is shown to Leo. Barbara's card is shown to Amy. Leo's card is shown to Amy. Amy's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Leo does not know whether or not everyone picked a red card. It is publicly announced that Amy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Barbara can now know whether Amy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Leo","Amy"],"index":36033,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994366765,"difficulty":0.0005633235}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Linda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agentc knows that (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Richard can now know that John can know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Donna","Richard","John"],"index":52422,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994045496,"difficulty":0.0005954504}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen knows whether someone's forehead is muddy. It is publicly announced that Darcy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Ellen can now know that Darcy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Courtney","Rita","Darcy","Ellen"],"index":62505,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9904583693,"difficulty":0.0095416307}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah does not know whether Michaela is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Paul can now know whether Michaela can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michaela","James","Deborah","Paul"],"index":42311,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993932247,"difficulty":0.0006067753}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arturo's forehead is muddy. It is publicly announced that Arturo knows whether or not nobody's forehead is muddy. It is publicly announced that Cynthia does not know whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Cynthia can now know that Arturo can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cynthia","Richard","Arturo"],"index":66926,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991855025,"difficulty":0.0008144975}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruben knows whether someone's forehead is muddy. It is publicly announced that Ralph's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Ralph can now know whether Ruben's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ralph","Ruben"],"index":23959,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9976218343,"difficulty":0.0023781657}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keisha knows whether Adalberto's forehead is muddy. It is publicly announced that Amy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Adalberto can now know whether Amy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Walter","Amy","Keisha","Adalberto"],"index":58595,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994713664,"difficulty":0.0005286336}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty. It is publicly announced that Alton does not know whether Richard is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty. It is publicly announced that Richard does not know whether Alton is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Michael can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Michael","Alton"],"index":46429,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994891882,"difficulty":0.0005108118}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tim knows whether Eva's forehead is muddy. It is publicly announced that Erika knows whether Erika's forehead is muddy. It is publicly announced that Erika's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Thomas can now know that Tim can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Erika","Thomas","Tim","Eva"],"index":19451,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990245104,"difficulty":0.0009754896}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melvin's forehead is muddy. It is publicly announced that Melvin's forehead is muddy. It is publicly announced that Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Paul can now know that Melvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Minnie","Paul","Melvin"],"index":66989,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8794289231,"difficulty":0.1205710769}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Clarence. Betty's card is shown to Clarence. Clarence's card is shown to Jeffrey. Betty's card is shown to Jeffrey. Jeffrey's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jeffrey can now know that Clarence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clarence","Betty","Jeffrey","Willie"],"index":48808,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9428229928,"difficulty":1.9428229928}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that Juana knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Christine can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Juana","James","Christine"],"index":49800,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992670417,"difficulty":0.0007329583}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lewis's card is shown to Lewis. Lewis's card is shown to Jane. Patricia's card is shown to Jane. Patricia's card is shown to Patricia. Jane's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jane can now know whether James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lewis","Jane","Patricia","James"],"index":16396,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992208481,"difficulty":0.0007791519}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andre does not know whether Andre's forehead is muddy. It is publicly announced that Raymond does not know whether or not everyone's forehead is muddy. It is publicly announced that Jill knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Jill can now know that Andre's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andre","Raymond","Jeffrey","Jill"],"index":5161,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6644993424,"difficulty":1.6644993424}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Winnie's card is shown to Winnie. Francisco's card is shown to Francisco. Andrea's card is shown to Francisco. Winnie's card is shown to Andrea. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Andrea can now know whether Francisco can know whether Winnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Winnie","Francisco","Andrea"],"index":11329,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9989032745,"difficulty":1.9989032745}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Kyung is thirsty. It is publicly announced that Joseph does not know whether John is thirsty. It is publicly announced that Kyung does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"John can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Leigh","Joseph","Kyung"],"index":10205,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999384284,"difficulty":0.000615716}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Don's card is shown to Ashley. Kathy's card is shown to Ashley. Don's card is shown to Don. Kathy's card is shown to Don. Kathy's card is shown to Linda. Don's card is shown to Kathy. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Don picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Don can now know that Linda can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ashley","Don","Linda","Kathy"],"index":10229,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9906518459,"difficulty":0.0093481541}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy. It is publicly announced that Bob knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Bob can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bob","Ruth"],"index":47926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987872243,"difficulty":0.0012127757}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Coleen's card is shown to Coleen. Jesse's card is shown to Coleen. Coleen's card is shown to Jesse. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Jesse picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Jesse can now know whether Coleen can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Coleen","Jesse"],"index":8891,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9963130355,"difficulty":0.0036869645}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Peter can now know whether Megan can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dan","Peter","Megan"],"index":24388,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993287325,"difficulty":0.0006712675}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Anthony can now know that Vernon can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wanda","Vernon","Anthony","James"],"index":30513,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989528656,"difficulty":0.0010471344}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vicki can now know that Mary can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vicki","Mary","Melissa"],"index":35950,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992780089,"difficulty":0.0007219911}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arthur does not know whether Esther is thirsty. It is publicly announced that Arthur does not know whether Steve is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Arthur can now know whether Esther can know that Steve is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Esther","Arthur","Steve"],"index":21733,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.990308702,"difficulty":0.009691298}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eduardo is not thirsty. It is publicly announced that Eduardo does not know whether Robert is thirsty. It is publicly announced that Rosetta does not know whether Mary is thirsty. It is publicly announced that Rosetta does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Robert can now know whether Mary can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosetta","Robert","Eduardo","Mary"],"index":23433,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9735537171,"difficulty":1.9735537171}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"James can now know that Betty can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Betty","James"],"index":23544,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989171028,"difficulty":0.0010828972}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Demetrice does not know whether Demetrice's forehead is muddy. It is publicly announced that Shana knows whether Demetrice's forehead is muddy. It is publicly announced that Chuck knows whether Chuck's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Chuck can now know that Demetrice's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Chuck","Demetrice","Shana"],"index":47876,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9246591926,"difficulty":0.0753408074}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Abram's card is shown to Joseph. Joseph's card is shown to Abram. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Abram can now know that Joseph can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Abram"],"index":51828,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993596673,"difficulty":0.0006403327}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucille does not know whether or not everyone is thirsty. It is publicly announced that Lucille does not know whether Jennifer is thirsty. It is publicly announced that Annette does not know whether Jennifer is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ada can now know that Ada is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ada","Annette","Jennifer","Lucille"],"index":8025,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9924013615,"difficulty":0.0075986385}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeanna's card is shown to Jeanna. Ellen's card is shown to Dollie. Steven's card is shown to Ellen. It is publicly announced that someone picked a red card. It is publicly announced that Ellen does not know whether Ellen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ellen can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeanna","Dollie","Ellen","Steven"],"index":41227,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990385771,"difficulty":0.0009614229}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Matthew. Jose's card is shown to Helen. Jose's card is shown to Ginger. It is publicly announced that someone picked a red card. It is publicly announced that Jose picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Helen can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Jose","Helen","Ginger"],"index":33266,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9883745909,"difficulty":0.0116254091}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Edward can now know that Anne can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edward","Anne"],"index":47485,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994245768,"difficulty":0.0005754232}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Venessa can now know whether Elizabeth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Venessa","Richard","Elizabeth","Esther"],"index":25421,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9810910225,"difficulty":0.0189089775}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Steven can now know that Ellena can know that Ellena's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Alice","Ellena","Betty"],"index":2029,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997412622,"difficulty":0.002587378}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentc knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Laura can now know that Tracy can know that Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brandy","Diane","Laura","Tracy"],"index":55868,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976626635,"difficulty":0.0023373365}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether someone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] 0","hypothesis":"David can now know whether Karen can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Karen","David"],"index":61380,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9920631051,"difficulty":0.0079368949}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna's forehead is not muddy. It is publicly announced that Victor knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Anna can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Victor","Anna","Maria"],"index":55161,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988104105,"difficulty":0.0011895895}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sara does not know whether Era is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Era can now know that Sara can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sara","Era"],"index":44811,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993599057,"difficulty":0.0006400943}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Bettie knows whether someone's forehead is muddy. It is publicly announced that Laura knows whether Bettie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Bettie can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Robert","James","Bettie"],"index":6090,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987963438,"difficulty":0.0012036562}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herman knows whether Herman's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Trisha can now know whether Tim can know whether Tim's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Trisha","Tim","Herman"],"index":25727,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9822351933,"difficulty":1.9822351933}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Johnny's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Jeff can now know that Joe can know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeff","Johnny","Joe"],"index":60848,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9944203496,"difficulty":0.0055796504}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Krista can now know whether William can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","William","Krista","Caryn"],"index":61874,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993334413,"difficulty":0.0006665587}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Loyd. Loyd's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether Patricia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Loyd","Patricia"],"index":55517,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994508624,"difficulty":0.0005491376}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Paul. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether someone picked a red card. It is publicly announced that Charles does not know whether Paul picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Charles can now know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Paul"],"index":64660,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8412932158,"difficulty":1.8412932158}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Andrew. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Andrew picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Donald can now know that Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrew","Donald","Raymond"],"index":7033,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9913411736,"difficulty":0.0086588264}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arron does not know whether Rosalie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Arron can now know that Lucille can know whether Rosalie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Arron","Rosalie","Lucille"],"index":60184,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965462089,"difficulty":0.0034537911}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Claire's forehead is muddy. It is publicly announced that Maggie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Claire can now know whether Maggie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maggie","Claire"],"index":43828,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994555116,"difficulty":0.0005444884}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether Delores's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Delores can now know that Jeffrey can know whether Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeffrey","Delores"],"index":32421,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931374788,"difficulty":0.0068625212}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wilfred knows whether Rita is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Wilfred can now know whether Rita can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rita","Wilfred"],"index":40753,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9948071837,"difficulty":0.0051928163}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy knows whether Timothy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Tammy can now know whether Timothy can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tammy","Anna","Patricia","Timothy"],"index":61741,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994751811,"difficulty":0.0005248189}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lauretta's forehead is not muddy. It is publicly announced that Mark knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Mark can now know that Stacy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lauretta","Mark","Stacy"],"index":63170,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984794259,"difficulty":0.0015205741}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Jerry can now know that Richard can know that Jerry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerry","Richard","Peter","John"],"index":41555,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975782037,"difficulty":0.0024217963}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know whether Magen can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Magen","Bobby","James","Helen"],"index":17933,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982392788,"difficulty":0.0017607212}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know whether Betty can know whether Betty is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","Guy","Betty"],"index":35856,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9856966734,"difficulty":0.0143033266}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Renee. Peter's card is shown to Peter. Christopher's card is shown to Christopher. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Keith","Renee","Peter","Christopher"],"index":67652,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9877748489,"difficulty":1.9877748489}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Lucy. Evelyn's card is shown to Lucy. Dennis's card is shown to Dennis. Evelyn's card is shown to Dennis. George's card is shown to Dennis. Dennis's card is shown to Evelyn. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Dennis knows whether George picked a red card. It is publicly announced that George does not know whether Lucy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Evelyn can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lucy","Dennis","Evelyn","George"],"index":37724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994438291,"difficulty":0.0005561709}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Kristen. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Annie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Annie","Roland","Kristen"],"index":3155,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9938568473,"difficulty":0.0061431527}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Steven. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Steven knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Steven can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Steven","James"],"index":37162,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993823767,"difficulty":0.0006176233}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Gregorio can now know whether Jessica can know whether Clarence's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Gregorio","Clarence","Francis"],"index":37663,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993216991,"difficulty":0.0006783009}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy's forehead is not muddy. It is publicly announced that Judith's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Derek can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Derek","Judith","Dorothy"],"index":32558,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993548989,"difficulty":0.0006451011}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that David knows whether Reginald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Reginald can now know whether David can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Rebekah","Reginald"],"index":8047,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994538426,"difficulty":0.0005461574}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ian's card is shown to Ian. Pablo's card is shown to Ian. Pablo's card is shown to Pablo. Julie's card is shown to Pablo. Ian's card is shown to Sarah. Pablo's card is shown to Sarah. Ian's card is shown to Julie. Julie's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Ian knows whether Ian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ian can now know whether Pablo can know whether Ian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ian","Pablo","Sarah","Julie"],"index":60619,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987615347,"difficulty":0.0012384653}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Matthew. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Matthew knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Matthew can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Matthew","Douglas"],"index":48252,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994136095,"difficulty":0.0005863905}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Virgil knows whether Teresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Teresa can now know whether Virgil can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Virgil","Dorothea","Teresa"],"index":21918,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992477894,"difficulty":0.0007522106}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Carolyn can now know that Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Albert","Rosemarie","Carolyn"],"index":46037,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979470372,"difficulty":0.0020529628}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Paul can now know that James can know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Paul","Ginger","Donna"],"index":19033,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994103909,"difficulty":0.0005896091}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqueline's card is shown to Jacqueline. Diane's card is shown to Jacqueline. Diane's card is shown to Diane. It is publicly announced that someone picked a red card. It is publicly announced that Diane does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Diane can now know whether Jacqueline can know that Jacqueline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jacqueline","Diane"],"index":13681,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6916381717,"difficulty":1.6916381717}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark knows whether or not nobody is thirsty. It is publicly announced that Mark does not know whether Jaime is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mark can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Jaime","Jonathan"],"index":23221,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989925027,"difficulty":0.0010074973}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Nicole can now know that Carmen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arthur","Nicole","Jo","Carmen"],"index":27341,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998190701,"difficulty":0.001809299}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mae knows whether someone's forehead is muddy. It is publicly announced that Trinidad does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Mae can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mae","Trinidad","Elizabeth","Mark"],"index":64654,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994572997,"difficulty":0.0005427003}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Jose. Zenaida's card is shown to Jose. Elaine's card is shown to Elaine. Elaine's card is shown to Zenaida. Zenaida's card is shown to Zenaida. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Jose picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Elaine can now know whether Jose can know that Elaine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jose","Elaine","Zenaida"],"index":9305,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9392780662,"difficulty":0.0607219338}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katrina knows whether Kenneth's forehead is muddy. It is publicly announced that Katrina's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Kenneth can now know that Katrina can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenneth","Katrina"],"index":67207,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994447827,"difficulty":0.0005552173}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dora's card is shown to Dora. Dora's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Dora does not know whether Scott picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Scott can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dora","Scott"],"index":45201,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988490343,"difficulty":0.0011509657}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shannon knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Sherri can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherri","Shannon","Margaret"],"index":44877,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987843633,"difficulty":0.0012156367}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer does not know whether Teddy is thirsty. It is publicly announced that Adam does not know whether Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Adam can now know that Jennifer can know that Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jack","Teddy","Jennifer","Adam"],"index":55456,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9864931703,"difficulty":0.0135068297}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Florence can now know whether Margo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Florence","Margo"],"index":29771,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994075298,"difficulty":0.0005924702}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Maria can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Amy","Connie","Marjorie"],"index":57149,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998971343,"difficulty":0.001028657}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jack is not thirsty. It is publicly announced that Jack knows whether or not everyone is thirsty. It is publicly announced that Marcus does not know whether Richard is thirsty. It is publicly announced that Richard knows whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Marcus can now know that Richard can know whether Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jack","Marcus","Richard"],"index":31916,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979835749,"difficulty":0.0020164251}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Johnny knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Charlotte can now know that Johnny can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Irene","Charlotte","Johnny"],"index":63527,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989057779,"difficulty":0.0010942221}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Matthew. Matthew's card is shown to Roger. Roger's card is shown to Roger. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Alan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jose can now know whether Jose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Jose","Alan","Roger"],"index":56123,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5780153275,"difficulty":1.5780153275}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Thomas can now know whether Martha can know whether Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Teresa","Martha","Patricia"],"index":48430,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994476438,"difficulty":0.0005523562}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Laura's card is shown to Laura. Joseph's card is shown to Kristen. It is publicly announced that someone picked a red card. It is publicly announced that Joseph picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Laura can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Laura","Kristen","David"],"index":18552,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965590835,"difficulty":0.0034409165}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Essie can now know that Jared can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Laura","Essie","Jared"],"index":7977,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989520311,"difficulty":0.0010479689}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Phil. Cassondra's card is shown to Cassondra. Francis's card is shown to Cassondra. Ann's card is shown to Cassondra. Cassondra's card is shown to Francis. Francis's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Ann does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Cassondra can now know that Ann picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Phil","Cassondra","Francis","Ann"],"index":10579,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8196542263,"difficulty":0.1803457737}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Betty can now know that Lakesha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Lakesha","Julissa","Levi"],"index":26794,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973157048,"difficulty":0.0026842952}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry does not know whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Amy can now know that Henry can know that Henry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Henry","Harold","Amy"],"index":62403,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9797404408,"difficulty":0.0202595592}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leonard's card is shown to Dorothy. Leonard's card is shown to Gloria. Gloria's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy does not know whether Dorothy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dorothy can now know that Leonard can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Leonard","Gloria"],"index":47721,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993991852,"difficulty":0.0006008148}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy knows whether or not everyone's forehead is muddy. It is publicly announced that Randy knows whether Merlin's forehead is muddy. It is publicly announced that Randy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Merlin can now know that Randy can know whether Randy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randy","Merlin"],"index":15096,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989927411,"difficulty":0.0010072589}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Ian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Gary can now know whether Megan can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Gary","Megan","Ian"],"index":25317,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990866184,"difficulty":0.0009133816}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marc does not know whether Marc's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Jacob can now know whether Jeremy can know that Jacob's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacob","Doris","Jeremy","Marc"],"index":21127,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9765333533,"difficulty":0.0234666467}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elmer's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Carlos can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Elmer","Carlos","Nicolas"],"index":7179,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987620115,"difficulty":0.0012379885}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Earl's card is shown to David. David's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"David can now know whether Michael can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","David","Earl"],"index":22139,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993872643,"difficulty":0.0006127357}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Jonathan. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Catherine picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Catherine can now know whether Jonathan can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jonathan","Catherine"],"index":56295,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994615912,"difficulty":0.0005384088}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Ruby can now know whether Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Barbara","Ruby"],"index":20121,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990614057,"difficulty":0.0009385943}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cory knows whether Cory's forehead is muddy. It is publicly announced that Cory's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agentb knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Elizabeth can now know that Randall can know whether Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cory","Elizabeth","Randall","Edward"],"index":11745,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993928671,"difficulty":0.0006071329}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Kari's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Kari can now know that Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kari","Robert"],"index":63633,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5816839933,"difficulty":1.5816839933}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Julie. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Julie knows whether or not nobody picked a red card. It is publicly announced that Evelyn knows whether Julie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Evelyn can now know whether Julie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Julie","Evelyn"],"index":3561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9830806851,"difficulty":0.0169193149}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wilfred does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Patricia can know that Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Wilfred","John","Joseph"],"index":66511,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6138326526,"difficulty":0.3861673474}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Hubert can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Hubert","Stacy","Tony"],"index":7210,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992884398,"difficulty":0.0007115602}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Jeffrey. Lucille's card is shown to Lucille. Ann's card is shown to Lucille. Ann's card is shown to Barbara. Jeffrey's card is shown to Ann. Lucille's card is shown to Ann. Barbara's card is shown to Ann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ann can now know whether Lucille can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Lucille","Barbara","Ann"],"index":56298,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993950129,"difficulty":0.0006049871}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether or not nobody's forehead is muddy. It is publicly announced that Myriam knows whether Dana's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Dana can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dana","Myriam"],"index":28098,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999268353,"difficulty":0.000731647}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Helen can now know that Michelle can know that Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Kevin","Michelle","Jack"],"index":29052,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983798265,"difficulty":0.0016201735}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marietta knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Marietta can now know that Kyle can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marietta","Kyle"],"index":60446,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987891316,"difficulty":0.0012108684}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Amber can now know that Jennifer can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Jennifer","Amber"],"index":47474,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989696741,"difficulty":0.0010303259}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether or not nobody's forehead is muddy. It is publicly announced that Nancy does not know whether Nancy's forehead is muddy. It is publicly announced that Nancy does not know whether Nancy's forehead is muddy. It is publicly announced that Nancy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Nancy can now know that Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harold","Pamela","Nancy"],"index":13948,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.663208127,"difficulty":0.336791873}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brittany's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Willie can now know that Jimmie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brittany","Jimmie","Willie"],"index":16411,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988779426,"difficulty":0.0011220574}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Betty can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Krista","Betty"],"index":15579,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998947084,"difficulty":0.001052916}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Gerry can now know whether Erin can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erin","Christina","Gerry"],"index":9661,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993809462,"difficulty":0.0006190538}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Fay is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Fay can now know that Craig can know that Craig is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Fay","Craig","Joanne"],"index":22142,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966077805,"difficulty":0.0033922195}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason does not know whether Christina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Sarah can now know whether Christina can know whether Jason is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Jason","Christina"],"index":54144,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991944432,"difficulty":0.0008055568}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry's forehead is not muddy. It is publicly announced that Harry's forehead is not muddy. It is publicly announced that Harry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Melvin can now know whether Steven can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Harry","Randy","Melvin"],"index":28603,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999382019,"difficulty":0.000617981}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebekah knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Christopher can now know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebekah","Christopher","Lee","Jennifer"],"index":29195,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9853583574,"difficulty":0.0146416426}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Dale can know that Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Lila","Dale","Lashanda"],"index":10770,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977229238,"difficulty":0.0022770762}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wilma does not know whether Nancy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Nancy can now know whether Lisa can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Wilma","Nancy","Alexis"],"index":65337,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989694357,"difficulty":0.0010305643}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Sylvia can now know that William can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sylvia","William"],"index":20761,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.995136559,"difficulty":0.004863441}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa knows whether or not everyone is thirsty. It is publicly announced that Steven is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(2) ] Agenta knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"John can now know that Lisa can know whether Lisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Steven","Lisa","Robert"],"index":65453,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998144865,"difficulty":0.001855135}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew's forehead is not muddy. It is publicly announced that Andrew's forehead is not muddy. It is publicly announced that Andrew's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Andrew can now know whether Lisa can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kay","Andrew","Phillip","Lisa"],"index":3808,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993551373,"difficulty":0.0006448627}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Louis. Shanon's card is shown to Louis. Michelle's card is shown to Michelle. Louis's card is shown to Shanon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michelle can now know whether Louis can know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louis","Michelle","Shanon"],"index":7536,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983657002,"difficulty":0.0016342998}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Micheal knows whether Julio's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julio does not know whether Julio's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Zenobia can now know whether Micheal's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Micheal","Zenobia","Julio"],"index":35418,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989929795,"difficulty":0.0010070205}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Iola's card is shown to Bernice. Cortez's card is shown to Bernice. Iola's card is shown to Iola. Bernice's card is shown to Cortez. Iola's card is shown to Cortez. Cortez's card is shown to Cortez. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cortez can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bernice","Iola","Cortez"],"index":18114,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994015694,"difficulty":0.0005984306}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Classie's card is shown to Mary. Mary's card is shown to Classie. Classie's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Classie can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Classie","Patricia"],"index":29768,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8596377969,"difficulty":0.1403622031}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Aurora is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Aurora can now know that Marjory can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marjory","Aurora"],"index":50991,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993942976,"difficulty":0.0006057024}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Diana can now know whether Delmar can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Diana","Mary","Delmar","Judith"],"index":64551,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994594455,"difficulty":0.0005405545}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arthur does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Arthur can now know that Earl is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pamela","Arthur","John","Earl"],"index":17367,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9755868316,"difficulty":0.0244131684}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robbie's card is shown to Kevin. Jeremy's card is shown to Wendell. Robbie's card is shown to Wendell. Jeremy's card is shown to Jeremy. Jeremy's card is shown to Robbie. It is publicly announced that someone picked a red card. It is publicly announced that Kevin does not know whether Jeremy picked a red card. It is publicly announced that Jeremy picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] Agentd knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Robbie can now know that Jeremy can know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Wendell","Jeremy","Robbie"],"index":29564,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8795459867,"difficulty":0.1204540133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Cherie can now know that Richard can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amber","Richard","Cherie","Joseph"],"index":35323,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989947677,"difficulty":0.0010052323}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gloria can now know that Keith can know whether Keith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Gloria","Tiffiny","Gary"],"index":36246,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960336089,"difficulty":0.0039663911}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Renee. Anthony's card is shown to Robert. Rhoda's card is shown to Rhoda. Robert's card is shown to Anthony. Rhoda's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Rhoda does not know whether Robert picked a red card. It is publicly announced that Renee knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that Anthony can know that Renee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Renee","Robert","Rhoda","Anthony"],"index":63253,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9894869328,"difficulty":0.0105130672}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmelita's card is shown to Carmelita. Bradley's card is shown to Bradley. It is publicly announced that someone picked a red card. It is publicly announced that Bradley picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Bradley can now know that Bradley picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Carmelita","Bradley"],"index":63516,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9954684973,"difficulty":0.0045315027}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose does not know whether Jose's forehead is muddy. It is publicly announced that Tyson's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] 0","hypothesis":"Tyson can now know that Charles can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Jose","Matthew","Tyson"],"index":26848,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990009665,"difficulty":0.0009990335}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhonda's forehead is not muddy. It is publicly announced that Micheal knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Micheal can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lorraine","Rhonda","Micheal","Clifford"],"index":5842,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994466901,"difficulty":0.0005533099}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Russell's card is shown to Jessica. Terry's card is shown to Jessica. Russell's card is shown to Terry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Russell","Jessica","Terry"],"index":54305,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5943257809,"difficulty":0.4056742191}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lenore does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Bessie can now know that Barbara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Madeline","Bessie","Lenore"],"index":12799,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9397543073,"difficulty":0.0602456927}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Debra can now know that Patricia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Debra","Patricia","Jeff","Kristin"],"index":12481,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988456964,"difficulty":0.0011543036}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Melissa can now know that Melissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Melissa","Rodney","Felicia","Clarence"],"index":9292,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.6379493475,"difficulty":1.6379493475}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to Ralph. Jesus's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Ralph knows whether Ralph picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jesus can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ralph","Jesus"],"index":9212,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994527698,"difficulty":0.0005472302}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Sarah. Sarah's card is shown to Dora. Ronald's card is shown to Dora. Sarah's card is shown to Ronald. Dora's card is shown to Ronald. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dora can now know whether Sarah can know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Dora","Ronald"],"index":49398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9975226521,"difficulty":0.0024773479}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tina does not know whether Howard is thirsty. It is publicly announced that Tina does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Tina can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tina","Howard"],"index":2404,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984192848,"difficulty":0.0015807152}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darlene does not know whether Natalie is thirsty. It is publicly announced that Betty is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agentc knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Roy can now know whether Darlene can know that Natalie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Darlene","Roy","Natalie"],"index":31097,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9926463366,"difficulty":0.0073536634}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Curtis's card is shown to Dorothy. Curtis's card is shown to Curtis. Tim's card is shown to Curtis. Jeffery's card is shown to Tim. Curtis's card is shown to Jeffery. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know whether Tim can know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Curtis","Tim","Jeffery"],"index":44138,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8990504146,"difficulty":0.1009495854}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Leonard can now know that Clara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Victor","Leonard","Clara"],"index":55214,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988075495,"difficulty":0.0011924505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Stuart knows whether Jamie's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Jamie can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stuart","James","Jamie","William"],"index":42426,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957440495,"difficulty":0.0042559505}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Sam's forehead is muddy. It is publicly announced that Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Daniel can now know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sam","Daniel","Jane","Elizabeth"],"index":1221,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965094924,"difficulty":0.0034905076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Manuel knows whether someone is thirsty. It is publicly announced that Betty does not know whether Manuel is thirsty. It is publicly announced that Betty is thirsty. It is publicly announced that Raymond does not know whether Manuel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Betty can now know whether Betty is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Betty","Manuel","Raymond"],"index":15374,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974384308,"difficulty":0.0025615692}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Brenda is thirsty. It is publicly announced that Brenda knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Brenda can now know whether Brenda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Donna","Brenda","Hugo"],"index":18962,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979349375,"difficulty":0.0020650625}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd knows whether someone's forehead is muddy. It is publicly announced that Kevin knows whether or not nobody's forehead is muddy. It is publicly announced that Kevin knows whether Lloyd's forehead is muddy. It is publicly announced that Jim knows whether Jim's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lloyd can now know that Jim can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lloyd","Jim","Kevin"],"index":4333,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988904595,"difficulty":0.0011095405}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jeanette can now know that William can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeanette","James","William"],"index":28877,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994501472,"difficulty":0.0005498528}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hannah's card is shown to Hannah. Angelo's card is shown to Angelo. It is publicly announced that someone picked a red card. It is publicly announced that Angelo does not know whether Hannah picked a red card. It is publicly announced that Hannah knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Angelo can now know that Hannah can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Hannah","Angelo"],"index":21668,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976569414,"difficulty":0.0023430586}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Ida. Robert's card is shown to Robert. Ida's card is shown to Vivian. Robert's card is shown to Vivian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brenda can now know whether Ida can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ida","Robert","Brenda","Vivian"],"index":62313,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992340803,"difficulty":0.0007659197}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Latasha can now know that Edith is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Latasha","Jason","Mark","Edith"],"index":13568,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9898827672,"difficulty":0.0101172328}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Claire knows whether Carrie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Claire can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carrie","Claire","Richard","Lisa"],"index":5113,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990685582,"difficulty":0.0009314418}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Della can now know whether Jennie can know that Franklin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Della","Jennie","Kathleen","Franklin"],"index":19176,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9625943899,"difficulty":0.0374056101}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Myrtice is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Robert does not know whether Myrtice is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joyce can now know that Myrtice can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","Myrtice","Selina","Robert"],"index":60516,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994484782,"difficulty":0.0005515218}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Valerie's card is shown to Diane. Diane's card is shown to Diane. Valerie's card is shown to Joseph. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Valerie knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Valerie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Valerie","Diane","Joseph"],"index":6860,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999063313,"difficulty":0.000936687}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether Allan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Allan can now know that Dana can know that Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","Rebecca","Allan","Dana"],"index":62917,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983654618,"difficulty":0.0016345382}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether or not nobody is thirsty. It is publicly announced that Sharon does not know whether Mary is thirsty. It is publicly announced that Travis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Travis can now know whether Sharon can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Mary","Travis"],"index":16024,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9914181232,"difficulty":0.0085818768}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chester does not know whether Bobby is thirsty. It is publicly announced that Tyler does not know whether Bobby is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Richard can now know whether Tyler is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tyler","Richard","Bobby","Chester"],"index":50215,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9936093092,"difficulty":0.0063906908}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rose is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Rose can now know that Erin can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Erin","Rose"],"index":21411,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8422931433,"difficulty":0.1577068567}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Nicholas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Andrew can now know that Michael can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Nicholas","Andrew"],"index":43003,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993579984,"difficulty":0.0006420016}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Amelia can now know whether Robin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robin","Amelia"],"index":14348,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.996933341,"difficulty":0.003066659}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori does not know whether Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Gene can now know that Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gene","Maria","Joann","Lori"],"index":34394,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9905208349,"difficulty":0.0094791651}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Marion. Marion's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Marion can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marion","James"],"index":7889,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956816435,"difficulty":0.0043183565}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joe is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Regina can now know whether Joe can know whether Regina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Regina","Joe","Eduardo","Willie"],"index":43578,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988627434,"difficulty":0.0011372566}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Pamela can now know that David can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pamela","David"],"index":6483,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9920525551,"difficulty":0.0079474449}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peggy does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"David can now know whether Peggy can know that Lois is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Peggy","Lois"],"index":59161,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9923079014,"difficulty":0.0076920986}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenell's card is shown to Edgar. Kristy's card is shown to Jim. Jenell's card is shown to Kristy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jim can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edgar","Jim","Kristy","Jenell"],"index":22231,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989060163,"difficulty":0.0010939837}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Richard. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Kevin picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Kevin can now know that Richard can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Kevin"],"index":56107,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6359754205,"difficulty":1.6359754205}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Jaime is thirsty. It is publicly announced that Jeffrey does not know whether William is thirsty. It is publicly announced that Jaime does not know whether or not everyone is thirsty. It is publicly announced that Angela does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentd knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Angela can now know whether Jaime can know that Angela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Jeffrey","Angela","Jaime"],"index":5467,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9560352564,"difficulty":0.0439647436}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kim knows whether someone is thirsty. It is publicly announced that Eric does not know whether Irene is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Kim can now know whether Kim is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kim","Eric","Irene"],"index":6373,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.988627255,"difficulty":0.011372745}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martin knows whether someone's forehead is muddy. It is publicly announced that Martin knows whether Martin's forehead is muddy. It is publicly announced that Angel knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Angel can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Martin","Barbara","Angel"],"index":52111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992492795,"difficulty":0.0007507205}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dean knows whether or not nobody is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Dean can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dean","Ernest","Clara"],"index":67529,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993100166,"difficulty":0.0006899834}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"William can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Brian","Michael","Timothy"],"index":51478,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994730353,"difficulty":0.0005269647}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard does not know whether or not everyone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that Leonard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Carol can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Leonard","Mary"],"index":22564,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994359612,"difficulty":0.0005640388}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Audrey knows whether Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jessica can now know that Audrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Audrey","Jessica","Adrian"],"index":19202,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983265996,"difficulty":0.0016734004}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louis's card is shown to Louis. Eric's card is shown to Louis. Stanley's card is shown to Louis. Eric's card is shown to Eric. Stanley's card is shown to Stanley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Louis can now know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Louis","Eric","Stanley"],"index":64288,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8044627905,"difficulty":0.1955372095}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Ralph. Ralph's card is shown to Victor. Victor's card is shown to Evelyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Victor can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Victor","Evelyn"],"index":8771,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955626726,"difficulty":0.0044373274}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Anne. Anne's card is shown to Leena. Leena's card is shown to Leena. Dean's card is shown to Leena. Dean's card is shown to Dean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leena can now know whether Anne can know that Dean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anne","Leena","Dean"],"index":24183,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.931119144,"difficulty":0.068880856}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Randy. Justin's card is shown to Justin. It is publicly announced that someone picked a red card. It is publicly announced that Randy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Randy can now know whether Justin can know that Randy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randy","Justin"],"index":62810,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.863463819,"difficulty":0.136536181}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lois knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lois can now know whether Lee is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lois","Lee","Daniel"],"index":46706,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966716766,"difficulty":0.0033283234}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlene does not know whether Charlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Clinton can now know whether Carmen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charlene","Clinton","Melina","Carmen"],"index":59949,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990334511,"difficulty":0.0009665489}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harvey knows whether or not nobody's forehead is muddy. It is publicly announced that Angelique's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Angelique can now know that Harvey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Dorothy","Harvey","Angelique"],"index":27272,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9946485162,"difficulty":0.0053514838}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Bridget is thirsty. It is publicly announced that James does not know whether Bridget is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Bridget can now know whether Bridget is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julie","Bridget","Samuel","James"],"index":11025,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974905252,"difficulty":0.0025094748}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sergio does not know whether Harriett is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Harriett can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harriett","Ray","Sergio"],"index":24122,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994840622,"difficulty":0.0005159378}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Benjamin's card is shown to Benjamin. Mike's card is shown to Benjamin. Benjamin's card is shown to Sebastian. Mike's card is shown to Mike. Mike's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sebastian can now know whether Benjamin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Benjamin","Sebastian","Mike","Lisa"],"index":16233,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7797218561,"difficulty":0.2202781439}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Hugh. Laura's card is shown to Hugh. Joan's card is shown to Joan. Joan's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Hugh picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Hugh can now know that Laura can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Hugh","Joan","Laura"],"index":57353,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948108196,"difficulty":0.0051891804}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katherine is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Katherine can now know that Saundra can know whether Katherine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katherine","Vincent","Saundra"],"index":33362,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9848831296,"difficulty":0.0151168704}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathleen's card is shown to Agustin. Agustin's card is shown to Agustin. Daniel's card is shown to Agustin. Agustin's card is shown to Daniel. Cathleen's card is shown to Phillip. It is publicly announced that someone picked a red card. It is publicly announced that Cathleen knows whether Phillip picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Daniel can now know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cathleen","Agustin","Daniel","Phillip"],"index":496,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5789374709,"difficulty":1.5789374709}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Pamela can now know whether Donald can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Pamela","Byron","Philip"],"index":45740,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994685054,"difficulty":0.0005314946}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janie is not thirsty. It is publicly announced that Inez is not thirsty. It is publicly announced that Janie does not know whether Rebecca is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Janie can now know whether Nelson can know that Janie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Janie","Nelson","Inez"],"index":18651,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9851934314,"difficulty":0.0148065686}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Douglas knows whether Douglas is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Connie can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Douglas","Connie","Brittany"],"index":53155,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994354844,"difficulty":0.0005645156}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norma's card is shown to David. Stacie's card is shown to David. Stacie's card is shown to Norma. Ella's card is shown to Norma. David's card is shown to Stacie. Stacie's card is shown to Stacie. Ella's card is shown to Stacie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stacie can now know that Norma can know that Ella picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Norma","Stacie","Ella"],"index":35798,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977641106,"difficulty":0.0022358894}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josephine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Marie can now know that Josephine can know whether Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marie","Josephine"],"index":35991,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979325533,"difficulty":0.0020674467}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Polly can now know that Consuelo can know that Consuelo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Consuelo","Fay","Polly"],"index":14786,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9923019409,"difficulty":0.0076980591}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick's forehead is muddy. It is publicly announced that Frederick knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Laura can now know that Frederick can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frederick","Laura"],"index":21432,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994779229,"difficulty":0.0005220771}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Salvatore knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Salvatore can now know whether Dan can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dan","Lakisha","Cheryl","Salvatore"],"index":37668,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992986917,"difficulty":0.0007013083}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Jeanette's card is shown to Jeanette. James's card is shown to Jeanette. Bradley's card is shown to Bradley. It is publicly announced that someone picked a red card. It is publicly announced that Jeanette does not know whether Valerie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Valerie can now know that James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Valerie","Jeanette","James","Bradley"],"index":4455,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953971505,"difficulty":0.0046028495}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Brenda. Joan's card is shown to George. Brenda's card is shown to Joan. George's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that George knows whether or not nobody picked a red card. It is publicly announced that George does not know whether Brenda picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"George can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brenda","George","Joan"],"index":7525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935203195,"difficulty":0.0064796805}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann's forehead is muddy. It is publicly announced that Ann knows whether Esteban's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Esteban can now know that Pamela can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Esteban","Pamela","Ann"],"index":53690,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989247918,"difficulty":0.0010752082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marlene knows whether someone is thirsty. It is publicly announced that Michael does not know whether Joyce is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Marlene knows whether Marlene is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Michael can now know that Joyce can know that Marlene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Ann","Marlene","Michael"],"index":64225,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969710112,"difficulty":0.0030289888}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Steve. Steve's card is shown to Patrick. Joseph's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Patrick picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Joseph can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Steve","Patrick","Mary"],"index":62355,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6732701659,"difficulty":1.6732701659}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyung's card is shown to Aaron. Regina's card is shown to Aaron. Angela's card is shown to Angela. Angela's card is shown to Regina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kyung can now know whether Aaron can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aaron","Kyung","Angela","Regina"],"index":26000,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993891716,"difficulty":0.0006108284}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janeen's card is shown to Janeen. Janeen's card is shown to Amos. Amos's card is shown to Amos. Joyce's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Joyce knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Amos can now know that Janeen can know whether Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Janeen","Amos","John"],"index":62429,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6859180331,"difficulty":0.3140819669}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Valerie can now know that Erika can know that Valerie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Valerie","Erika"],"index":36479,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998511374,"difficulty":0.001488626}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dylan's card is shown to Lisa. Barbara's card is shown to Lisa. Lisa's card is shown to Dylan. It is publicly announced that someone picked a red card. It is publicly announced that Dylan does not know whether Barbara picked a red card. It is publicly announced that Lisa does not know whether Lisa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lisa can now know that Dylan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Dylan","Barbara"],"index":39656,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994146824,"difficulty":0.0005853176}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yesenia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jennifer can now know that Yesenia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Jennifer","Yesenia"],"index":2603,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994742274,"difficulty":0.0005257726}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lauren knows whether or not nobody's forehead is muddy. It is publicly announced that Brenda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Lauren can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynn","Brenda","Lauren"],"index":36670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998765707,"difficulty":0.001234293}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michele knows whether Michele's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Michele can now know whether Michael can know that Michele's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bridgette","Michael","Michele","Lindsay"],"index":5102,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9512017965,"difficulty":1.9512017965}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy. It is publicly announced that Maria's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Charles can now know whether Maria can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Maria","Daniel"],"index":33424,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9949376583,"difficulty":0.0050623417}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Marilyn can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karla","Andy","Marilyn","Gregory"],"index":56314,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939014912,"difficulty":0.0060985088}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Leroy can now know that Jean can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leroy","Jean","Sadie","John"],"index":50778,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981067181,"difficulty":0.0018932819}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Alan. Robert's card is shown to Robert. Mary's card is shown to Robert. Robert's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alan","Robert","Mary"],"index":22628,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943189025,"difficulty":0.0056810975}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Brian can now know that Gregory can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Gregory","Daniel","William"],"index":25314,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991660118,"difficulty":0.0008339882}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reed's card is shown to Meredith. Meredith's card is shown to Reed. It is publicly announced that someone picked a red card. It is publicly announced that Reed knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Reed can now know whether Reed picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Meredith","Reed"],"index":1272,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6086460352,"difficulty":1.6086460352}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Melissa can now know that Anna can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anna","Melissa"],"index":14568,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989340901,"difficulty":0.0010659099}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Carla. Jesse's card is shown to Jesse. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Jesse knows whether Carla picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jesse can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carla","Jesse"],"index":43514,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990144968,"difficulty":0.0009855032}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mae does not know whether Thomas is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Thomas does not know whether Gary is thirsty. It is publicly announced that Gary does not know whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Thomas can now know whether Mae can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Mae","Thomas"],"index":67189,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994015694,"difficulty":0.0005984306}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether Donald's forehead is muddy. It is publicly announced that Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] Agentb knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] 0","hypothesis":"Linda can now know that Bobby can know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Linda","Bobby","Donald"],"index":66672,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992564321,"difficulty":0.0007435679}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Yesenia. Donna's card is shown to Eliza. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bernice can now know that Bernice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernice","Yesenia","Donna","Eliza"],"index":56153,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966756105,"difficulty":0.0033243895}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonnie does not know whether or not everyone's forehead is muddy. It is publicly announced that Lori knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Lori can now know whether Judith can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bonnie","Judith","Rodrigo","Lori"],"index":40904,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994816184,"difficulty":0.0005183816}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Ashley can now know that William can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ashley","William","Joseph"],"index":39641,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977274537,"difficulty":0.0022725463}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Britt can now know that Julie can know that Britt's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Julie","Susan","Britt"],"index":63351,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9927887321,"difficulty":0.0072112679}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rodney's card is shown to Rodney. Norman's card is shown to Rodney. Rodney's card is shown to Norman. Norman's card is shown to Norman. Julie's card is shown to Norman. Norman's card is shown to Julie. Julie's card is shown to Julie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rodney can now know whether Norman can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rodney","Norman","Julie"],"index":32556,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9820641279,"difficulty":1.9820641279}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Debra. Allen's card is shown to Beth. Beth's card is shown to Allen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Beth can now know whether Allen can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Debra","Beth","Allen"],"index":19672,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993543029,"difficulty":0.0006456971}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jamie's card is shown to Michelle. Jamie's card is shown to Jamie. It is publicly announced that someone picked a red card. It is publicly announced that Michelle knows whether Jamie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jamie can now know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michelle","Jamie"],"index":11499,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6071138978,"difficulty":0.3928861022}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen knows whether someone's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ellen can now know whether John can know whether Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellen","John","Helen"],"index":52322,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988017082,"difficulty":0.0011982918}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Maria. George's card is shown to Marco. Jane's card is shown to Marco. Jane's card is shown to George. Marco's card is shown to Jane. Jane's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Jane does not know whether George picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Marco can now know whether George can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Marco","George","Jane"],"index":1562,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9750801921,"difficulty":0.0249198079}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jack is not thirsty. It is publicly announced that Glenn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Walter can now know whether Glenn can know that Glenn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Glenn","Walter","Lizeth","Jack"],"index":62848,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9924437404,"difficulty":0.0075562596}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Peggy's card is shown to Linda. Linda's card is shown to Jeffery. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeffery can now know that Linda can know that Jeffery picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Jeffery","Peggy"],"index":58191,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976544976,"difficulty":0.0023455024}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Todd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] 0","hypothesis":"Donna can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Michelle","Todd","Leonard"],"index":39184,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994242191,"difficulty":0.0005757809}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clifford's card is shown to Clifford. Ian's card is shown to Clifford. Clifford's card is shown to Jason. Ian's card is shown to Ian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ian can now know whether Clifford can know whether Ian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clifford","Jason","Ian"],"index":43730,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983861446,"difficulty":0.0016138554}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Eloy. Jessie's card is shown to Eloy. Elizabeth's card is shown to Emma. Emma's card is shown to Jessie. Jessie's card is shown to Jessie. It is publicly announced that someone picked a red card. It is publicly announced that Jessie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Eloy can now know whether Elizabeth can know that Jessie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eloy","Elizabeth","Emma","Jessie"],"index":4653,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9690033793,"difficulty":0.0309966207}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Agatha knows whether Agatha's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Martin can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Martin","Agatha"],"index":63479,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992365837,"difficulty":0.0007634163}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know whether Glen can know that Glen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Glen","Emma"],"index":33032,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6045281291,"difficulty":1.6045281291}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Suzanne. James's card is shown to James. Suzanne's card is shown to Pat. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Suzanne can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Glenda","Suzanne","James","Pat"],"index":57755,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993962049,"difficulty":0.0006037951}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Johnnie can now know that Joshua can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Johnnie","Randall","Joshua"],"index":8196,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981903434,"difficulty":0.0018096566}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Novella can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mike","Novella","Jeanne"],"index":5713,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989466071,"difficulty":0.0010533929}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joshua's card is shown to Isabelle. Ashlee's card is shown to Isabelle. Joshua's card is shown to Perry. Isabelle's card is shown to Ashlee. Ashlee's card is shown to Ashlee. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joshua can now know whether Isabelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Isabelle","Perry","Joshua","Ashlee"],"index":60680,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5057765841,"difficulty":0.4942234159}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurice's card is shown to Amy. Maurice's card is shown to Maurice. It is publicly announced that someone picked a red card. It is publicly announced that Maurice does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Amy can now know that Maurice can know that Maurice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Amy","Maurice"],"index":41726,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.511588335,"difficulty":0.488411665}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Sherry is thirsty. It is publicly announced that Helen does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Sherry can now know that Michael can know that Jonathan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Jonathan","Sherry","Helen"],"index":1126,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983798265,"difficulty":0.0016201735}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martin's card is shown to Tracy. Sonia's card is shown to Tracy. Martin's card is shown to Martin. Martin's card is shown to Sonia. It is publicly announced that someone picked a red card. It is publicly announced that Martin knows whether Martin picked a red card. It is publicly announced that Martin does not know whether or not everyone picked a red card. It is publicly announced that Tracy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Sonia can now know that Martin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracy","Martin","Sonia"],"index":63072,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999437511,"difficulty":0.000562489}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Audrey does not know whether Madeline is thirsty. It is publicly announced that Madeline does not know whether Benjamin is thirsty. It is publicly announced that Benjamin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Lillian can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lillian","Madeline","Benjamin","Audrey"],"index":31469,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998785913,"difficulty":0.001214087}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that Jodi knows whether someone's forehead is muddy. It is publicly announced that Jodi knows whether Mary's forehead is muddy. It is publicly announced that Jodi knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that David can know that Jodi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Mary","Jodi"],"index":57488,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9950248599,"difficulty":0.0049751401}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know whether Kevin can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bette","Eleanor","Kevin","David"],"index":63247,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99939394,"difficulty":0.00060606}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dustin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Dustin can now know whether Rebecca can know that Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Byron","Dustin","Rebecca","Miguel"],"index":8363,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7071505189,"difficulty":1.7071505189}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aaron's card is shown to Donald. Lois's card is shown to Sean. Donald's card is shown to Aaron. Sean's card is shown to Aaron. Donald's card is shown to Lois. Sean's card is shown to Lois. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1,2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know that Aaron can know that Sean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Sean","Aaron","Lois"],"index":67322,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978994131,"difficulty":0.0021005869}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cecil does not know whether Terri is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Cecil can now know that Michael can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Terri","Cecil","Michael"],"index":20103,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993546605,"difficulty":0.0006453395}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Shannon can now know that Victor's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hazel","Victor","Shannon"],"index":4079,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9700474739,"difficulty":0.0299525261}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dusti's card is shown to Alaina. Dusti's card is shown to Dusti. It is publicly announced that someone picked a red card. It is publicly announced that Dusti does not know whether Alaina picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alaina can now know whether Dusti can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alaina","Dusti"],"index":28940,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992367029,"difficulty":0.0007632971}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Nola. Timothy's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Nola does not know whether Timothy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Nola can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nola","Timothy","Jeffrey"],"index":3810,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990332127,"difficulty":0.0009667873}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Walter can now know that Nita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shannon","Nita","Walter","Alicia"],"index":49635,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964247346,"difficulty":0.0035752654}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Larry's card is shown to John. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether John picked a red card. It is publicly announced that John knows whether someone picked a red card. It is publicly announced that John knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Larry can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Larry"],"index":16150,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994086027,"difficulty":0.0005913973}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether Ralph's forehead is muddy. It is publicly announced that Bernard knows whether Bernard's forehead is muddy. It is publicly announced that Bernard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentb knows whether (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Myrna can now know whether Ralph can know that Ralph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bernard","Myrna","Roy","Ralph"],"index":20024,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993588328,"difficulty":0.0006411672}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ivana does not know whether or not everyone is thirsty. It is publicly announced that Ivana does not know whether Jeffrey is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ivana can now know whether Robert can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ivana","Robert","Jeffrey"],"index":31992,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992727637,"difficulty":0.0007272363}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vicki is thirsty. It is publicly announced that Dennis knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Calvin can now know that Vicki can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dennis","Edna","Vicki","Calvin"],"index":12018,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994298816,"difficulty":0.0005701184}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ida knows whether or not everyone's forehead is muddy. It is publicly announced that Bruce's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Ida can now know whether Bruce can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ida","Bruce"],"index":27507,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994328618,"difficulty":0.0005671382}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Asley can now know whether Kevin can know that Asley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Asley","Frank"],"index":60354,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994569421,"difficulty":0.0005430579}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Adam can now know that Joyce can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joyce","Adam"],"index":45175,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994509816,"difficulty":0.0005490184}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Corey's card is shown to Corey. Gregory's card is shown to Corey. Richard's card is shown to Gregory. Corey's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Corey picked a black card. It is publicly announced that Richard knows whether Richard picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Corey can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Corey","Gregory"],"index":22458,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9137570858,"difficulty":0.0862429142}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Raymond can now know that William can know that Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Raymond","William"],"index":5437,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978517294,"difficulty":0.0021482706}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Randall. Betty's card is shown to Tracie. Randall's card is shown to Kyle. Betty's card is shown to Kyle. Kyle's card is shown to Betty. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tracie can now know whether Betty can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randall","Tracie","Kyle","Betty"],"index":36304,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993954897,"difficulty":0.0006045103}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Carlos knows whether Juan's forehead is muddy. It is publicly announced that Maria knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Carlos can now know that Juan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carlos","Michael","Juan","Maria"],"index":12105,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9941233993,"difficulty":0.0058766007}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know that Donald can know that Keith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Keith","Carl","Clayton"],"index":3581,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964888096,"difficulty":0.0035111904}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy does not know whether Nancy's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Myrna knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Myrna can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Mary","Elizabeth","Myrna"],"index":32414,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Nancy. Robert's card is shown to Nancy. Nancy's card is shown to Jason. Nancy's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jason can now know that Nancy can know that Nancy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Jason","Robert"],"index":31050,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944095016,"difficulty":0.0055904984}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Jerri can know that Jerri's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerri","Stephanie","Gary","John"],"index":32745,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960455298,"difficulty":0.0039544702}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlene's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Charlene knows whether Kelly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Charlene can now know that James can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charlene","Kelly","James"],"index":22610,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992871881,"difficulty":0.0007128119}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that Matthew knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michael can now know that Elizabeth can know whether Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","John","Michael","Elizabeth"],"index":27398,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994270802,"difficulty":0.0005729198}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether Kimber is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentd knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Katie can now know whether Brenda can know that Katie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Donna","Kimber","Katie"],"index":28907,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9661875963,"difficulty":0.0338124037}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julia's card is shown to Julia. Walter's card is shown to Julia. Walter's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether Julia picked a red card. It is publicly announced that Walter does not know whether or not everyone picked a red card. It is publicly announced that Walter does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Walter can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Julia","Walter"],"index":49096,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998285234,"difficulty":0.001714766}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Analisa can now know that Analisa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Fernando","Analisa","Doyle"],"index":8330,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9193362594,"difficulty":0.0806637406}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Linda is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Linda can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vincent","Linda","James"],"index":2698,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9858524799,"difficulty":0.0141475201}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Fred does not know whether Pamela is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Fred can now know that Cynthia can know that Cynthia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Fred","Pamela","Terry"],"index":61541,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997041285,"difficulty":0.002958715}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether Nancy's forehead is muddy. It is publicly announced that Martha knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Martha can now know that Nancy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Martha"],"index":11912,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994016886,"difficulty":0.0005983114}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Zachary does not know whether Zachary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Zachary can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Zachary","Ernest","Ronald"],"index":10529,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994341731,"difficulty":0.0005658269}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patrick does not know whether David is thirsty. It is publicly announced that Elizabeth does not know whether David is thirsty. It is publicly announced that Elizabeth does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 3) ] (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"David can now know whether Leroy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","Leroy","David","Elizabeth"],"index":11738,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983464479,"difficulty":0.0016535521}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terri's card is shown to Terri. Terri's card is shown to Maria. Terri's card is shown to Steven. Maria's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that Steven does not know whether Steven picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Steven can now know that Teresa can know whether Terri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Terri","Maria","Steven","Teresa"],"index":56523,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5283541679,"difficulty":0.4716458321}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lee does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Donna can now know whether Cheryl can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Lee","Cheryl","Verline"],"index":62467,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974023104,"difficulty":0.0025976896}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen's forehead is muddy. It is publicly announced that Helen's forehead is muddy. It is publicly announced that Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Helen can now know whether Sam can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Sam","Mark","Juanita"],"index":50158,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9928295016,"difficulty":0.0071704984}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Pam can now know whether James can know that Pam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bobby","James","Pam","Frank"],"index":6045,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994200468,"difficulty":0.0005799532}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Rachel can now know that Lillian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lillian","Rachel"],"index":19209,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9889195561,"difficulty":0.0110804439}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether or not everyone is thirsty. It is publicly announced that Elizabeth knows whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","John"],"index":26812,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994968176,"difficulty":0.0005031824}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether Larry is thirsty. It is publicly announced that Larry does not know whether Colleen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Barry can now know that Colleen can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barry","Margaret","Colleen","Larry"],"index":51856,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993485808,"difficulty":0.0006514192}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Natasha is thirsty. It is publicly announced that Ellis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] 0","hypothesis":"Julie can now know that Julie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Natasha","Ellis","Julie","Thomas"],"index":44097,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9403594136,"difficulty":0.0596405864}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry's forehead is not muddy. It is publicly announced that Ricky knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Terry can now know that John can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ricky","John","Terry","Janet"],"index":22640,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996712327,"difficulty":0.003287673}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy. It is publicly announced that Erica knows whether or not everyone's forehead is muddy. It is publicly announced that Erica knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Kenneth can now know that Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kenneth","Erica"],"index":1722,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9496391416,"difficulty":0.0503608584}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joann does not know whether or not everyone's forehead is muddy. It is publicly announced that Joann does not know whether Joann's forehead is muddy. It is publicly announced that Joann does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Joann can now know whether Wayne can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joann","Wayne"],"index":35442,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994459748,"difficulty":0.0005540252}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether Marie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Stephen can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Marie","William","Stephen"],"index":41520,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989991784,"difficulty":0.0010008216}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Randal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Randal can now know whether Teresa can know that Randal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Teresa","Randal","Rudy"],"index":45804,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9031023383,"difficulty":0.0968976617}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether Jeane is thirsty. It is publicly announced that Melissa knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Ella can now know that Ella is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Pauline","Ella","Jeane"],"index":27283,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9908993244,"difficulty":0.0091006756}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guy knows whether Guy's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Clarence can now know that Tyler can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clarence","John","Guy","Tyler"],"index":27442,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977163076,"difficulty":0.0022836924}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Bridget knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Thomas can now know that Bridget's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Bridget","Keith"],"index":62590,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9935809374,"difficulty":0.0064190626}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Dennise can now know whether Billy can know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Maria","Billy","Dennise"],"index":53683,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994034767,"difficulty":0.0005965233}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kirsten's card is shown to Kirsten. Anna's card is shown to Kirsten. Vernon's card is shown to Anna. Anna's card is shown to Vernon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vernon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kirsten","Anna","Vernon"],"index":7465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993436933,"difficulty":0.0006563067}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antonio knows whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Henry can now know that Antonio can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eileen","Antonio","Henry","Maxine"],"index":22957,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989814162,"difficulty":0.0010185838}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Timothy's forehead is muddy. It is publicly announced that Kenneth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know whether Timothy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Barbara","Kenneth"],"index":59005,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993539453,"difficulty":0.0006460547}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Manuel knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Michelle can now know that James can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Manuel","Michelle","Samuel","James"],"index":36512,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967513084,"difficulty":0.0032486916}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to John. John's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Sharon knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Sharon can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","John","Linda"],"index":63238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940808415,"difficulty":0.0059191585}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Edward can now know whether Elizabeth can know that Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Elizabeth","Latonia","Edward"],"index":35042,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994119406,"difficulty":0.0005880594}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Andrew can now know that Carlos can know whether Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tyler","Andrew","Gary","Carlos"],"index":63728,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965839386,"difficulty":0.0034160614}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie knows whether Leslie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Leslie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leslie","Adrian","Erik"],"index":64489,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994183779,"difficulty":0.0005816221}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elaine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Aubrey can now know whether Elaine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ralph","Douglas","Aubrey","Elaine"],"index":7200,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7554412484,"difficulty":0.2445587516}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Timothy. Richard's card is shown to Timothy. Timothy's card is shown to Richard. Richard's card is shown to Richard. Melvin's card is shown to Richard. Timothy's card is shown to Melvin. Melvin's card is shown to Melvin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Timothy can now know that Richard can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Richard","Melvin"],"index":14160,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9720076919,"difficulty":1.9720076919}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tonya can now know that John can know that Tonya's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tonya","Ellen","John"],"index":36800,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998367846,"difficulty":0.001632154}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith's forehead is muddy. It is publicly announced that Clayton knows whether or not everyone's forehead is muddy. It is publicly announced that John knows whether Judith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clayton","John","Judith"],"index":62871,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985952973,"difficulty":0.0014047027}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenny's card is shown to Kenny. Kenny's card is shown to Jose. Jose's card is shown to Jose. It is publicly announced that someone picked a red card. It is publicly announced that Kenny knows whether or not nobody picked a red card. It is publicly announced that Kenny knows whether Jose picked a red card. It is publicly announced that Jose knows whether or not nobody picked a red card. It is publicly announced that Jose knows whether Jose picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jose can now know whether Jose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kenny","Jose"],"index":19191,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9777585268,"difficulty":0.0222414732}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruby knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ruby can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ruby","Kenneth","Robert","Damian"],"index":3993,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993441701,"difficulty":0.0006558299}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cortney does not know whether Lisa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Cortney can now know that Alvin can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alvin","Lisa","Cortney"],"index":27863,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994145632,"difficulty":0.0005854368}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Marlene can now know that Lisa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","Linda","Marlene"],"index":30055,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998941958,"difficulty":0.001058042}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Nicole does not know whether Nicole's forehead is muddy. It is publicly announced that Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Douglas can now know that Nicole can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicole","Douglas","Alexander"],"index":28116,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9938399196,"difficulty":0.0061600804}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Charles is thirsty. It is publicly announced that Daniel does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Daniel can now know that Daniel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Daniel","Charles"],"index":62750,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5261624455,"difficulty":0.4738375545}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilmer's card is shown to Wilmer. Diane's card is shown to Benjamin. Diane's card is shown to Diane. Wilmer's card is shown to Beulah. Beulah's card is shown to Beulah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilmer can now know that Diane can know whether Diane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wilmer","Benjamin","Diane","Beulah"],"index":46677,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6365565062,"difficulty":0.3634434938}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Kevin can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pamela","Jennifer","Kevin"],"index":19138,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993890524,"difficulty":0.0006109476}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamella knows whether Pamella's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kimberly can now know that Dominic can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dominic","James","Pamella","Kimberly"],"index":4820,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992890358,"difficulty":0.0007109642}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lonnie's card is shown to Mavis. Debra's card is shown to Mavis. Lonnie's card is shown to Lonnie. Debra's card is shown to Lonnie. Mavis's card is shown to Allison. Allison's card is shown to Debra. Debra's card is shown to Debra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mavis can now know that Lonnie can know that Debra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mavis","Lonnie","Allison","Debra"],"index":24029,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981455803,"difficulty":0.0018544197}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alex knows whether or not everyone's forehead is muddy. It is publicly announced that Alex knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Sandra can now know whether Alex can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cristi","Alex","Sandra"],"index":3870,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994485974,"difficulty":0.0005514026}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Johnny. Nidia's card is shown to Johnny. Johnny's card is shown to Nidia. It is publicly announced that someone picked a red card. It is publicly announced that Johnny knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Nidia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Johnny","Nidia"],"index":2449,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994142056,"difficulty":0.0005857944}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Antonio is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Rhett can now know that Antonio can know that Antonio is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antonio","Linda","Brian","Rhett"],"index":18487,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9904626012,"difficulty":0.0095373988}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Steven. Harry's card is shown to Harry. Harry's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Harry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Steven can now know that Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Steven","Harry","Alice"],"index":37782,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5065028071,"difficulty":0.4934971929}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Rebecca. Charlotte's card is shown to Ebony. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether or not everyone picked a red card. It is publicly announced that Ebony does not know whether Ebony picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ebony can now know that Rebecca can know whether Charlotte picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebecca","Ebony","Charlotte"],"index":48464,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7271595597,"difficulty":0.2728404403}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hazel does not know whether Mattie is thirsty. It is publicly announced that Peggy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Peggy can now know that Hazel can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Peggy","Mattie","Hazel"],"index":260,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990309477,"difficulty":0.0009690523}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan knows whether Juan's forehead is muddy. It is publicly announced that Douglas knows whether Edith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Douglas can now know that Juan can know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edith","Juan","Douglas"],"index":28439,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979670644,"difficulty":0.0020329356}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gustavo's card is shown to Beverly. Hazel's card is shown to Beverly. Beverly's card is shown to Jill. Gustavo's card is shown to Jill. Gustavo's card is shown to Gustavo. Gustavo's card is shown to Hazel. It is publicly announced that someone picked a red card. It is publicly announced that Gustavo does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Beverly can now know whether Hazel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverly","Jill","Gustavo","Hazel"],"index":3352,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5417573452,"difficulty":0.4582426548}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise knows whether Louise's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ashley can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Solomon","Charles","Louise","Ashley"],"index":35094,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989016056,"difficulty":0.0010983944}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia knows whether Donna is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Donna can now know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patricia","Donna"],"index":2532,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9957860112,"difficulty":1.9957860112}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rene's card is shown to Thelma. Thelma's card is shown to Patricia. Patricia's card is shown to Patricia. Rene's card is shown to Patricia. Thelma's card is shown to Rene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know whether Rene can know whether Thelma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thelma","Patricia","Rene"],"index":26836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986506104,"difficulty":0.0013493896}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Susan can now know whether Donald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Terisa","Donald"],"index":57922,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958623648,"difficulty":0.0041376352}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronnie does not know whether Richard is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that William knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Ronnie can now know that Richard can know whether Ronnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Ronnie","William"],"index":11046,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9623079896,"difficulty":1.9623079896}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eda's card is shown to Louis. Mildred's card is shown to Louis. Mildred's card is shown to Eda. Mildred's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Mildred does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Louis can now know that Eda can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Louis","Eda","Mildred"],"index":59847,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989412427,"difficulty":0.0010587573}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carol. William's card is shown to Carol. William's card is shown to Miguel. William's card is shown to Ralph. Ralph's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know whether Ralph can know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Miguel","Ralph","William"],"index":23758,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985544086,"difficulty":0.0014455914}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Paul knows whether Paul is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Rhonda can now know that Paul can know whether Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nathalie","Rhonda","Paul"],"index":42859,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987693429,"difficulty":0.0012306571}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lizzie's card is shown to Jennifer. Joe's card is shown to Jennifer. Joe's card is shown to Elliot. Jennifer's card is shown to Lizzie. Elliot's card is shown to Joe. Lizzie's card is shown to Joe. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joe can now know whether Jennifer can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Elliot","Lizzie","Joe"],"index":38390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6349657774,"difficulty":0.3650342226}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacqueline does not know whether or not everyone is thirsty. It is publicly announced that Jacqueline knows whether Jacqueline is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jacqueline can now know that Elizabeth can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dominga","Jacqueline","Elizabeth"],"index":28266,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9139254093,"difficulty":0.0860745907}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Peter can now know that Frances can know that Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ellen","Peter","Fae","Frances"],"index":27724,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928834438,"difficulty":0.0071165562}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Georgiana does not know whether Ruth is thirsty. It is publicly announced that Georgiana does not know whether Steven is thirsty. It is publicly announced that Ruth does not know whether Steven is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Georgiana can now know that Georgiana is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","James","Georgiana","Ruth"],"index":40721,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9889566302,"difficulty":0.0110433698}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma knows whether or not everyone's forehead is muddy. It is publicly announced that Theresa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Theresa can now know that Theresa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harold","Theresa","Thelma"],"index":46557,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9806431532,"difficulty":0.0193568468}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amber knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Ivan can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ivan","Amber"],"index":51770,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993332028,"difficulty":0.0006667972}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know that Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Jennifer","Terra","Tania"],"index":44396,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977317452,"difficulty":0.0022682548}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcia is thirsty. It is publicly announced that Bobby knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Bobby can now know that Marcia can know that Traci is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Traci","Bobby","Marcia"],"index":48867,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942100048,"difficulty":0.0057899952}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margareta's card is shown to Ann. Russell's card is shown to Eunice. Margareta's card is shown to Margareta. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margareta can now know that Ann can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ann","Eunice","Margareta","Russell"],"index":25732,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9921978116,"difficulty":0.0078021884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that Karen knows whether Karen's forehead is muddy. It is publicly announced that Karen knows whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Roderick can now know that Karen can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roderick","Thomas","Karen"],"index":44398,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994657636,"difficulty":0.0005342364}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Alex can now know whether Geraldine can know whether Geraldine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Geraldine","Alex"],"index":36388,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992675185,"difficulty":0.0007324815}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Vince can now know that Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Vince","Edward"],"index":28486,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963293672,"difficulty":0.0036706328}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Margaret can now know that Edgardo can know that Edgardo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Curtis","Margaret","Edgardo","Walter"],"index":17842,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9924162626,"difficulty":0.0075837374}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Jessica can now know that Marian can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marian","Jessica"],"index":26070,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986739159,"difficulty":0.0013260841}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jill does not know whether Lillie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jim can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jill","Lillie","Cheri","Jim"],"index":13068,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994069338,"difficulty":0.0005930662}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Boyd does not know whether Boyd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Edward can now know that Amy can know whether Stacey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amy","Stacey","Edward","Boyd"],"index":21596,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993152618,"difficulty":0.0006847382}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sharon can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Martha","Sharon","Jerry"],"index":27618,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993732572,"difficulty":0.0006267428}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brett does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Marie can now know that Brett can know whether Brett's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marie","Bruno","Stanley","Brett"],"index":42913,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5559135079,"difficulty":0.4440864921}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathryn does not know whether Kenneth is thirsty. It is publicly announced that Kenneth does not know whether Myron is thirsty. It is publicly announced that Myron does not know whether Kathryn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Myron can now know that Kenneth can know that Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Kathryn","Myron","Kenneth"],"index":48053,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984111786,"difficulty":0.0015888214}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Alfred is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Ramon can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ramon","Alfred"],"index":10470,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9960075021,"difficulty":0.0039924979}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wallace's card is shown to Diane. Emma's card is shown to Diane. Emma's card is shown to Wallace. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Wallace can now know that Diane can know whether Emma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Wallace","Emma"],"index":54717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7598770261,"difficulty":0.2401229739}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Jeffrey can now know that Sarah can know whether Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sarah","Jeffrey"],"index":25009,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994157553,"difficulty":0.0005842447}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Helen can now know that Pedro can know whether Pedro's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Pedro","Alfred","Gwenda"],"index":61444,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6055246592,"difficulty":0.3944753408}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christie does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Christie can now know that Allen can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Christie","Ann","Allen"],"index":57350,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992762208,"difficulty":0.0007237792}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Destiny does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Destiny can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Destiny","John","James","Brenda"],"index":55361,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9950880408,"difficulty":0.0049119592}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Daniel can now know that Ryan can know that Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eleanor","Ryan","Daniel","Patti"],"index":10016,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976515174,"difficulty":0.0023484826}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jackie does not know whether or not everyone is thirsty. It is publicly announced that Jackie does not know whether or not everyone is thirsty. It is publicly announced that Leonard knows whether Jackie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Jeanne can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jackie","Edith","Jeanne","Leonard"],"index":49149,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987757802,"difficulty":0.0012242198}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jamie can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hulda","Elizabeth","Jamie"],"index":38331,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991950393,"difficulty":0.0008049607}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is muddy. It is publicly announced that Lucas knows whether Gale's forehead is muddy. It is publicly announced that Kenneth knows whether Lucas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lucas can now know that Kenneth can know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Kenneth","Lucas","Gale"],"index":25213,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9720801115,"difficulty":1.9720801115}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Charles is thirsty. It is publicly announced that Regina does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know whether Dinah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Dinah","Regina","Charles"],"index":10210,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9912852645,"difficulty":0.0087147355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Shantel can now know whether Shantel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Paul","Barbara","Shantel"],"index":47201,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9809669256,"difficulty":0.0190330744}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Otis's card is shown to Otis. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card. It is publicly announced that Otis does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robert can now know that Otis can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Otis"],"index":5409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999427855,"difficulty":0.000572145}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roger's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Keith","Roger","John"],"index":60462,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987498522,"difficulty":0.0012501478}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Elbert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Denise","Paul","Elbert","Ava"],"index":49212,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9880481958,"difficulty":0.0119518042}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Alma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Joyce can now know whether Alma can know that Alma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","David","Alma","Mary"],"index":2945,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5492137671,"difficulty":0.4507862329}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. Jennifer's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank knows whether or not nobody picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1&2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1&2) ] 0","hypothesis":"Frank can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Frank","Jennifer"],"index":28911,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.986738205,"difficulty":0.013261795}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Drew's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Mark can now know that Leticia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leticia","Drew","Mark","Gene"],"index":18107,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982934594,"difficulty":0.0017065406}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Albert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Albert can now know that Jackie can know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jackie","Albert","Joseph"],"index":11885,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975036979,"difficulty":0.0024963021}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hong does not know whether Steven is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Jean can now know that Cindy can know whether Jean is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cindy","Steven","Jean","Hong"],"index":30070,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9921221137,"difficulty":0.0078778863}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cassie knows whether Cassie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Cassie can now know whether Carolyn can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carolyn","Cassie"],"index":10574,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993633628,"difficulty":0.0006366372}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Joan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Joan can now know that Romeo can know whether Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joan","Steven","Romeo"],"index":39166,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992228746,"difficulty":0.0007771254}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nelda knows whether Nelda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Scott can now know that Ashley can know that Nelda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ashley","Scott","Nelda"],"index":6107,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966907501,"difficulty":0.0033092499}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ida knows whether Queen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Queen","James","Ida"],"index":24298,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981431961,"difficulty":0.0018568039}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Micheal's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Kelly can now know that James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelly","Micheal","James"],"index":64331,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972705245,"difficulty":0.0027294755}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peggy's card is shown to Peggy. Peggy's card is shown to Caroline. Michael's card is shown to Caroline. Caroline's card is shown to Caroline. Peggy's card is shown to Lucia. Lucia's card is shown to Lucia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Peggy can now know that Michael can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peggy","Michael","Caroline","Lucia"],"index":38518,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9581737518,"difficulty":1.9581737518}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Myrtle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Myrtle","Pauline","Jimmy"],"index":28231,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984999895,"difficulty":0.0015000105}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Timothy can now know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Raymond","Timothy"],"index":29363,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977146387,"difficulty":0.0022853613}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Helen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Richard","Neal"],"index":40727,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990074039,"difficulty":0.0009925961}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Flossie is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Jeff can now know that Stewart can know that Flossie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stewart","Flossie","Jeffrey","Jeff"],"index":42103,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99519521,"difficulty":0.00480479}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] 0","hypothesis":"James can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Claude","Russ","James","Melissa"],"index":56993,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999432385,"difficulty":0.000567615}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hannah knows whether Jaclyn's forehead is muddy. It is publicly announced that Joyce does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jaclyn can now know that Joyce can know that Hannah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jaclyn","Hannah","Joyce"],"index":22133,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9233993888,"difficulty":0.0766006112}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linette knows whether Linette's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ellen can now know that Walter can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linette","Patricia","Ellen","Walter"],"index":31181,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989715815,"difficulty":0.0010284185}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Maryalice. Jesus's card is shown to Jesus. Maryalice's card is shown to Gerald. Gerald's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that Gerald knows whether Maryalice picked a red card. It is publicly announced that Jesus does not know whether Maryalice picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Maryalice can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maryalice","Jesus","Gerald"],"index":48599,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994463325,"difficulty":0.0005536675}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvette knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Donna knows whether Donna's forehead is muddy. It is publicly announced that Yvette knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Yvette can now know that Donna can know whether Yvette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amada","Donna","Yvette"],"index":13674,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9647461772,"difficulty":0.0352538228}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bessie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Ruth can now know whether Linda can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Bessie","Linda"],"index":21622,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993181229,"difficulty":0.0006818771}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Venice's card is shown to Venice. Ina's card is shown to Ina. Ina's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Venice can now know whether Venice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Venice","Ina","Elizabeth"],"index":63719,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6167059541,"difficulty":0.3832940459}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Marjorie's forehead is muddy. It is publicly announced that Lawrence knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Anthony","Thomas","Marjorie"],"index":18590,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988295436,"difficulty":0.0011704564}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gordon does not know whether Diana is thirsty. It is publicly announced that James does not know whether Diana is thirsty. It is publicly announced that Diana knows whether Diana is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentd knows whether 4) ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Gordon can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gordon","Melinda","James","Diana"],"index":48955,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989190102,"difficulty":0.0010809898}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aaron knows whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Kenneth can now know whether Aaron can know that Aaron's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tyrone","Aaron","Nicholas","Kenneth"],"index":6257,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9844213724,"difficulty":0.0155786276}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Nellie. Elizabeth's card is shown to Kay. It is publicly announced that someone picked a red card. It is publicly announced that Nellie knows whether Elizabeth picked a red card. It is publicly announced that Nellie does not know whether Donna picked a red card. It is publicly announced that Kay picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(4) ] (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Nellie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Nellie","Elizabeth","Kay"],"index":31020,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999478519,"difficulty":0.000521481}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Mark's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ryan can now know that Michael can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Ryan","Michael"],"index":65128,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994754195,"difficulty":0.0005245805}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Franklin. Jonathan's card is shown to Franklin. Jeremy's card is shown to Franklin. Jonathan's card is shown to Ruth. Jonathan's card is shown to Jeremy. Jeremy's card is shown to Jeremy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jonathan can now know whether Franklin can know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Franklin","Ruth","Jonathan","Jeremy"],"index":10645,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9264723659,"difficulty":0.0735276341}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwardo's card is shown to Edwardo. Virginia's card is shown to Edwardo. Edwardo's card is shown to Tom. Virginia's card is shown to Virginia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Virginia can now know that Tom can know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edwardo","Tom","Virginia"],"index":8405,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5791749358,"difficulty":1.5791749358}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy. It is publicly announced that Kimberly's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Kimberly can now know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Le","Norman","Kimberly","Thomas"],"index":13640,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963917136,"difficulty":0.0036082864}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Teresa's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Teresa can now know that Anthony can know whether Olin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olin","Anthony","Teresa","Jason"],"index":27430,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990813732,"difficulty":0.0009186268}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd knows whether Cheryl's forehead is muddy. It is publicly announced that Cheryl knows whether Cheryl's forehead is muddy. It is publicly announced that Lloyd knows whether Lloyd's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lloyd can now know that Cheryl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lloyd","Cheryl"],"index":34151,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9911795259,"difficulty":0.0088204741}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Emanuel can now know that Carol can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Emanuel","Jane","Carol"],"index":40488,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9878481627,"difficulty":0.0121518373}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Wayne knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Penny can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wayne","Penny"],"index":64452,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9870478511,"difficulty":0.0129521489}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether Sabrina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Eddie can now know that Craig can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eddie","Denise","Sabrina","Craig"],"index":61440,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988937974,"difficulty":0.0011062026}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Morgan knows whether Ramonita's forehead is muddy. It is publicly announced that Sandra's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Lara can now know that Lara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lara","Sandra","Morgan","Ramonita"],"index":53926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981714487,"difficulty":0.0018285513}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack's forehead is not muddy. It is publicly announced that Jack's forehead is not muddy. It is publicly announced that Jack's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Kenneth can now know that Jack can know that Jill's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jill","Jack","Kenneth","Evan"],"index":44311,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8221540451,"difficulty":0.1778459549}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Troy can now know that Carrie can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Troy","Carrie","William"],"index":52232,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993169308,"difficulty":0.0006830692}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. Linda's card is shown to Frank. Frank's card is shown to Linda. Linda's card is shown to Linda. Frank's card is shown to Michelle. Mabel's card is shown to Michelle. Michelle's card is shown to Mabel. Mabel's card is shown to Mabel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know whether Frank can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frank","Linda","Michelle","Mabel"],"index":49658,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9178465605,"difficulty":1.9178465605}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mariano's card is shown to Geneva. Nancy's card is shown to Nancy. Geneva's card is shown to Mariano. Nancy's card is shown to Mariano. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nancy can now know whether Mariano can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geneva","Nancy","Mariano"],"index":21889,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991939664,"difficulty":0.0008060336}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether or not everyone's forehead is muddy. It is publicly announced that Timothy knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Christy can now know that Jason can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christy","Timothy","Jason"],"index":55333,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994130135,"difficulty":0.0005869865}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether William is thirsty. It is publicly announced that Norman does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"William can now know that Norman can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Norman","William","Monique"],"index":32682,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997374773,"difficulty":0.002625227}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Elbert. Louie's card is shown to Elbert. Elbert's card is shown to Paul. Paul's card is shown to Sandra. Louie's card is shown to Sandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louie can now know that Elbert can know that Louie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elbert","Paul","Louie","Sandra"],"index":6485,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980431795,"difficulty":0.0019568205}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether Stephen's forehead is muddy. It is publicly announced that Steven knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Harry can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Harry","Ryan","Stephen"],"index":48584,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987621307,"difficulty":0.0012378693}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Byron's card is shown to Kenneth. Byron's card is shown to Joshua. Joshua's card is shown to Byron. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Joshua can now know whether Kenneth can know whether Byron picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Joshua","Byron"],"index":59211,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980322719,"difficulty":0.0019677281}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether Jessica's forehead is muddy. It is publicly announced that Javier knows whether Andrea's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jessica can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Laura","Andrea","Javier","Jessica"],"index":9562,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994192123,"difficulty":0.0005807877}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. David's card is shown to Linda. David's card is shown to Michael. Linda's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether David picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Linda","Michael"],"index":64471,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7558176517,"difficulty":0.2441823483}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene knows whether or not everyone's forehead is muddy. It is publicly announced that Connie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Kenneth can now know that Latoya's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Connie","Latoya","Irene","Kenneth"],"index":58108,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9936236739,"difficulty":0.0063763261}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rodney can now know that Brian can know whether Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Rodney","Catherine","Carol"],"index":37988,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993107319,"difficulty":0.0006892681}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Kathleen's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether Jason picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Kathleen knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jason can now know whether Kathleen can know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathleen","Jason"],"index":61519,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9342642426,"difficulty":0.0657357574}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alejandro does not know whether Alejandro's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Richard can now know that Walter can know that Walter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angel","Walter","Alejandro","Richard"],"index":62928,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949263334,"difficulty":0.0050736666}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Grace can now know whether Thomas can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Grace","Mari","Cathryn","Thomas"],"index":65192,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992123842,"difficulty":0.0007876158}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda knows whether or not nobody is thirsty. It is publicly announced that Erma does not know whether Brenda is thirsty. It is publicly announced that Ruthann does not know whether Erma is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Erma can now know whether Brenda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erma","Brenda","Ruthann"],"index":63536,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9944848418,"difficulty":0.0055151582}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Susan can now know that Stephen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Stephen","Roger"],"index":51646,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984593391,"difficulty":0.0015406609}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Lois can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lois","Patricia","Martha","Robert"],"index":48563,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8666030765,"difficulty":0.1333969235}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beulah's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Debra picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Debra can now know that Beulah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debra","Beulah"],"index":67453,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9702712297,"difficulty":1.9702712297}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathy's card is shown to Kathy. Kathy's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Kathy can now know that Thomas can know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kathy","Thomas"],"index":4691,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954196215,"difficulty":0.0045803785}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Zelda's forehead is muddy. It is publicly announced that Sandra knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"William can now know that Zelda can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Zelda","William"],"index":50019,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991754889,"difficulty":0.0008245111}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peggy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Peggy can now know whether Gary can know that Gary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gary","Peggy"],"index":28389,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9527747631,"difficulty":1.9527747631}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Joseph can now know that Linda can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Joseph"],"index":9014,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993609786,"difficulty":0.0006390214}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Troy's card is shown to Jacqulyn. Frank's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jacqulyn can now know that Frank can know whether Jacqulyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frank","Jacqulyn","Troy"],"index":61826,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7716271281,"difficulty":0.2283728719}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether Rose's forehead is muddy. It is publicly announced that Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Dennis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rose","Velma","Karen","Dennis"],"index":47968,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989532232,"difficulty":0.0010467768}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Benjamin's card is shown to Benjamin. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Benjamin can now know whether Ivory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Benjamin","Michael","Ivory"],"index":58885,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954853654,"difficulty":0.0045146346}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dustin knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Brian can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dustin","Brian"],"index":56387,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993563294,"difficulty":0.0006436706}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine knows whether Nellie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Nellie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Nellie","Catherine"],"index":32392,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990150928,"difficulty":0.0009849072}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Anthony's card is shown to Lorraine. It is publicly announced that someone picked a red card. It is publicly announced that Lorraine knows whether someone picked a red card. It is publicly announced that Lorraine does not know whether Lorraine picked a red card. It is publicly announced that Lorraine does not know whether Lorraine picked a red card. It is publicly announced that Lorraine does not know whether Lorraine picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lorraine can now know whether Anthony can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anthony","Lorraine"],"index":27684,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8356627226,"difficulty":1.8356627226}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd knows whether Lloyd's forehead is muddy. It is publicly announced that Phoebe knows whether Gordon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Gordon can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gordon","Allen","Lloyd","Phoebe"],"index":25928,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990053773,"difficulty":0.0009946227}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory's forehead is not muddy. It is publicly announced that Phyllis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Phyllis can now know that Phyllis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Phyllis","Gregory","Randall"],"index":40618,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979252815,"difficulty":0.0020747185}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Aaron can now know that Tiffany can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tandy","Tiffany","Roger","Aaron"],"index":34821,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993420243,"difficulty":0.0006579757}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Annie. Edna's card is shown to Annie. Charles's card is shown to Charles. Danielle's card is shown to Edna. Charles's card is shown to Danielle. It is publicly announced that someone picked a red card. It is publicly announced that Edna does not know whether or not everyone picked a red card. It is publicly announced that Charles knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Annie can now know whether Annie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Annie","Charles","Edna","Danielle"],"index":15224,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7667175531,"difficulty":0.2332824469}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katie knows whether or not everyone's forehead is muddy. It is publicly announced that Victor's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Katie can now know that Ruth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lauren","Victor","Katie","Ruth"],"index":27760,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987155199,"difficulty":0.0012844801}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Lance's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that Karen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know whether Kimberly can know that Lance's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Lance","Kimberly","David"],"index":38006,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9857818484,"difficulty":0.0142181516}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonnie knows whether Nicole's forehead is muddy. It is publicly announced that Anna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Johnny can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nicole","Johnny","Anna","Bonnie"],"index":57564,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993283749,"difficulty":0.0006716251}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Matthew. Keith's card is shown to Matthew. Bruce's card is shown to Bruce. Bruce's card is shown to Keith. Keith's card is shown to Keith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Keith can now know whether Bruce can know that Bruce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Bruce","Keith"],"index":20659,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8342635632,"difficulty":0.1657364368}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether or not everyone is thirsty. It is publicly announced that Nancy does not know whether Mark is thirsty. It is publicly announced that Mark knows whether Nancy is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Nancy can now know that Mark can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mark","Nancy"],"index":11778,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994372725,"difficulty":0.0005627275}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Dawn can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Evelyn","Jeanna","Dawn"],"index":43183,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989472032,"difficulty":0.0010527968}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derrick's card is shown to Derrick. Vera's card is shown to Maria. Derrick's card is shown to Vera. Vera's card is shown to Vera. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know that Vera picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Derrick","Maria","Vera"],"index":15316,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956234097,"difficulty":0.0043765903}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy. It is publicly announced that Erik knows whether Hilario's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Erik can now know that Hilario's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathryn","Hilario","Erik","Betty"],"index":51236,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9931922555,"difficulty":0.0068077445}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cathy knows whether Micheal is thirsty. It is publicly announced that Cathy knows whether Micheal is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Micheal can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cathy","Micheal"],"index":59831,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.962988019,"difficulty":1.962988019}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Roger can now know that James can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","James","Roger"],"index":47150,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995030165,"difficulty":0.0004969835}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Beatrice can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Velma","John","Beatrice"],"index":61195,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9922491312,"difficulty":0.0077508688}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lee's card is shown to Pamela. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julie","Lee","Pamela"],"index":47139,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994182587,"difficulty":0.0005817413}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ana's card is shown to Ana. Ana's card is shown to Anthony. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether Anthony picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ana can now know that Anthony can know that Ana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ana","Anthony"],"index":59186,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9327280521,"difficulty":0.0672719479}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether Terry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"John can now know that Terry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Kenneth","Terry"],"index":2659,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990284443,"difficulty":0.0009715557}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michele does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kenneth can now know that William can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michele","William","Matthew","Kenneth"],"index":42208,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988750815,"difficulty":0.0011249185}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris's forehead is muddy. It is publicly announced that Germaine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Arthur can now know that Germaine can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sharon","Arthur","Chris","Germaine"],"index":23863,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989266992,"difficulty":0.0010733008}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda does not know whether or not everyone's forehead is muddy. It is publicly announced that Ryan knows whether Ryan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ryan can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ryan","Wanda"],"index":38807,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.794721365,"difficulty":0.205278635}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris does not know whether Doris's forehead is muddy. It is publicly announced that Doris's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Doris can now know that Debra can know that Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Louise","Debra","David"],"index":41944,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971296191,"difficulty":0.0028703809}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Johanna does not know whether Charles is thirsty. It is publicly announced that Barbara is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agentc knows that (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Rose can now know that Charles can know whether Rose is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Johanna","Rose","Charles"],"index":49983,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9852617383,"difficulty":0.0147382617}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tessie's forehead is not muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kathy can now know whether Elizabeth can know whether Tessie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","Tessie","Kathy"],"index":25302,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993501306,"difficulty":0.0006498694}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Virginia. Anthony's card is shown to Anthony. Anthony's card is shown to Brooke. Brooke's card is shown to Brooke. Brooke's card is shown to Nola. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Anthony","Brooke","Nola"],"index":20129,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982509017,"difficulty":0.0017490983}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fredrick can now know whether Jon can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fredrick","Joanna","Carol","Jon"],"index":66455,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993873835,"difficulty":0.0006126165}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Huey does not know whether Aaron is thirsty. It is publicly announced that Lewis does not know whether Robert is thirsty. It is publicly announced that Huey knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lewis can now know whether Robert can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Aaron","Huey","Robert","Lewis"],"index":62121,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.994238615,"difficulty":0.005761385}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Eric can now know whether Alex can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Danny","Alex","Latonya"],"index":17908,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9947405457,"difficulty":0.0052594543}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Minh's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Minh can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steve","John","Minh","Laurence"],"index":63807,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988742471,"difficulty":0.0011257529}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether Frank is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Lisa can now know that Lisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Elizabeth","Patti","Lisa"],"index":60219,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9919281006,"difficulty":0.0080718994}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tessa knows whether Tessa is thirsty. It is publicly announced that Esperanza does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Tessa can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Tessa","Carol","Esperanza"],"index":41535,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9726501107,"difficulty":0.0273498893}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kimberly can now know whether David can know that Barrett's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barrett","Kimberly","Sheree","David"],"index":1920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.974088788,"difficulty":0.025911212}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laurie does not know whether Linda is thirsty. It is publicly announced that Laurie does not know whether or not everyone is thirsty. It is publicly announced that Dennis knows whether Laurie is thirsty. It is publicly announced that Linda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Dennis can now know that Linda can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Laurie","Linda"],"index":15672,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5504768491,"difficulty":0.4495231509}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bonnie does not know whether Ruth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Esther can now know that Thomas can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruth","Bonnie","Esther","Thomas"],"index":26036,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989320636,"difficulty":0.0010679364}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"John can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tony","Ray","John","Donald"],"index":9466,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993702769,"difficulty":0.0006297231}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clinton knows whether Melba's forehead is muddy. It is publicly announced that Charlie knows whether Melba's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Charlie can now know that Clinton can know that Charlie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clinton","Melba","Charlie"],"index":22308,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983231425,"difficulty":0.0016768575}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel's forehead is muddy. It is publicly announced that Daniel's forehead is muddy. It is publicly announced that Fernando's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Richard can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Noah","Richard","Fernando","Daniel"],"index":10062,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993365407,"difficulty":0.0006634593}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Douglas's card is shown to Douglas. Joseph's card is shown to Jeffrey. Douglas's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Douglas","Jeffrey"],"index":16312,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994027615,"difficulty":0.0005972385}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Kevin. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Kevin knows whether someone picked a red card. It is publicly announced that Kevin does not know whether or not everyone picked a red card. It is publicly announced that Kevin picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(1) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(1) ] 0","hypothesis":"Jonathan can now know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kevin","Jonathan"],"index":43264,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9673874974,"difficulty":0.0326125026}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allyson does not know whether Catherine is thirsty. It is publicly announced that Lucille is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Harry can now know whether Allyson is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harry","Lucille","Allyson","Catherine"],"index":45070,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9944738746,"difficulty":0.0055261254}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Malcolm's card is shown to Malcolm. Diane's card is shown to Malcolm. Malcolm's card is shown to Diane. Christina's card is shown to Diane. Malcolm's card is shown to Christina. Diane's card is shown to Christina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Malcolm can now know that Christina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Malcolm","Diane","Christina"],"index":46294,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997923851,"difficulty":0.002076149}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Catherine can now know whether Jackie can know that Jackie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","James","Catherine"],"index":38232,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9833812714,"difficulty":1.9833812714}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tamika can now know that Richard can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tamika","Richard","Marcell"],"index":51276,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9865684509,"difficulty":0.0134315491}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adrienne is thirsty. It is publicly announced that Adrienne knows whether Adrienne is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kathy can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Adrienne","Kathy"],"index":58619,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986306429,"difficulty":0.0013693571}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Charles. Charles's card is shown to James. James's card is shown to James. Charles's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Charles can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","James","Gary"],"index":40078,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993501306,"difficulty":0.0006498694}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Margaret can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Margaret","Alan","Monica","Helen"],"index":21367,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988962412,"difficulty":0.0011037588}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leo's card is shown to Steven. Leo's card is shown to Leo. It is publicly announced that someone picked a red card. It is publicly announced that Steven does not know whether or not everyone picked a red card. It is publicly announced that Steven does not know whether Steven picked a red card. It is publicly announced that Steven does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Leo can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Steven","Leo"],"index":42710,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994537234,"difficulty":0.0005462766}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather knows whether Nelson's forehead is muddy. It is publicly announced that Heather's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Nelson can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Heather","Nelson","Geraldine"],"index":52008,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993615746,"difficulty":0.0006384254}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edgar knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kimberly can now know whether William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kimberly","Edgar","William"],"index":34774,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954742789,"difficulty":0.0045257211}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Becky can now know whether Janie can know whether Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Janie","Becky"],"index":6755,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994102716,"difficulty":0.0005897284}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Scott can now know that Lola can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lola","Scott","Charles"],"index":18521,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989590645,"difficulty":0.0010409355}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessie's card is shown to Patricia. Jessie's card is shown to Jessie. Jessie's card is shown to Alicia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alicia can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Jessie","Alicia","Brian"],"index":67436,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993682504,"difficulty":0.0006317496}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Sheila. Sheila's card is shown to John. John's card is shown to John. John's card is shown to Sharon. Sharon's card is shown to Sharon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sheila can now know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sheila","John","Sharon"],"index":65684,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948921204,"difficulty":0.0051078796}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wanda knows whether Wanda is thirsty. It is publicly announced that Janis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Janis can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amy","Wanda","John","Janis"],"index":21473,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9812760353,"difficulty":0.0187239647}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Idell. Idell's card is shown to Adam. Adam's card is shown to Adam. Lillian's card is shown to Adam. Idell's card is shown to Lillian. It is publicly announced that someone picked a red card. It is publicly announced that Lillian does not know whether or not everyone picked a red card. It is publicly announced that Adam knows whether Lillian picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Adam can now know whether Lillian can know whether Lillian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Idell","Adam","Lillian"],"index":64342,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9966391325,"difficulty":0.0033608675}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa does not know whether William is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty. It is publicly announced that William does not know whether Marilyn is thirsty. It is publicly announced that William does not know whether Marilyn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Marilyn can now know that Lisa can know whether Lisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","William","Marilyn"],"index":28549,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7972884774,"difficulty":0.2027115226}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernice does not know whether Donald is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Bernice can now know whether Donald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Bernice","Donald"],"index":14975,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978345037,"difficulty":0.0021654963}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether or not everyone is thirsty. It is publicly announced that David knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Brian can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Brian"],"index":21338,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994978905,"difficulty":0.0005021095}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether someone's forehead is muddy. It is publicly announced that Aaron knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Helen can now know whether Albert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jason","Aaron","Albert","Helen"],"index":14668,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993477464,"difficulty":0.0006522536}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy does not know whether Troy's forehead is muddy. It is publicly announced that Josiah knows whether Josiah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Annie can now know whether Josiah can know whether Annie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ted","Annie","Josiah","Troy"],"index":52049,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987539053,"difficulty":0.0012460947}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose knows whether someone's forehead is muddy. It is publicly announced that Ethan knows whether Jennifer's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Jennifer can now know that Rose can know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Ethan","Kenneth","Jennifer"],"index":66525,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9855070114,"difficulty":0.0144929886}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Tina can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carolyn","Tina","James","Janice"],"index":2617,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9950908422,"difficulty":0.0049091578}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] 0","hypothesis":"John can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Flora","Harry"],"index":17256,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6135285497,"difficulty":0.3864714503}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Karen. Mildred's card is shown to Mildred. Gary's card is shown to Mildred. Annie's card is shown to Annie. Karen's card is shown to Gary. Mildred's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Gary does not know whether Annie picked a red card. It is publicly announced that Mildred picked a black card. It is publicly announced that Mildred knows whether Gary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Annie can now know that Karen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Mildred","Annie","Gary"],"index":62200,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990021586,"difficulty":0.0009978414}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to David. Salvador's card is shown to Gregory. Jeannette's card is shown to Gregory. Jeannette's card is shown to Salvador. Gregory's card is shown to Jeannette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Gregory","Salvador","Jeannette"],"index":39181,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960104227,"difficulty":0.0039895773}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Anna is thirsty. It is publicly announced that Lorenzo is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Victor can now know whether Daniel can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Victor","Lorenzo","Daniel","Anna"],"index":52063,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994757771,"difficulty":0.0005242229}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether Micaela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Micaela can now know whether Robert can know whether Micaela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Robert","Micaela"],"index":33512,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994069338,"difficulty":0.0005930662}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Ruth. Gregory's card is shown to Ruth. Gregory's card is shown to Robert. Ruth's card is shown to Gregory. Ruth's card is shown to Stephanie. It is publicly announced that someone picked a red card. It is publicly announced that Stephanie does not know whether Robert picked a red card. It is publicly announced that Stephanie does not know whether Stephanie picked a red card. It is publicly announced that Robert does not know whether Stephanie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Gregory can now know whether Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Robert","Gregory","Stephanie"],"index":27023,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994286895,"difficulty":0.0005713105}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Flora knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Flora can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nicole","Walter","Flora"],"index":16578,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993183613,"difficulty":0.0006816387}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra's forehead is muddy. It is publicly announced that Sandra knows whether Mary's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Mary can now know that Martin can know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Martin","Sandra"],"index":58541,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993500113,"difficulty":0.0006499887}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Katie can now know whether Christian can know that Katie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alphonse","Katie","Ray","Christian"],"index":29412,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.910674572,"difficulty":0.089325428}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to Doris. Doris's card is shown to Monica. Monica's card is shown to Thanh. It is publicly announced that someone picked a red card. It is publicly announced that Thanh knows whether Monica picked a red card. It is publicly announced that Monica does not know whether Thanh picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Doris can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Doris","Monica","Thanh"],"index":42718,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932987094,"difficulty":0.0067012906}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty's forehead is muddy. It is publicly announced that James knows whether Randy's forehead is muddy. It is publicly announced that Randy does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Betty can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Betty","Randy","Francisco","James"],"index":57967,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6446692944,"difficulty":1.6446692944}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Douglas can now know whether Kent can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Richard","Kent"],"index":30191,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991346002,"difficulty":0.0008653998}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy. It is publicly announced that Deon knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Robert can now know that Hazel can know that Hazel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deon","Robert","Hannah","Hazel"],"index":36446,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9599466324,"difficulty":0.0400533676}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Lawrence. Stanley's card is shown to John. Jessica's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stanley can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Stanley","Jessica","John"],"index":23674,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971619844,"difficulty":0.0028380156}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kristine can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Kristine","Frances","Robert"],"index":64226,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9871399999,"difficulty":0.0128600001}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paige does not know whether Luis is thirsty. It is publicly announced that Eddie does not know whether Luis is thirsty. It is publicly announced that Ronald does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Luis can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eddie","Ronald","Luis","Paige"],"index":53502,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990763664,"difficulty":0.0009236336}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Brian can now know that Tara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Irma","Tara"],"index":32485,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988300204,"difficulty":0.0011699796}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy knows whether Nancy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"James can now know that Nancy can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Herman","Beatrice","James"],"index":21911,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9520531893,"difficulty":0.0479468107}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Ronda knows whether Arthur's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Joseph can now know that Arthur can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronda","Joseph","Arthur"],"index":49226,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9826548696,"difficulty":0.0173451304}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"James can now know whether Katherine can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Katherine","James"],"index":50588,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993050098,"difficulty":0.0006949902}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Wesley can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","John","Wesley"],"index":41202,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992777705,"difficulty":0.0007222295}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Frank can now know that Frank's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Carol","Frank","Yolanda"],"index":41221,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9949725866,"difficulty":0.0050274134}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Zachery's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Leah can now know that Zachery's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Imogene","Zachery","Leah","Essie"],"index":54988,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957459569,"difficulty":0.0042540431}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lindsay knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know that Grace's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lindsay","Grace","James","Ben"],"index":17097,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975764155,"difficulty":0.0024235845}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony knows whether or not everyone's forehead is muddy. It is publicly announced that Rickie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Tony can now know whether Gregory can know whether Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tony","Rickie","Gregory"],"index":21634,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7974098325,"difficulty":0.2025901675}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Jason can now know that Crystal's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","John","Crystal","Jason"],"index":3472,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.986107707,"difficulty":0.013892293}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tim knows whether Frederica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Frederica can now know that Thomas can know that Frederica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Frederica","Tim"],"index":16821,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9875795245,"difficulty":0.0124204755}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether Julie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ana can now know that Richard can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Julie","Richard","Ana"],"index":31632,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992043376,"difficulty":0.0007956624}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey does not know whether Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Preston can now know whether Vita can know whether Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Preston","William","Vita"],"index":47131,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988533258,"difficulty":0.0011466742}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Wanda's card is shown to Thomas. Wanda's card is shown to Anthony. Thomas's card is shown to Wanda. Anthony's card is shown to Wanda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Wanda can know whether Wanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Anthony","Wanda"],"index":34909,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5090569854,"difficulty":1.5090569854}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cathy knows whether Cathy's forehead is muddy. It is publicly announced that Jessica knows whether Cathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Cathy can now know that Kelly can know that Kelly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessica","Cathy","Kelly","Nellie"],"index":26763,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978758097,"difficulty":0.0021241903}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cherry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Anthony can know that Anthony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cherry","Viola","Joseph","Anthony"],"index":40047,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974176884,"difficulty":0.0025823116}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arturo does not know whether Lisa is thirsty. It is publicly announced that Lisa is not thirsty. It is publicly announced that Elizabeth does not know whether Arturo is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Elizabeth can now know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Arturo","Elizabeth","Lisa"],"index":36182,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9889365435,"difficulty":1.9889365435}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tommy knows whether or not everyone's forehead is muddy. It is publicly announced that Tommy knows whether Fred's forehead is muddy. It is publicly announced that Tommy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Fred can now know that Tommy can know that Tommy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tommy","Fred"],"index":28294,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963829517,"difficulty":0.0036170483}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louis's card is shown to Louis. Terrance's card is shown to Terrance. Melissa's card is shown to Terrance. Rose's card is shown to Rose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rose can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Louis","Terrance","Rose","Melissa"],"index":60610,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989405274,"difficulty":0.0010594726}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gregory can now know that Odell can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gregory","Katharine","Odell"],"index":31659,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998852253,"difficulty":0.001147747}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether someone's forehead is muddy. It is publicly announced that Elizabeth knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] Agenta knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Tyler can now know that Elizabeth can know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tyler","Elizabeth"],"index":17947,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9941313863,"difficulty":0.0058686137}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derek's card is shown to Pam. Eileen's card is shown to Eileen. Derek's card is shown to Derek. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eileen can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pam","Eileen","Derek"],"index":64524,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943945408,"difficulty":0.0056054592}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barry's card is shown to Barry. Darren's card is shown to Darren. Darren's card is shown to Sherri. Sherri's card is shown to Sherri. It is publicly announced that someone picked a red card. It is publicly announced that Barry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Barry can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barry","Darren","Sherri"],"index":1635,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9503216743,"difficulty":0.0496783257}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rene knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Ryan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ryan","David","Rene"],"index":23829,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986540079,"difficulty":0.0013459921}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis does not know whether Travis's forehead is muddy. It is publicly announced that Edna knows whether Edna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Edna can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edna","Joyce","Travis"],"index":24975,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99941957,"difficulty":0.00058043}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley does not know whether Shirley's forehead is muddy. It is publicly announced that Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 0","hypothesis":"Shirley can now know whether Michele can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rufus","Joanne","Michele","Shirley"],"index":4199,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994823933,"difficulty":0.0005176067}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judith does not know whether Annie is thirsty. It is publicly announced that Annie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"George can now know whether Annie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Judith","Annie","George"],"index":36732,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9887390137,"difficulty":0.0112609863}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Jimmy is thirsty. It is publicly announced that Travis does not know whether Jimmy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Travis can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Lawrence","Travis","Jimmy"],"index":64573,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994526505,"difficulty":0.0005473495}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Sandy. Travis's card is shown to Travis. Travis's card is shown to Jake. It is publicly announced that someone picked a red card. It is publicly announced that Travis does not know whether Maria picked a red card. It is publicly announced that Travis does not know whether Maria picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sandy can now know whether Sandy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Sandy","Travis","Jake"],"index":52461,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5903315544,"difficulty":0.4096684456}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mae's card is shown to Cora. Maritza's card is shown to Denise. Cora's card is shown to Maritza. Denise's card is shown to Maritza. Maritza's card is shown to Maritza. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cora can now know whether Mae can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mae","Cora","Denise","Maritza"],"index":34191,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9713780284,"difficulty":0.0286219716}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Julia can now know that Cecile can know whether Cecile's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cecile","Phyllis","Nancy","Julia"],"index":20558,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9919483662,"difficulty":0.0080516338}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ana's card is shown to Mildred. Luke's card is shown to Paula. Paula's card is shown to Paula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know that Luke can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Luke","Ana","Paula"],"index":21042,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989681244,"difficulty":0.0010318756}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Brenda's card is shown to Brenda. Robert's card is shown to Catherine. Robert's card is shown to Margaret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Margaret can know whether Catherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Brenda","Catherine","Margaret"],"index":31178,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974889755,"difficulty":0.0025110245}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adell does not know whether Adell's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Wayne can now know that Adell can know whether Adell's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wayne","Inez","Adell"],"index":8215,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7574685216,"difficulty":0.2425314784}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arthur does not know whether Jayne is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Frankie can now know whether Arthur is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frankie","Arthur","Brian","Jayne"],"index":17124,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941620231,"difficulty":0.0058379769}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alison knows whether Alison's forehead is muddy. It is publicly announced that Alison's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Alison can now know whether Sidney can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alison","Keith","Sidney","Debra"],"index":64364,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994069338,"difficulty":0.0005930662}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clay knows whether Roger's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Roger can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roger","Brandon","Clay"],"index":32985,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9694606066,"difficulty":0.0305393934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Krista knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jack can now know that Krista can know that Stacy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jack","Stacy","Carl","Krista"],"index":36943,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9824455976,"difficulty":0.0175544024}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mae does not know whether Mae's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Teresa can now know whether Mae can know that Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mae","Teresa","Tina","Julio"],"index":24814,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8241956234,"difficulty":0.1758043766}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Margaret. Sally's card is shown to Teddy. Teddy's card is shown to Dawn. Dawn's card is shown to Dawn. Sally's card is shown to Dawn. Teddy's card is shown to Sally. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sally can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margaret","Teddy","Dawn","Sally"],"index":57207,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993181229,"difficulty":0.0006818771}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessie's card is shown to Kathleen. Alma's card is shown to Kathleen. Alma's card is shown to Jessie. Jessie's card is shown to Alma. Alma's card is shown to Alma. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen knows whether Jessie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Kathleen can now know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Jessie","Alma"],"index":41757,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9843324423,"difficulty":0.0156675577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Dana can now know that James can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jenifer","Angelina","James","Dana"],"index":51929,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992941618,"difficulty":0.0007058382}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fernando knows whether Lori's forehead is muddy. It is publicly announced that Kristine does not know whether Kristine's forehead is muddy. It is publicly announced that Sam knows whether Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Sam can now know whether Lori can know whether Kristine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lori","Sam","Fernando","Kristine"],"index":29300,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986593723,"difficulty":0.0013406277}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether Ronald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Elenora can now know that Debra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Debra","Steven","Elenora"],"index":43203,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982625842,"difficulty":0.0017374158}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shelia does not know whether Amy is thirsty. It is publicly announced that Emil does not know whether Amy is thirsty. It is publicly announced that Emil is not thirsty. It is publicly announced that Shelia is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! ~(3) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! ~(3) ] 0","hypothesis":"Emil can now know whether Shelia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emil","Amy","Shelia"],"index":45762,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8959765434,"difficulty":0.1040234566}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Viola. Hyman's card is shown to Viola. Viola's card is shown to Mark. Mark's card is shown to Mark. Mark's card is shown to Hyman. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mark can now know whether Hyman can know that Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Viola","Mark","Hyman"],"index":57861,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9263889194,"difficulty":0.0736110806}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Kenneth. Kenneth's card is shown to Maria. Maria's card is shown to Maria. Robert's card is shown to Maria. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know that Maria can know that Maria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Maria","Robert"],"index":29599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953502417,"difficulty":0.0046497583}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie does not know whether Leslie's forehead is muddy. It is publicly announced that Leslie knows whether Linda's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Leslie can now know that Leslie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Leslie","Linda"],"index":40367,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9639163017,"difficulty":0.0360836983}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Michael can now know whether Kevin can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carlos","Michael","Kevin"],"index":63390,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994013309,"difficulty":0.0005986691}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Norma is not thirsty. It is publicly announced that Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] Agentb knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"John can now know whether Joseph can know that Matthew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","John","Joseph","Norma"],"index":56067,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9940699339,"difficulty":0.0059300661}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angel knows whether or not nobody's forehead is muddy. It is publicly announced that Angel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Angel","John"],"index":15935,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966709018,"difficulty":0.0033290982}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Stephanie can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","James","Stephanie"],"index":28312,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996710062,"difficulty":0.003289938}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Ray can now know that Suzie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ray","Josh","Suzie"],"index":20805,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9745156169,"difficulty":0.0254843831}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Donald can now know that Joann can know whether Anthony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Donald","Joann","Michael"],"index":16218,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994251728,"difficulty":0.0005748272}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Jesus. Linda's card is shown to Ruth. Ruth's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Linda can now know whether Ruth can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jesus","Ruth","Linda"],"index":55120,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6252473593,"difficulty":0.3747526407}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Andy can now know that George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lori","George","Andy","Guillermo"],"index":66209,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9898062348,"difficulty":0.0101937652}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Leonard can now know whether William can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leonard","William","Kenneth"],"index":20383,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993500113,"difficulty":0.0006499887}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric does not know whether Eric's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Eric can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Andrea","Erin"],"index":35997,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9837377071,"difficulty":0.0162622929}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pat does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Pat can now know that Sarah can know whether Sarah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sarah","Pat","Evan","Joyce"],"index":35564,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9613476396,"difficulty":0.0386523604}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose does not know whether Danielle is thirsty. It is publicly announced that Jose does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jose can now know that Deborah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danielle","Deborah","Charles","Jose"],"index":29298,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980308414,"difficulty":0.0019691586}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catalina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Edwin can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Catalina","Manuel","Edwin"],"index":48971,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994530082,"difficulty":0.0005469918}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roland knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Roland can now know whether Jonathan can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Jonathan","Audra","Roland"],"index":21885,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993146658,"difficulty":0.0006853342}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Curtis does not know whether Curtis's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Deborah can now know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Curtis","Deborah"],"index":61968,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996018827,"difficulty":0.003981173}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana does not know whether Dana's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Dana can now know whether Jodie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jodie","Stephanie","Dana"],"index":57549,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994334579,"difficulty":0.0005665421}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that Dean knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Dean can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dean","James"],"index":16964,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9733226895,"difficulty":1.9733226895}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Alex. Aurelia's card is shown to Alex. Carolyn's card is shown to Lois. Lois's card is shown to Lois. Carolyn's card is shown to Aurelia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lois can now know that Carolyn can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Alex","Lois","Aurelia"],"index":4140,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990178347,"difficulty":0.0009821653}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ramon knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Ramon can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","John","Ramon"],"index":3358,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984931946,"difficulty":0.0015068054}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rafael's card is shown to Rafael. Gertrude's card is shown to Gertrude. Rafael's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Clarence does not know whether Clarence picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gertrude can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rafael","Gertrude","Clarence"],"index":12084,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994488358,"difficulty":0.0005511642}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Thomas can now know that Dorothy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Mike","Dorothy"],"index":41206,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994572997,"difficulty":0.0005427003}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Roderick can know whether Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Roderick","Rafael","Richard"],"index":66475,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993572831,"difficulty":0.0006427169}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Michael can now know that Antoinette can know whether Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Michael","Mary","Antoinette"],"index":26245,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999113977,"difficulty":0.000886023}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roseann knows whether Roseann's forehead is muddy. It is publicly announced that Warren knows whether Roseann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jorge can now know whether Ashley can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Warren","Roseann","Jorge","Ashley"],"index":44476,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999342382,"difficulty":0.000657618}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Malcolm can now know that Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Elena","Thomas","Malcolm"],"index":59206,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979990125,"difficulty":0.0020009875}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gregory can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","John","Karen","Gregory"],"index":7672,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988864064,"difficulty":0.0011135936}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Larae can now know whether Larae's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Larae","Leonard","Robert"],"index":62057,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8027211428,"difficulty":0.1972788572}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth does not know whether Ruth's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Ruth can now know whether Junior can know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Eric","Junior"],"index":7727,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9468311667,"difficulty":0.0531688333}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Louis is thirsty. It is publicly announced that William does not know whether Louis is thirsty. It is publicly announced that William does not know whether Louis is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"William can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["William","Louis"],"index":62297,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994384646,"difficulty":0.0005615354}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Hazel. Hazel's card is shown to Leon. Hazel's card is shown to Sheila. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Hazel can now know whether Hazel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hazel","Jennifer","Leon","Sheila"],"index":32053,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9017612338,"difficulty":1.9017612338}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Raymond. Robert's card is shown to Raymond. Raymond's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Robert picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Robert picked a red card. It is publicly announced that Robert picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] [ ! 2 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Raymond can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Raymond","Robert"],"index":38823,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987693429,"difficulty":0.0012306571}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Madge's card is shown to Madge. Erik's card is shown to Madge. Madge's card is shown to Barbara. Barbara's card is shown to Barbara. David's card is shown to Barbara. Erik's card is shown to Barbara. Madge's card is shown to David. Barbara's card is shown to Erik. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Madge can now know that David can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Madge","Barbara","David","Erik"],"index":24240,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979656935,"difficulty":0.0020343065}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether Helen's forehead is muddy. It is publicly announced that Robert knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jesse can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Helen","Jesse","Kenisha"],"index":5776,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989207983,"difficulty":0.0010792017}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lee can now know that Sam's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sam","Andrew","Susan","Lee"],"index":42737,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952962995,"difficulty":0.0047037005}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eda's card is shown to Eda. Joseph's card is shown to Eda. Jean's card is shown to Eda. Joseph's card is shown to Joseph. Jean's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Eda picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jean can now know whether Jean picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eda","Joseph","Jean"],"index":32012,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.831535697,"difficulty":0.168464303}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Belle does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Paul can now know whether James can know whether Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","James","Belle"],"index":43963,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988949895,"difficulty":0.0011050105}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Michael can now know that Leroy can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Kenneth","Alice","Leroy"],"index":1495,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9901928902,"difficulty":0.0098071098}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Ryan. Ryan's card is shown to Marla. Ryan's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marla can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","Marla","Elizabeth","Phillip"],"index":4829,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989702702,"difficulty":0.0010297298}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether or not nobody's forehead is muddy. It is publicly announced that Gary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Margaret can now know whether Gary can know that Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Terry","Gary"],"index":42418,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9926422238,"difficulty":0.0073577762}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerri's card is shown to Linda. Linda's card is shown to Jerri. It is publicly announced that someone picked a red card. It is publicly announced that Linda knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Linda can now know that Jerri can know that Jerri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Linda","Jerri"],"index":10879,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.731734395,"difficulty":0.268265605}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bruce does not know whether or not everyone is thirsty. It is publicly announced that Leon knows whether someone is thirsty. It is publicly announced that Tomas does not know whether Leon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Leon can now know that Leon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leon","Tomas","Bruce"],"index":56721,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8309529424,"difficulty":0.1690470576}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Margaret can now know that Felix can know whether George is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Felix","Margaret","Charles"],"index":66114,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967845678,"difficulty":0.0032154322}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. Dianne's card is shown to David. Dianne's card is shown to Dianne. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"David can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Dianne"],"index":14184,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993541837,"difficulty":0.0006458163}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fred's card is shown to Barbara. Fred's card is shown to Fred. Fred's card is shown to Adam. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fred can now know whether Barbara can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Barbara","Fred","Adam"],"index":43209,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9956308603,"difficulty":0.0043691397}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Shannon's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"John can now know whether Shannon can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shannon","John"],"index":23071,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990130663,"difficulty":0.0009869337}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Henry can now know that Christine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Henry","Christine"],"index":27151,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.5346060395,"difficulty":1.5346060395}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Bradley can now know whether James can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bradley","James","Iris"],"index":38875,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994328618,"difficulty":0.0005671382}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether Yen is thirsty. It is publicly announced that Lacey does not know whether Yen is thirsty. It is publicly announced that Yen does not know whether Elizabeth is thirsty. It is publicly announced that Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Lacey can now know whether Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lacey","Yen","Elizabeth"],"index":37574,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9879698753,"difficulty":0.0120301247}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] 0","hypothesis":"Armando can now know that Armando is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Armando"],"index":59525,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8298880458,"difficulty":0.1701119542}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nichole is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Nichole can now know that Shirley can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Nichole","Leatha","Shirley"],"index":9335,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5512362123,"difficulty":0.4487637877}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Timothy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Timothy","Jo","James"],"index":48949,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987930059,"difficulty":0.0012069941}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tony's card is shown to Sheila. Alexander's card is shown to Scott. Tony's card is shown to Scott. Tony's card is shown to Tony. It is publicly announced that someone picked a red card. It is publicly announced that Scott does not know whether Sheila picked a red card. It is publicly announced that Alexander does not know whether Sheila picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Sheila can now know that Tony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alexander","Sheila","Scott","Tony"],"index":84,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9923651814,"difficulty":0.0076348186}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy. It is publicly announced that Eddie does not know whether Eddie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"William can now know that Charles can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Eddie","William"],"index":14288,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9647070169,"difficulty":0.0352929831}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Isaac can now know that Keith can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Jason","Edward","Isaac"],"index":61770,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992331266,"difficulty":0.0007668734}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Ruby. Ruby's card is shown to Ruby. Ruby's card is shown to Esther. Esther's card is shown to Esther. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Ruby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Ruby","Robert","Esther"],"index":35712,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965118766,"difficulty":0.0034881234}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Cora. Kimberly's card is shown to Maria. Cora's card is shown to John. Kimberly's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kimberly can now know that Cora can know whether Kimberly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cora","Maria","Kimberly","John"],"index":20539,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7267801166,"difficulty":0.2732198834}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Quinton's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Joann can now know that Quinton can know that Joann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Quinton","Joann","Jill"],"index":42635,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979008436,"difficulty":0.0020991564}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brent knows whether or not nobody's forehead is muddy. It is publicly announced that Brent's forehead is muddy. It is publicly announced that Rose's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Paul can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","Brent","Rose","Marjorie"],"index":4270,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994755387,"difficulty":0.0005244613}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know whether Crystal can know whether Don's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Margaret","Don"],"index":32336,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992007613,"difficulty":0.0007992387}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Edward's card is shown to Joseph. Alta's card is shown to Joseph. Joseph's card is shown to Edward. Patrica's card is shown to Patrica. Joseph's card is shown to Alta. Patrica's card is shown to Alta. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Edward","Patrica","Alta"],"index":15124,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943777919,"difficulty":0.0056222081}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Heidi can now know whether Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Heidi","Michael","Maria","Amber"],"index":47194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980991483,"difficulty":0.0019008517}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Ramona. Ramona's card is shown to Willie. Ramona's card is shown to Carol. Willie's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ramona can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ramona","Willie","Carol"],"index":9433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988974333,"difficulty":0.0011025667}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"William can now know whether Eduardo can know whether Eduardo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charlie","William","Eduardo"],"index":28713,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994232655,"difficulty":0.0005767345}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty. It is publicly announced that Norman does not know whether David is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether David can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","David","Norman"],"index":19423,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9965456128,"difficulty":0.0034543872}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether Teresa's forehead is muddy. It is publicly announced that Corrine knows whether Maxine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Maxine can now know that Corrine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joan","Maxine","Corrine","Teresa"],"index":26090,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973852038,"difficulty":0.0026147962}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel is thirsty. It is publicly announced that Terrell does not know whether Laura is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Laura can now know that Daniel can know whether Terrell is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Terrell","Laura"],"index":41369,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942307472,"difficulty":0.0057692528}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jodi knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Steve can now know that Jodi can know that Jodi's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steve","Jodi"],"index":8557,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9331839681,"difficulty":1.9331839681}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Helen can now know that Sha can know that Josephine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Sha","Jessica","Josephine"],"index":67455,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9910131097,"difficulty":0.0089868903}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Milton can now know whether Arthur can know whether Milton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arthur","Milton","Bruce","Kevin"],"index":17394,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994274378,"difficulty":0.0005725622}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Donna is thirsty. It is publicly announced that Donald knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Patricia can now know whether David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Donald","David","Patricia"],"index":23366,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981642365,"difficulty":0.0018357635}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Larry can now know that Adelia can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Larry","Adelia"],"index":12511,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9838828444,"difficulty":0.0161171556}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Anna. Armando's card is shown to Edwin. Edwin's card is shown to Armando. Armando's card is shown to Armando. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Armando can now know whether Anna can know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anna","Edwin","Armando"],"index":11939,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9975683093,"difficulty":0.0024316907}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vincent's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Paul can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","Edith","Vincent","Josephine"],"index":2816,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992883801,"difficulty":0.0007116199}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kim knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kim can now know that Billy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kim","Marc","Harry","Billy"],"index":23692,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988503456,"difficulty":0.0011496544}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Adam can now know that Tanya can know whether Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tanya","Jeffrey","Adam","Beryl"],"index":2355,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992406368,"difficulty":0.0007593632}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joann's card is shown to Joann. Kim's card is shown to Kim. Kelly's card is shown to Kelly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joann can now know whether Heather can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","Joann","Kim","Kelly"],"index":45969,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994190931,"difficulty":0.0005809069}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert is thirsty. It is publicly announced that Jesica does not know whether or not everyone is thirsty. It is publicly announced that Robert does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Michael can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Joseph","Robert","Jesica"],"index":1504,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990677238,"difficulty":0.0009322762}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Hilda can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hilda","Earl","David"],"index":25375,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992960691,"difficulty":0.0007039309}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Connie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Connie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Juan","Jennifer","Connie","Victoria"],"index":28554,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989874959,"difficulty":0.0010125041}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tina does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know that Maureen can know that Ian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Tina","Ian","Maureen"],"index":1239,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7465624213,"difficulty":0.2534375787}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeri does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Marcelino can now know whether Cherise can know whether Eduardo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eduardo","Jeri","Cherise","Marcelino"],"index":40506,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993171692,"difficulty":0.0006828308}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Paul. Elaine's card is shown to Daniel. Paul's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Elaine does not know whether or not everyone picked a red card. It is publicly announced that Elaine does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elaine","Paul","Daniel"],"index":18764,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985578656,"difficulty":0.0014421344}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbra knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Irene can now know that Randy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbra","Irene","Randy"],"index":33923,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991984963,"difficulty":0.0008015037}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna knows whether someone is thirsty. It is publicly announced that Erin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Kenneth can now know whether Erin can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Donna","Erin"],"index":18167,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9968486428,"difficulty":0.0031513572}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jane does not know whether or not everyone is thirsty. It is publicly announced that Jane does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Anita can now know that Jane can know that Jane is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anita","Jane"],"index":17342,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5330412984,"difficulty":1.5330412984}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Alice can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alice","Chester","Johnny"],"index":52235,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9972085357,"difficulty":0.0027914643}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Norman can now know that James can know whether Ernest's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Norman","Ernest"],"index":43554,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992787242,"difficulty":0.0007212758}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara knows whether Lonnie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Barbara can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Barbara","Lonnie"],"index":3948,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994027615,"difficulty":0.0005972385}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Valerie. Adelia's card is shown to Valerie. Valerie's card is shown to Tracy. Tracy's card is shown to Tracy. Adelia's card is shown to Tracy. Charles's card is shown to Tracy. Tracy's card is shown to Adelia. Charles's card is shown to Adelia. Valerie's card is shown to Charles. Adelia's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Valerie can now know that Tracy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Valerie","Tracy","Adelia","Charles"],"index":5532,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974105954,"difficulty":0.0025894046}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Dionne can now know whether Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sean","Maria","Dionne","Beatrice"],"index":28856,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985995889,"difficulty":0.0014004111}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julio's card is shown to Joseph. Bob's card is shown to Bob. Bob's card is shown to Julio. It is publicly announced that someone picked a red card. It is publicly announced that Bob does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Julio can now know that Julio picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Bob","Julio"],"index":51857,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8208397627,"difficulty":0.1791602373}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Laura. Justin's card is shown to Justin. Justin's card is shown to Victor. Victor's card is shown to Victor. Victor's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Victor can now know that Victor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Justin","Victor","John"],"index":47055,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9861664772,"difficulty":0.0138335228}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alice knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Alice can now know that Sarah can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sarah","Alice","Jami"],"index":31322,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998803854,"difficulty":0.001196146}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda's forehead is muddy. It is publicly announced that Nancy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Nancy can now know that Amanda can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Amanda"],"index":38758,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994213581,"difficulty":0.0005786419}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty. It is publicly announced that Timothy does not know whether Neil is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"John can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Olive","Neil","John","Timothy"],"index":48592,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9106624126,"difficulty":1.9106624126}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katie knows whether Katie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Edwin can now know that Katie can know that Katie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachel","Margaret","Katie","Edwin"],"index":67018,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.995845139,"difficulty":0.004154861}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Anita can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ofelia","Anita","Robert","Mary"],"index":47043,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993751645,"difficulty":0.0006248355}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter's forehead is not muddy. It is publicly announced that Krystle's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Walter can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Krystle","Walter"],"index":18191,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993183613,"difficulty":0.0006816387}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian knows whether Brian is thirsty. It is publicly announced that Robert does not know whether Brian is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Robert can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brian","Robert"],"index":17988,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994878769,"difficulty":0.0005121231}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Jack is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Gloria can now know whether Janie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janie","Jack","Darryl","Gloria"],"index":19945,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995075464,"difficulty":0.0004924536}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Heather. Mary's card is shown to Albert. Virginia's card is shown to Virginia. Heather's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heather can now know whether Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Heather","Albert","Virginia","Mary"],"index":36863,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995106101,"difficulty":0.004893899}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angel knows whether or not nobody is thirsty. It is publicly announced that David does not know whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Charles can now know that Linda can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","David","Linda","Angel"],"index":14197,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990150928,"difficulty":0.0009849072}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joel's card is shown to Tracy. Joel's card is shown to Mary. John's card is shown to John. Mary's card is shown to Joel. John's card is shown to Joel. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Mary picked a red card. It is publicly announced that Tracy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joel can now know whether John can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracy","Mary","John","Joel"],"index":5752,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994532466,"difficulty":0.0005467534}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Samuel can now know whether William can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Samuel","Karen"],"index":30266,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991436005,"difficulty":0.0008563995}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Lori knows whether Lori's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lori can now know that Eva can know whether Eva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lori","Eva"],"index":15566,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992615581,"difficulty":0.0007384419}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nancy can now know whether Nelly can know that Nelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Ralph","Nelly","James"],"index":28394,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964109063,"difficulty":0.0035890937}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dominick's card is shown to Dominick. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mary can now know whether Dominick can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dominick","Mary"],"index":27027,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994437099,"difficulty":0.0005562901}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sara knows whether or not everyone's forehead is muddy. It is publicly announced that Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Maria can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maria","Diane","Sara","Bridget"],"index":49749,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993768334,"difficulty":0.0006231666}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Ann can now know that Clarence can know that Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ann","Donald","Clarence"],"index":54929,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973249435,"difficulty":0.0026750565}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alison does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kevin can now know whether Alison can know that Alison is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Walter","Alison","Kevin","Amy"],"index":56782,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9650874734,"difficulty":0.0349125266}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is muddy. It is publicly announced that Magdalena's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Patricia can now know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Magdalena","Mary","Harvey","Patricia"],"index":30325,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8797534108,"difficulty":0.1202465892}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marguerite's card is shown to Marguerite. Glenna's card is shown to Marguerite. Marguerite's card is shown to Thomas. Thomas's card is shown to Thomas. Anita's card is shown to Anita. Marguerite's card is shown to Glenna. Thomas's card is shown to Glenna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marguerite can now know that Glenna can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marguerite","Thomas","Anita","Glenna"],"index":23454,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993963242,"difficulty":0.0006036758}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth does not know whether Louis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Kenneth can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beatrice","Louis","Marilyn","Kenneth"],"index":33770,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987994432,"difficulty":0.0012005568}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie does not know whether or not everyone's forehead is muddy. It is publicly announced that Jamie does not know whether Jamie's forehead is muddy. It is publicly announced that Jamie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jamie can now know that Justin can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jamie","Justin"],"index":35194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.68327564,"difficulty":0.31672436}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Donna can now know whether Harold can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donna","Harold","William"],"index":3342,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990221262,"difficulty":0.0009778738}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rafael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Carole can now know whether Rafael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carole","Levi","Rafael"],"index":22852,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994774461,"difficulty":0.0005225539}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Dorothy. Michelle's card is shown to Francis. Francis's card is shown to Michelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Francis","Michelle"],"index":1307,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989784956,"difficulty":0.0010215044}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Sandra can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","Sandra","William","Lisa"],"index":2422,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998842299,"difficulty":0.001157701}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Ron is thirsty. It is publicly announced that Jeremiah knows whether Jeremiah is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Michael can now know whether Clifton can know that Ron is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Ron","Clifton","Jeremiah"],"index":64868,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9913798571,"difficulty":0.0086201429}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roberta's card is shown to Dorothy. John's card is shown to Dorothy. Dorothy's card is shown to James. Dorothy's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know whether Roberta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roberta","Dorothy","James","John"],"index":34783,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9938957095,"difficulty":0.0061042905}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Doris can now know that Raymond can know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karl","Doris","Raymond","Anthony"],"index":25266,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999360621,"difficulty":0.000639379}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodore's card is shown to Theodore. Sonia's card is shown to Sonia. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Theodore does not know whether Kenneth picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Sonia does not know whether Kenneth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Theodore can now know whether Kenneth can know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Theodore","Sonia","Kenneth"],"index":11577,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973521233,"difficulty":0.0026478767}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know that Joan can know that Larry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Sue","Joan","Thomas"],"index":7519,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6937219501,"difficulty":1.6937219501}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brad knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Brad can now know that Darren's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Darren","Brad","Dorothy"],"index":6685,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982795715,"difficulty":0.0017204285}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Jerry. David's card is shown to David. James's card is shown to David. Jerry's card is shown to James. David's card is shown to James. James's card is shown to James. David's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that George can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","David","James","George"],"index":17476,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992811084,"difficulty":0.0007188916}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Heath is thirsty. It is publicly announced that Suzanne knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentc knows that (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Heath can now know that Scott can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Myrtle","Scott","Heath","Suzanne"],"index":14231,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994482398,"difficulty":0.0005517602}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicholas is thirsty. It is publicly announced that Angela is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Angela can now know that Tracy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracy","Nicholas","Angela"],"index":17661,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994801879,"difficulty":0.0005198121}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelica knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Wayne can now know whether Amanda can know that Angelica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","Amanda","Ernest","Angelica"],"index":25168,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8739395142,"difficulty":0.1260604858}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Billy knows whether Billy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Chad can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Billy","Miles","Chad","Adam"],"index":47954,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998929441,"difficulty":0.001070559}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Donna can now know whether Gertrude can know that June's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donna","June","Gertrude"],"index":8137,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994213581,"difficulty":0.0005786419}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frieda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Patricia can now know whether Lisa can know that Lisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ashley","Patricia","Frieda","Lisa"],"index":29339,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7944648266,"difficulty":0.2055351734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eartha does not know whether or not everyone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Eartha can now know whether Patricia can know that Eartha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Merry","Emma","Eartha"],"index":5696,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6475159526,"difficulty":0.3524840474}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry's forehead is muddy. It is publicly announced that Dennis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Terry can now know whether Dennis can know whether Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dennis","Terry"],"index":16132,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994546771,"difficulty":0.0005453229}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"David can now know that Frederick can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Frederick","David"],"index":6712,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987296462,"difficulty":0.0012703538}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Shirley. David's card is shown to Shirley. David's card is shown to Margaret. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shirley","David","Margaret"],"index":59929,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7794524431,"difficulty":1.7794524431}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley does not know whether Bradley's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Danny can now know that Mary can know that Bradley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bradley","Mary","Danny"],"index":56655,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9610592127,"difficulty":0.0389407873}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Roxana can now know that Dorothy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dorothy","Roxana"],"index":35795,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.972325027,"difficulty":0.027674973}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Andrew is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Andrew can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andrew","Elizabeth"],"index":61028,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99903512,"difficulty":0.00096488}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Hattie can now know whether Sylvia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvia","William","Hattie","Jessica"],"index":14581,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992685914,"difficulty":0.0007314086}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know whether William can know whether Jacquelyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Jacquelyn","James","William"],"index":26017,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999252975,"difficulty":0.000747025}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Inez's card is shown to Inez. Inez's card is shown to James. James's card is shown to James. Inez's card is shown to Logan. Logan's card is shown to Logan. It is publicly announced that someone picked a red card. It is publicly announced that Inez does not know whether Logan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Roberta can now know whether Logan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Inez","James","Roberta","Logan"],"index":9926,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9370428324,"difficulty":0.0629571676}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Everett's card is shown to Dolores. Joe's card is shown to Dolores. Dolores's card is shown to Lori. Dolores's card is shown to Joe. Joe's card is shown to Joe. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Everett can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Everett","Dolores","Lori","Joe"],"index":40356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989921451,"difficulty":0.0010078549}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francisco's card is shown to Francisco. Francisco's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether William picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"William can now know whether Francisco can know whether Francisco picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Francisco","William"],"index":66029,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985855818,"difficulty":0.0014144182}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bessie does not know whether Frances is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] 0","hypothesis":"Bessie can now know that Frances can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bessie","Frances"],"index":39785,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994020462,"difficulty":0.0005979538}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna does not know whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Donna can now know that Thomas can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Everett","Thomas","William","Donna"],"index":38320,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.989371419,"difficulty":0.010628581}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether Madge's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Edward can now know whether Madge can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Madge","Mary","Edward"],"index":29998,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993694425,"difficulty":0.0006305575}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joey's card is shown to Joey. Joey's card is shown to Thomas. Dorian's card is shown to Thomas. Dorian's card is shown to Dorian. Thomas's card is shown to Ralph. Ralph's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Ralph does not know whether Dorian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Joey can now know whether Dorian can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joey","Thomas","Dorian","Ralph"],"index":34591,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9455100894,"difficulty":0.0544899106}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Donna can now know whether Glen can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Audrey","Donna","Theresa","Glen"],"index":22522,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993721843,"difficulty":0.0006278157}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Robert can now know that Joyce can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joyce","Robert"],"index":51451,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992189407,"difficulty":0.0007810593}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmel's card is shown to Carmel. Jonathon's card is shown to Carmel. Carmel's card is shown to Jonathon. Jonathon's card is shown to Jonathon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Jonathon can now know whether Carmel can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carmel","Jonathon"],"index":17522,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999407053,"difficulty":0.000592947}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paige knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Frances can now know whether Paige's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tara","Paige","Frances","Jason"],"index":35250,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994002581,"difficulty":0.0005997419}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Charles can now know whether Tiffany can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Rosemary","Tiffany"],"index":1863,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993453622,"difficulty":0.0006546378}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gabriel's forehead is not muddy. It is publicly announced that Ryan's forehead is muddy. It is publicly announced that Gabriel knows whether Gabriel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ashley can now know that Gabriel can know that Gabriel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gabriel","Ryan","Ashley"],"index":33898,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9441152215,"difficulty":0.0558847785}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether or not everyone's forehead is muddy. It is publicly announced that Paul does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Arron can now know whether Arron's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Paul","Arron"],"index":16460,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9409171939,"difficulty":1.9409171939}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Charles can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","John","James","Mary"],"index":11032,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990210533,"difficulty":0.0009789467}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jesus can now know whether Earnest can know that Earnest is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leona","Edward","Jesus","Earnest"],"index":59141,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9762785435,"difficulty":0.0237214565}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carol. Mark's card is shown to Mark. Michael's card is shown to Mark. Virginia's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Carol picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mark can now know that Michael can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Mark","Michael","Virginia"],"index":58294,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7185395956,"difficulty":0.2814604044}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Joan can now know that Michael can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Joan"],"index":57668,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.991899848,"difficulty":0.008100152}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Kenneth. Jack's card is shown to Jack. Anastasia's card is shown to Anastasia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carolee can now know whether Anastasia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Carolee","Jack","Anastasia"],"index":51852,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7052266598,"difficulty":1.7052266598}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tiffany does not know whether Amy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Amy can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amy","Martin","Tiffany","James"],"index":39764,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983330369,"difficulty":0.0016669631}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucille does not know whether Jose is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lucille can now know whether Jose can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lucille","Jose","Michael","Ione"],"index":43662,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957183003,"difficulty":0.0042816997}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred knows whether Patrick's forehead is muddy. It is publicly announced that Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Jose can now know whether Alan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Alan","Fred","Patrick"],"index":13822,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993927479,"difficulty":0.0006072521}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Tommy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Tommy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristen","Donald","Tommy"],"index":57428,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9907923937,"difficulty":0.0092076063}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cortney's card is shown to Cortney. Dorothy's card is shown to Cortney. Nicholas's card is shown to Dorothy. Nicholas's card is shown to Nicholas. Charles's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cortney","Dorothy","Nicholas","Charles"],"index":9512,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989973903,"difficulty":0.0010026097}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy does not know whether or not everyone's forehead is muddy. It is publicly announced that Amos knows whether or not nobody's forehead is muddy. It is publicly announced that Tracy does not know whether Tracy's forehead is muddy. It is publicly announced that Amos knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Amos can now know that Tracy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tracy","Amos"],"index":16383,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9019305706,"difficulty":0.0980694294}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Steven. Fred's card is shown to Steven. Daisy's card is shown to Steven. Daisy's card is shown to Frank. Steven's card is shown to Daisy. Fred's card is shown to Daisy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know that Frank can know that Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Fred","Frank","Daisy"],"index":38225,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982424974,"difficulty":0.0017575026}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Edward can now know that Jose can know that Jose is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Florence","Jose"],"index":61865,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5150931478,"difficulty":0.4849068522}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elisa's card is shown to Elisa. Dean's card is shown to Elisa. Dean's card is shown to Dean. It is publicly announced that someone picked a red card. It is publicly announced that Dean knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Dean can now know that Elisa can know that Elisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elisa","Dean"],"index":40601,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8022732735,"difficulty":1.8022732735}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce's forehead is muddy. It is publicly announced that Laura's forehead is muddy. It is publicly announced that Erika does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Lewis can now know whether Joyce can know that Joyce's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","Laura","Lewis","Erika"],"index":37251,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9934849143,"difficulty":0.0065150857}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether Deana is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Linda can now know that Deana is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deana","Mark","Linda"],"index":67263,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9917926192,"difficulty":0.0082073808}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gabriel does not know whether Gabriel's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Esther can now know that Gabriel can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hubert","Gabriel","Esther","Helen"],"index":55819,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9950165153,"difficulty":0.0049834847}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annett's card is shown to Belinda. Annett's card is shown to Annett. It is publicly announced that someone picked a red card. It is publicly announced that Belinda does not know whether Belinda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Annett can now know whether Belinda can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Belinda","Annett"],"index":5134,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999430716,"difficulty":0.000569284}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristina does not know whether or not everyone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that Kristina does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Freddie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Freddie","Kristina","Mary"],"index":9102,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999466002,"difficulty":0.000533998}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terina's card is shown to Marylou. Bethann's card is shown to Bethann. Marylou's card is shown to Terina. Terina's card is shown to Terina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terina can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marylou","Bethann","Terina"],"index":45253,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989533424,"difficulty":0.0010466576}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Stanley's card is shown to James. James's card is shown to Stanley. Stanley's card is shown to Stanley. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether or not nobody picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"James can now know whether Stanley can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Stanley"],"index":4704,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999407649,"difficulty":0.000592351}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tami knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Tami can now know that Brenda can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tami","Brenda","Jason"],"index":33107,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9858576059,"difficulty":0.0141423941}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Jerome. Doreen's card is shown to Louis. Louis's card is shown to George. Louis's card is shown to Doreen. Doreen's card is shown to Doreen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doreen can now know whether Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jerome","Louis","George","Doreen"],"index":28536,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5427087545,"difficulty":1.5427087545}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Lisa can now know that Deanna can know whether Minnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Troy","Lisa","Minnie","Deanna"],"index":48391,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.994074285,"difficulty":0.005925715}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether Fay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Virginia can now know that Donna can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Virginia","Charles","Fay"],"index":14811,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994155169,"difficulty":0.0005844831}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vivian can now know that Larry can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steven","Vivian","Larry"],"index":35591,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988666773,"difficulty":0.0011333227}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Barbara can now know whether James can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Barbara"],"index":63806,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9945764542,"difficulty":0.0054235458}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brett's card is shown to Brett. Nicole's card is shown to Nicole. Ruby's card is shown to Nicole. Ruby's card is shown to Ruby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ruby can now know whether Brett picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brett","Nicole","Ruby"],"index":26645,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9867998362,"difficulty":0.0132001638}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Margot knows whether Douglas's forehead is muddy. It is publicly announced that Margot knows whether someone's forehead is muddy. It is publicly announced that Margot's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Douglas can now know whether Dixie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Margot","Dixie","Douglas"],"index":34891,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9966501594,"difficulty":0.0033498406}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Susan. Cindy's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Susan knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Cindy can now know that Cindy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Susan","Cindy"],"index":15192,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.959964633,"difficulty":0.040035367}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Suzanne's card is shown to Leanne. Leanne's card is shown to Patricia. Leanne's card is shown to David. Leanne's card is shown to Suzanne. Suzanne's card is shown to Suzanne. It is publicly announced that someone picked a red card. It is publicly announced that Leanne does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Patricia can now know that Suzanne can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leanne","Patricia","David","Suzanne"],"index":17497,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994174242,"difficulty":0.0005825758}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorraine's card is shown to Anna. Catherine's card is shown to Gregory. Gregory's card is shown to Lorraine. Anna's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Catherine does not know whether or not everyone picked a red card. It is publicly announced that Gregory picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Anna can now know whether Catherine can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anna","Gregory","Lorraine","Catherine"],"index":17893,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8195930123,"difficulty":0.1804069877}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee knows whether or not everyone's forehead is muddy. It is publicly announced that Lee does not know whether Lee's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lee can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Johnny","Lee"],"index":57029,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990614057,"difficulty":0.0009385943}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Nicole can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carrie","Nicole","Janice","Robert"],"index":14837,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998233676,"difficulty":0.001766324}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gladys can now know that Susan can know whether Gladys's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Celia","Susan","Caroline","Gladys"],"index":2480,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9956633449,"difficulty":0.0043366551}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Lavern. Carla's card is shown to Lavern. James's card is shown to James. Lavern's card is shown to Carla. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lavern can now know whether Carla picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lavern","James","Carla"],"index":42479,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5874456167,"difficulty":1.5874456167}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie does not know whether Gloria is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Veronica knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Julie can now know whether Gloria can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julie","Gloria","Veronica"],"index":44155,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994285703,"difficulty":0.0005714297}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roosevelt knows whether someone's forehead is muddy. It is publicly announced that Roosevelt's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] 0","hypothesis":"Joseph can now know whether Joyce's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roosevelt","Joyce","Joseph"],"index":1271,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993749261,"difficulty":0.0006250739}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sanjuana knows whether Sanjuana's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Daniel can now know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sanjuana","Lexie","Melissa","Daniel"],"index":49135,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976213574,"difficulty":0.0023786426}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Faith can now know that Bobby can know that Eva's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bobby","Faith","John","Eva"],"index":32354,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979684949,"difficulty":0.0020315051}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beckie's card is shown to Lisa. Lisa's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rachel can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rachel","Beckie","Lisa"],"index":49314,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989847541,"difficulty":0.0010152459}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Lisa. Lisa's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Lisa","Annabelle"],"index":11644,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Eileen. Jack's card is shown to Valerie. Jack's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Valerie does not know whether Valerie picked a red card. It is publicly announced that Eileen does not know whether Jack picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jack can now know whether Valerie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eileen","Jack","Valerie","Robert"],"index":31462,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992171526,"difficulty":0.0007828474}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy. It is publicly announced that Jose knows whether or not nobody's forehead is muddy. It is publicly announced that Jose does not know whether Jose's forehead is muddy. It is publicly announced that Ronald knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kevin can now know that Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kevin","Jose","Ronald"],"index":57173,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9676434994,"difficulty":0.0323565006}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Evelyn. Evelyn's card is shown to Philip. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn knows whether Evelyn picked a red card. It is publicly announced that Evelyn knows whether Philip picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Evelyn can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Evelyn","Philip"],"index":5858,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994365573,"difficulty":0.0005634427}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Paul knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know that Paul can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","John"],"index":52907,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994273186,"difficulty":0.0005726814}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Gary can now know that Shirley can know that Gary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gary","Holly","Shirley"],"index":41416,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966574907,"difficulty":0.0033425093}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Sarah is thirsty. It is publicly announced that Richard does not know whether Mildred is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Richard can now know whether Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Mildred","Sarah"],"index":983,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9967561364,"difficulty":0.0032438636}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felicia's card is shown to Mary. Jean's card is shown to Jean. Ruben's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Felicia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know that Felicia can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Felicia","Mary","Jean","Ruben"],"index":20247,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.871368885,"difficulty":0.128631115}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Barbara can now know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Scott","Barbara","Pamela"],"index":31335,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982415438,"difficulty":0.0017584562}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Nicole can now know that Doris can know whether Doris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicole","Richard","Doris","Cristina"],"index":20861,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994270802,"difficulty":0.0005729198}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eduardo is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Eduardo can now know that James can know whether Eduardo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eduardo","James"],"index":14714,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.986374855,"difficulty":0.013625145}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bridget knows whether Bridget is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robin can now know that Walter can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robin","Walter","Bridget"],"index":9547,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994346499,"difficulty":0.0005653501}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Caryl. Richard's card is shown to Joanna. Cecilia's card is shown to Joanna. Caryl's card is shown to Cecilia. Joanna's card is shown to Cecilia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Joanna can know that Joanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Caryl","Richard","Joanna","Cecilia"],"index":9219,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977235198,"difficulty":0.0022764802}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly does not know whether Troy is thirsty. It is publicly announced that Kelly is thirsty. It is publicly announced that Troy is thirsty. It is publicly announced that Troy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] Agentb knows whether (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Troy can now know whether Kelly can know whether Kelly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kelly","Troy"],"index":54716,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987441301,"difficulty":0.0012558699}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenny's card is shown to Michael. Frederick's card is shown to Frederick. Michael's card is shown to Jenny. It is publicly announced that someone picked a red card. It is publicly announced that Jenny does not know whether Frederick picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Michael can now know that Frederick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Frederick","Jenny"],"index":53372,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959775805,"difficulty":0.0040224195}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Israel's card is shown to Natalie. Israel's card is shown to Israel. Dolores's card is shown to Israel. Edith's card is shown to Israel. Israel's card is shown to Edith. Edith's card is shown to Edith. It is publicly announced that someone picked a red card. It is publicly announced that Natalie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Natalie can now know that Israel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Natalie","Israel","Dolores","Edith"],"index":9395,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8370681405,"difficulty":1.8370681405}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aubrey's card is shown to Paula. Robert's card is shown to Brenda. Paula's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paula","Brenda","Robert","Aubrey"],"index":28986,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993879795,"difficulty":0.0006120205}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lizette's card is shown to Lizette. Alvin's card is shown to Lizette. Lizette's card is shown to Max. Alvin's card is shown to Max. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alvin can now know that Lizette can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lizette","Alvin","Max"],"index":32038,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994124174,"difficulty":0.0005875826}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arturo's card is shown to Arturo. Wendy's card is shown to Eric. Arturo's card is shown to Beatrice. Eric's card is shown to Wendy. It is publicly announced that someone picked a red card. It is publicly announced that Arturo does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Wendy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arturo","Eric","Beatrice","Wendy"],"index":19832,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994327426,"difficulty":0.0005672574}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Patrick can now know that Emory can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patrick","Danny","William","Emory"],"index":23372,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9963257909,"difficulty":0.0036742091}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edythe knows whether or not nobody's forehead is muddy. It is publicly announced that Edythe does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Edythe can now know whether Edythe's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rosa","Edythe"],"index":1022,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9226933718,"difficulty":1.9226933718}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Edna can now know whether Barbara can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edna","Michael","Barbara"],"index":60174,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993796349,"difficulty":0.0006203651}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Mildred's card is shown to Mildred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Mildred","Sharon","Steve"],"index":57107,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.97356987,"difficulty":0.02643013}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Herbert. Ruth's card is shown to Ruth. Robert's card is shown to Ruth. Herbert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether Herbert picked a red card. It is publicly announced that Ruth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ruth can now know whether Herbert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Herbert","Ruth","Robert"],"index":22495,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7788379192,"difficulty":1.7788379192}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Olga can now know that Robert can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Olga","Velda","Robert"],"index":31108,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993621707,"difficulty":0.0006378293}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maggie's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Patricia","Maggie"],"index":17178,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993273139,"difficulty":0.006726861}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leah's card is shown to Leah. Priscilla's card is shown to Priscilla. Leah's card is shown to Elizabeth. Priscilla's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Leah does not know whether or not everyone picked a red card. It is publicly announced that Priscilla knows whether Priscilla picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Priscilla can now know whether Leah can know whether Priscilla picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leah","Priscilla","Elizabeth"],"index":65363,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980395436,"difficulty":0.0019604564}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edna knows whether Edna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Laura can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edna","Robert","Laura","Terrence"],"index":14570,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995074272,"difficulty":0.0004925728}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Trina does not know whether Frederick is thirsty. It is publicly announced that Trina knows whether Trina is thirsty. It is publicly announced that Frederick does not know whether Trina is thirsty. It is publicly announced that Isreal does not know whether Trina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Trina can now know that Frederick can know whether Isreal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frederick","Trina","Isreal"],"index":39150,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.792539537,"difficulty":0.207460463}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Maryland's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Matthew can now know that Robert can know that Essie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Essie","Maryland","Matthew","Robert"],"index":25792,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982349873,"difficulty":0.0017650127}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Mary can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deanna","Blanca","Mary","Elliot"],"index":66468,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989890456,"difficulty":0.0010109544}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heidi is thirsty. It is publicly announced that Heidi knows whether Heidi is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Heidi can now know that Stanley can know that Heidi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Stanley","Heidi"],"index":54236,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8126294613,"difficulty":1.8126294613}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicholas can now know that Karissa can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robin","Sharon","Nicholas","Karissa"],"index":3116,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988610744,"difficulty":0.0011389256}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy's forehead is muddy. It is publicly announced that Emmy's forehead is muddy. It is publicly announced that Mark does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Susan can now know that Emmy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathy","Emmy","Susan","Mark"],"index":4425,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9527118802,"difficulty":0.0472881198}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lavonne knows whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Patricia can now know whether Lavonne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","William","Sharon","Lavonne"],"index":56531,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990137815,"difficulty":0.0009862185}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Selma's card is shown to Heather. Lisa's card is shown to Lisa. Nora's card is shown to Lisa. Nora's card is shown to Selma. Heather's card is shown to Nora. Lisa's card is shown to Nora. Selma's card is shown to Nora. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nora can now know that Lisa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","Lisa","Selma","Nora"],"index":22310,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993879795,"difficulty":0.0006120205}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith knows whether George's forehead is muddy. It is publicly announced that Judith knows whether Judith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Judith can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Judith","George"],"index":36186,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989023209,"difficulty":0.0010976791}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Ebony can now know that Eduardo can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eduardo","Christy","Ebony"],"index":38397,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994302392,"difficulty":0.0005697608}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Van can now know whether Eula can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Van","Eula","Gladys","Sean"],"index":19038,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9743382335,"difficulty":0.0256617665}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christina knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Christina can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Faith","Kevin","Ryan","Christina"],"index":10719,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8852376938,"difficulty":0.1147623062}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Beatrice does not know whether James is thirsty. It is publicly announced that James does not know whether Beatrice is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"James can now know that Beatrice can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Beatrice","James"],"index":22834,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8863668442,"difficulty":0.1136331558}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shawn knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Shawn can now know whether William can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Shawn"],"index":12092,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994014502,"difficulty":0.0005985498}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carole's card is shown to Wesley. Carole's card is shown to Carole. Joseph's card is shown to Carole. Wesley's card is shown to Joshua. Carole's card is shown to Joshua. Wesley's card is shown to Joseph. Joshua's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Wesley does not know whether Joshua picked a red card. It is publicly announced that Wesley knows whether Carole picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Carole can now know that Joseph can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wesley","Carole","Joshua","Joseph"],"index":19950,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994284511,"difficulty":0.0005715489}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel knows whether Nohemi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Marie can now know whether Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nohemi","Marie","Joel","Glenn"],"index":60200,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939104319,"difficulty":0.0060895681}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith knows whether or not everyone's forehead is muddy. It is publicly announced that Dana does not know whether Dana's forehead is muddy. It is publicly announced that Cindi knows whether Robert's forehead is muddy. It is publicly announced that Dana does not know whether Dana's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] (Agentc knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Keith can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Cindi","Keith","Dana"],"index":10233,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985774755,"difficulty":0.0014225245}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rene knows whether Jackie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Jackie can now know whether Jackie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harvey","Rene","Jackie","John"],"index":33275,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9832652807,"difficulty":0.0167347193}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Eleanor is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Bettie can now know that Linda can know that Bettie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bettie","Linda","Eleanor","Stephanie"],"index":45552,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976423383,"difficulty":0.0023576617}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica does not know whether Jessica's forehead is muddy. It is publicly announced that Gretchen knows whether Jessica's forehead is muddy. It is publicly announced that Gretchen does not know whether Gretchen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Catherine can now know that Gretchen can know that Ellen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Ellen","Gretchen","Jessica"],"index":42734,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956145287,"difficulty":0.0043854713}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Fawn can now know that Margaret can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Melissa","Fawn"],"index":22588,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99941957,"difficulty":0.00058043}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to Rhonda. Lonnie's card is shown to Rhonda. Rhonda's card is shown to Michael. Michael's card is shown to Michael. Lonnie's card is shown to Michael. William's card is shown to Michael. Michael's card is shown to Lonnie. William's card is shown to Lonnie. Rhonda's card is shown to William. Lonnie's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether Lonnie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rhonda","Michael","Lonnie","William"],"index":35153,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994223118,"difficulty":0.0005776882}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamala's card is shown to Jorge. Jorge's card is shown to Jorge. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Pamala can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pamala","Jorge","Luanne"],"index":52393,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994106293,"difficulty":0.0005893707}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathy is thirsty. It is publicly announced that Donna does not know whether John is thirsty. It is publicly announced that Kathy knows whether Kathy is thirsty. It is publicly announced that Donna does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","John","Kathy"],"index":23441,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999463141,"difficulty":0.000536859}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Shane's card is shown to Shane. It is publicly announced that someone picked a red card. It is publicly announced that Shane does not know whether Linda picked a red card. It is publicly announced that Linda knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Shane can now know that Linda can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Linda","Shane"],"index":36203,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.500010252,"difficulty":0.499989748}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judith knows whether Judith is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Nicholas can now know whether Kim is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicholas","Kim","Henry","Judith"],"index":33859,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980632663,"difficulty":0.0019367337}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Stephen. Margaret's card is shown to Margaret. Maria's card is shown to Margaret. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Robert picked a red card. It is publicly announced that Stephen does not know whether Margaret picked a red card. It is publicly announced that Maria does not know whether or not everyone picked a red card. It is publicly announced that Margaret does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Margaret can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Margaret","Maria","Robert"],"index":36571,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.798142612,"difficulty":0.201857388}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenn does not know whether Glenn's forehead is muddy. It is publicly announced that Dorothy knows whether Glenn's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Glenn can now know whether James can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","James","Dorothy","Glenn"],"index":12121,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9324876666,"difficulty":0.0675123334}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brock does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Robert can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Brock","James"],"index":5310,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994334579,"difficulty":0.0005665421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Wilson can now know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wilson","Jennifer","Leandra"],"index":23263,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9909033179,"difficulty":0.0090966821}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geoffrey knows whether Geoffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Geoffrey can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Geoffrey","Anthony","Kathy"],"index":51972,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989424348,"difficulty":0.0010575652}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy. It is publicly announced that Steven's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"David can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Myron","Steven"],"index":13138,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988150597,"difficulty":0.0011849403}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christina does not know whether Todd is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Kristen can now know that Todd can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christina","Todd","Kristen"],"index":26929,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994256496,"difficulty":0.0005743504}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy. It is publicly announced that Dan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Betty can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dan","Frank","Betty"],"index":19151,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993681312,"difficulty":0.0006318688}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Toshiko knows whether someone's forehead is muddy. It is publicly announced that Toshiko knows whether someone's forehead is muddy. It is publicly announced that Arturo knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Toshiko can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Arturo","Toshiko"],"index":14032,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994794726,"difficulty":0.0005205274}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether or not everyone is thirsty. It is publicly announced that Joseph knows whether or not nobody is thirsty. It is publicly announced that Eunice does not know whether Opal is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Opal can now know that Joseph can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Opal","Eunice"],"index":64898,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990321398,"difficulty":0.0009678602}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Martin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"James can now know whether Martin can know that Barry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Martin","James","Barry","Nancy"],"index":28808,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994542003,"difficulty":0.0005457997}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Maria can now know that Vivian can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vivian","Maria"],"index":13467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994601607,"difficulty":0.0005398393}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Gerald can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shelby","Donald","Gerald","Ronald"],"index":61815,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990003705,"difficulty":0.0009996295}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy. It is publicly announced that Kathleen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Kathleen can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Rodney","Kathleen","Mary"],"index":66365,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990339279,"difficulty":0.0009660721}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Amanda can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Robert","Amanda"],"index":58971,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999476254,"difficulty":0.000523746}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Opal. Ruth's card is shown to Ruth. Kelly's card is shown to Ruth. Opal's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Opal does not know whether Opal picked a red card. It is publicly announced that Ruth picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Ruth can now know that Kelly can know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Opal","Ruth","Kelly"],"index":4717,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9564827085,"difficulty":0.0435172915}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debbie knows whether someone's forehead is muddy. It is publicly announced that Archie does not know whether Archie's forehead is muddy. It is publicly announced that Jennifer does not know whether or not everyone's forehead is muddy. It is publicly announced that Debbie knows whether Debbie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Debbie can now know that Sandy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Archie","Debbie","Sandy","Jennifer"],"index":23434,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8755301833,"difficulty":0.1244698167}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reginald's card is shown to Reginald. Melissa's card is shown to Reginald. Melissa's card is shown to Melissa. Naomi's card is shown to Melissa. Alane's card is shown to Naomi. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Reginald can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alane","Reginald","Melissa","Naomi"],"index":64330,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990133047,"difficulty":0.0009866953}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Melvin. Leo's card is shown to Leo. It is publicly announced that someone picked a red card. It is publicly announced that Leo knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Melvin can now know that Leo can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melvin","Leo"],"index":35229,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994124174,"difficulty":0.0005875826}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Linda knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Mary can now know whether Antonia can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Mary","Antonia"],"index":370,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975050092,"difficulty":0.0024949908}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Derrick. Myles's card is shown to Derrick. Mark's card is shown to Mark. Derrick's card is shown to Myles. It is publicly announced that someone picked a red card. It is publicly announced that Derrick does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know that Myles can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Derrick","Mark","Myles"],"index":4163,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994258881,"difficulty":0.0005741119}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua knows whether or not nobody is thirsty. It is publicly announced that Marc does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Tamara can now know that Joshua can know that Tamara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tamara","Marc","Joshua"],"index":30700,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8632206917,"difficulty":0.1367793083}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nickie does not know whether Richard is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Michael can now know whether Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Nickie","Michael"],"index":6065,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974238873,"difficulty":0.0025761127}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Constance's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Constance can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Barbara","Constance"],"index":17291,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993047714,"difficulty":0.0006952286}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Neal's card is shown to Lisa. Lisa's card is shown to Neal. Lisa's card is shown to Timothy. Neal's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know whether Timothy can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Neal","Timothy"],"index":51757,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992384911,"difficulty":0.0007615089}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Betty is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know whether Betty is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Betty"],"index":2397,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9740346074,"difficulty":0.0259653926}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Rafael can now know that James can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Rafael"],"index":49121,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9733956456,"difficulty":0.0266043544}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tameka's card is shown to Marvin. Marvin's card is shown to Ryan. Tameka's card is shown to Ryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marvin can now know whether Ryan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marvin","Ryan","Tameka"],"index":26910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974666834,"difficulty":0.0025333166}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Brandon can now know that Scott can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Marie","Brandon"],"index":33229,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994321465,"difficulty":0.0005678535}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Ivan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kim can now know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kim","Elizabeth","Ivan","Jennifer"],"index":17506,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7868430614,"difficulty":0.2131569386}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Christie can now know that Antonia can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christie","Antonia","Charles"],"index":2242,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993595481,"difficulty":0.0006404519}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Catherine. Humberto's card is shown to Humberto. Catherine's card is shown to Rosemary. Humberto's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Catherine does not know whether Humberto picked a red card. It is publicly announced that Lawrence knows whether Humberto picked a red card. It is publicly announced that Catherine does not know whether Rosemary picked a red card. It is publicly announced that Humberto knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Rosemary can now know whether Lawrence can know that Catherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Catherine","Humberto","Rosemary","Lawrence"],"index":2856,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9270514846,"difficulty":0.0729485154}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Christine. Shannon's card is shown to Lawrence. Vanessa's card is shown to Vanessa. Lawrence's card is shown to Shannon. Vanessa's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Vanessa does not know whether Lawrence picked a red card. It is publicly announced that Christine knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Shannon can now know that Lawrence can know that Vanessa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Lawrence","Vanessa","Shannon"],"index":35551,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9258621931,"difficulty":0.0741378069}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamal knows whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jamal can now know that Cecelia can know that Cecelia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jamal","Patricia","Shirley","Cecelia"],"index":18770,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982362986,"difficulty":0.0017637014}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Antonia knows whether Yvette is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Antonia can now know whether Antonia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Yvette","Antonia"],"index":36915,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987001419,"difficulty":0.0012998581}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"George can now know that Charlene can know whether George is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Alex","Charlene","Jacqueline"],"index":2868,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9876674414,"difficulty":0.0123325586}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vera is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Daniel can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Gerald","Vera","Russell"],"index":28891,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999545157,"difficulty":0.000454843}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deirdre knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"William can now know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deirdre","Irma","William"],"index":19668,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969009161,"difficulty":0.0030990839}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Cathy. Terri's card is shown to Terri. Cathy's card is shown to Kathleen. Kathleen's card is shown to Kathleen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathleen can now know whether Terri picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cathy","Terri","Kathleen"],"index":26847,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.964158833,"difficulty":0.035841167}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether Sherryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Betty can now know that Sherryl can know that Ralph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sherryl","Betty","Ralph"],"index":27524,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982256293,"difficulty":0.0017743707}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Karen. Richard's card is shown to Karen. Robin's card is shown to Robin. Kareem's card is shown to Robin. Richard's card is shown to Robin. Robin's card is shown to Kareem. Robin's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Kareem knows whether Robin picked a red card. It is publicly announced that Richard does not know whether Karen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Richard can now know that Karen can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Robin","Kareem","Richard"],"index":66983,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994163513,"difficulty":0.0005836487}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hazel knows whether or not nobody's forehead is muddy. It is publicly announced that Erika's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Hazel can now know whether Erika's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sherri","Erika","Hazel"],"index":6112,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994764924,"difficulty":0.0005235076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarissa does not know whether Clarissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Helen can now know that Clarissa can know whether Clarissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brenda","Helen","Melda","Clarissa"],"index":56481,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.979628861,"difficulty":0.020371139}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Frank. Frank's card is shown to Victor. Victor's card is shown to Victor. Frank's card is shown to Rebecca. Rebecca's card is shown to Rebecca. It is publicly announced that someone picked a red card. It is publicly announced that Victor knows whether Frank picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Frank can now know whether Victor can know whether Rebecca picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frank","Victor","Rebecca"],"index":46798,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9988797307,"difficulty":1.9988797307}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori does not know whether Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Diana can now know that Lance can know whether Lance's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tiffany","Diana","Lori","Lance"],"index":8818,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940900207,"difficulty":0.0059099793}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Salvatore","Michael","Leonard"],"index":27456,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9877442718,"difficulty":0.0122557282}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Devin can now know whether David can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Devin","Angela","David"],"index":45911,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992437363,"difficulty":0.0007562637}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jessica can now know that Joyce's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Raymond","Helen","Jessica"],"index":21623,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971681237,"difficulty":0.0028318763}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ilda does not know whether or not everyone is thirsty. It is publicly announced that Jay knows whether someone is thirsty. It is publicly announced that Christopher does not know whether Jay is thirsty. It is publicly announced that Christopher does not know whether Tom is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Ilda can now know that Jay can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jay","Tom","Christopher","Ilda"],"index":58086,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994851351,"difficulty":0.0005148649}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Karen can now know whether Mavis can know whether Mavis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Mavis","Brandon","Karen"],"index":2161,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994138479,"difficulty":0.0005861521}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Paul","John"],"index":33002,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992916584,"difficulty":0.0007083416}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Gerald. James's card is shown to Gerald. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Gerald picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Gerald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gerald","James"],"index":62392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990500808,"difficulty":0.0009499192}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Fred. Fred's card is shown to Brenda. Brenda's card is shown to Brenda. Fred's card is shown to Larisa. Brenda's card is shown to Larisa. Fred's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Brenda picked a black card. It is publicly announced that Brenda does not know whether Robert picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Brenda can now know whether Larisa can know that Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fred","Brenda","Larisa","Robert"],"index":55148,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9379214644,"difficulty":0.0620785356}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anne is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Anne can now know that Joseph can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Anne","Tina"],"index":33209,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980800152,"difficulty":0.0019199848}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christy knows whether Margarita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Richard can now know that Christy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Christy","Richard","Margarita"],"index":40651,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997975409,"difficulty":0.002024591}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dennis can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danny","Corey","Dennis","Walter"],"index":25301,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9607108235,"difficulty":0.0392891765}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether or not nobody's forehead is muddy. It is publicly announced that Evelia does not know whether Evelia's forehead is muddy. It is publicly announced that Evelia does not know whether Evelia's forehead is muddy. It is publicly announced that Evelia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Aaron can now know that Aaron's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Aaron","Martha","Evelia"],"index":31502,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8347405791,"difficulty":0.1652594209}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Louis can now know that Kenneth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Louis","Britni"],"index":30136,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9944831729,"difficulty":0.0055168271}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Georgene's card is shown to Mary. Mary's card is shown to Georgene. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Benito picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Benito can now know that William can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Mary","Benito","Georgene"],"index":42021,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993304014,"difficulty":0.0006695986}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mollie knows whether or not nobody is thirsty. It is publicly announced that Daniel does not know whether Mollie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mollie can now know that Cruz can know that Daniel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Mollie","Cruz"],"index":401,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998263061,"difficulty":0.001736939}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Robert can now know that Allison's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Mark","William","Allison"],"index":33285,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9909732938,"difficulty":0.0090267062}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"George can now know that Bertha is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","George","Javier","Bertha"],"index":41305,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9931541681,"difficulty":0.0068458319}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether or not nobody's forehead is muddy. It is publicly announced that Allan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Walter can now know that Shannon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Walter","Allan","Shannon"],"index":59514,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980136156,"difficulty":0.0019863844}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Bonnie. Carolyn's card is shown to Bonnie. Bonnie's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Terry's card is shown to Carolyn. Carolyn's card is shown to Terry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bonnie can now know whether Carolyn can know whether Bonnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Carolyn","Terry"],"index":6842,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980845451,"difficulty":0.0019154549}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether or not nobody's forehead is muddy. It is publicly announced that Donald's forehead is muddy. It is publicly announced that Donald knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lesley can now know that Donald can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donald","Lesley"],"index":56804,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989853501,"difficulty":0.0010146499}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Rosalie's forehead is muddy. It is publicly announced that Olga knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Olga can now know that Charles can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Olga","Rosalie","Charles"],"index":65470,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989930987,"difficulty":0.0010069013}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward does not know whether or not everyone's forehead is muddy. It is publicly announced that Natalia knows whether Natalia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Natalia can now know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Natalia","Edward"],"index":22449,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8982861042,"difficulty":0.1017138958}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Patrick. Wayne's card is shown to Wayne. It is publicly announced that someone picked a red card. It is publicly announced that Patrick knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Wayne can now know whether Patrick can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patrick","Wayne"],"index":17984,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993970394,"difficulty":0.0006029606}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Millard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Millard can now know that Sheri can know that Son's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sheri","James","Son","Millard"],"index":60410,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977850914,"difficulty":0.0022149086}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Alicia's forehead is muddy. It is publicly announced that Veronica knows whether or not nobody's forehead is muddy. It is publicly announced that Alicia knows whether Veronica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (Agentc knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Alicia can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gary","Veronica","Alicia"],"index":32785,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994671941,"difficulty":0.0005328059}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Donald can now know whether Jessie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Jessie","Donald"],"index":8310,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.795943141,"difficulty":1.795943141}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tonya does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Tonya knows whether someone is thirsty. It is publicly announced that Tonya knows whether Tonya is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Tonya can now know that Carrie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tonya","Carrie"],"index":37237,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994568229,"difficulty":0.0005431771}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] 0","hypothesis":"Vanessa can now know that Thomas can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Vanessa","Thomas"],"index":14276,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988766313,"difficulty":0.0011233687}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Robin. Beatrice's card is shown to Desmond. Beatrice's card is shown to Beatrice. Georgia's card is shown to Beatrice. Desmond's card is shown to Georgia. It is publicly announced that someone picked a red card. It is publicly announced that Desmond knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Georgia can now know that Beatrice can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Desmond","Beatrice","Georgia"],"index":35202,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993917942,"difficulty":0.0006082058}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samuel knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Max can now know whether Max's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Viola","Samuel","Harriet","Max"],"index":60425,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9910645485,"difficulty":0.0089354515}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josefina is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Gordon can now know whether Josefina can know whether Josefina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gordon","Josefina"],"index":4374,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988435507,"difficulty":0.0011564493}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carlos's card is shown to Dale. Carlos's card is shown to Carlos. It is publicly announced that someone picked a red card. It is publicly announced that Dale knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Dale can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dale","Carlos"],"index":29762,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989540577,"difficulty":0.0010459423}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonio's card is shown to Antonio. Antonio's card is shown to William. Anne's card is shown to Anne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Antonio can now know that Anne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Antonio","Werner","William","Anne"],"index":6120,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965482354,"difficulty":0.0034517646}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Lori can now know whether Bret can know whether Bret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Bret","Lori"],"index":17832,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993890524,"difficulty":0.0006109476}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Omar knows whether Mack's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Omar can now know that Omar's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Omar","Mack"],"index":9043,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936182499,"difficulty":0.0063817501}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Wendy can now know that Margaret can know that Wendy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Felicia","Wendy","Melissa","Margaret"],"index":16322,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.850569427,"difficulty":0.149430573}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Mary can now know that Lori can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lori","Mary","Mark"],"index":331,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6916395426,"difficulty":1.6916395426}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Ruby's forehead is muddy. It is publicly announced that Katherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Ruby can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ruby","Travis","Katherine","Linda"],"index":17142,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992651343,"difficulty":0.0007348657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donna can now know whether Thomas can know that Louise's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesus","Donna","Louise","Thomas"],"index":37070,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9776664376,"difficulty":0.0223335624}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Tonya can now know whether Edward can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Janette","Ashley","Tonya"],"index":56497,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993875027,"difficulty":0.0006124973}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Roger can now know that Annette can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Annette","Frances","Roger"],"index":10897,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989186525,"difficulty":0.0010813475}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether Catherine can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Catherine","Flora"],"index":43192,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994545579,"difficulty":0.0005454421}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne knows whether Yvonne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Matthew can now know whether Irene can know whether Yvonne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Irene","Yvonne","Ethel"],"index":67010,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993935823,"difficulty":0.0006064177}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Lorraine can now know whether Alvin can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lorraine","Alvin","Richard"],"index":60964,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993923903,"difficulty":0.0006076097}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Lisa. Carolyn's card is shown to Doris. Carolyn's card is shown to Carolyn. Lisa's card is shown to Anne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doris can now know whether Carolyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Doris","Carolyn","Anne"],"index":21319,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8173213601,"difficulty":1.8173213601}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Enrique does not know whether Enrique's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Debra can now know whether Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Enrique","Debra","Carmella","Patricia"],"index":24305,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9899616241,"difficulty":0.0100383759}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie does not know whether Amber is thirsty. It is publicly announced that William does not know whether Willie is thirsty. It is publicly announced that Willie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Bertha can know that Willie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Bertha","Amber","William"],"index":49219,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9491813779,"difficulty":1.9491813779}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oscar knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Oscar","Robert","Carolyn","Kenneth"],"index":64847,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992724061,"difficulty":0.0007275939}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carolyn. Rita's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carolyn can now know whether Rita can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Rita","Carol"],"index":51301,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991974235,"difficulty":0.0008025765}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Quinton knows whether Christine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Quinton can now know that Debbie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debbie","Eunice","Quinton","Christine"],"index":40786,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982833862,"difficulty":0.0017166138}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darla knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Christine can now know whether Darla is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Christine","Darla"],"index":695,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9870501757,"difficulty":0.0129498243}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty does not know whether Betty's forehead is muddy. It is publicly announced that Betty does not know whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Vanessa can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vanessa","Betty","Heather","Juliann"],"index":4773,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994533658,"difficulty":0.0005466342}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Earline can now know whether Scott is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tonya","Earline","Scott","John"],"index":50146,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6849397421,"difficulty":1.6849397421}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Shirley can now know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daniel","Debra","Shirley","Frank"],"index":65582,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979792237,"difficulty":0.0020207763}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Audrey does not know whether Sheila is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Audrey can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Norman","Audrey","Sheila"],"index":9737,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993713498,"difficulty":0.0006286502}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keely's card is shown to Lucille. Lucille's card is shown to Keely. It is publicly announced that someone picked a red card. It is publicly announced that Keely does not know whether Keely picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lucille can now know whether Keely can know whether Keely picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lucille","Keely"],"index":36769,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9957619309,"difficulty":0.0042380691}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Kenneth's card is shown to Maria. Maria's card is shown to Kenneth. Kelly's card is shown to Kenneth. Maria's card is shown to Kelly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maria","Kenneth","Kelly"],"index":26753,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993299246,"difficulty":0.0006700754}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"James can now know that Jason can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jason","Mark","John","James"],"index":9357,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988827109,"difficulty":0.0011172891}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monte does not know whether or not everyone's forehead is muddy. It is publicly announced that Monte's forehead is muddy. It is publicly announced that Monte knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Donald can now know that Monte can know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Monte","Donald"],"index":20771,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7709727883,"difficulty":0.2290272117}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Reba's card is shown to Joseph. Joseph's card is shown to Joyce. Joyce's card is shown to Reba. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joyce can now know that Joseph can know whether Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Joyce","Reba"],"index":24695,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.716406405,"difficulty":0.283593595}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Richard can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","James","Russell"],"index":47762,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993494153,"difficulty":0.0006505847}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Christopher can now know that Tracy can know that Tracy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tracy","Paul","Christopher"],"index":20496,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.6718227267,"difficulty":0.3281772733}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Maria. Samantha's card is shown to Ruth. Robin's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Ruth picked a red card. It is publicly announced that Robin picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(4) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(4) ] 0","hypothesis":"Samantha can now know that Robin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Samantha","Maria","Ruth","Robin"],"index":51167,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8380479813,"difficulty":0.1619520187}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margarita knows whether Margarita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Margarita can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Margarita","Debbie"],"index":22137,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993546605,"difficulty":0.0006453395}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jo knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"James can now know whether Jo can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jo","James"],"index":37222,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993230104,"difficulty":0.0006769896}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Larry. Yvonne's card is shown to Vernon. Larry's card is shown to Graham. Graham's card is shown to Graham. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vernon can now know that Graham picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Vernon","Graham","Yvonne"],"index":23346,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996437788,"difficulty":0.003562212}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie is thirsty. It is publicly announced that Karen knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Gwendolyn can now know whether Julie can know whether Gwendolyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Martin","Julie","Gwendolyn"],"index":65798,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989852309,"difficulty":0.0010147691}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jonas does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jason can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jason","Jonas","Jeffrey","Jeffery"],"index":47423,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994827509,"difficulty":0.0005172491}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Susan can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Juanita","Robert"],"index":66859,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5012505054,"difficulty":1.5012505054}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Alan's card is shown to Barbara. Christopher's card is shown to Alan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Christopher can know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Christopher","Alan"],"index":51351,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973517656,"difficulty":0.0026482344}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nellie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Adam can now know whether Nellie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julie","Nellie","Adam"],"index":14503,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987580776,"difficulty":0.0012419224}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jonnie does not know whether or not everyone is thirsty. It is publicly announced that Margaret does not know whether or not everyone is thirsty. It is publicly announced that Jermaine knows whether Jermaine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Germaine can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Germaine","Jermaine","Margaret","Jonnie"],"index":41768,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9566866159,"difficulty":0.0433133841}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ellen can now know whether Miguel can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elton","Miguel","Willie","Ellen"],"index":11102,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993445277,"difficulty":0.0006554723}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know whether Ursula can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Ursula","Jean","Lisa"],"index":38900,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992995262,"difficulty":0.0007004738}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara knows whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bethany can now know that Shirley can know that Shirley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bethany","Barbara","Shirley"],"index":50590,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9839305282,"difficulty":0.0160694718}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Robert can now know that Luann can know whether Luann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Anthony","Luann"],"index":13714,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993650317,"difficulty":0.0006349683}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eleanor's card is shown to George. Eleanor's card is shown to Carl. Wanda's card is shown to Carl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know that Eleanor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eleanor","George","Carl","Wanda"],"index":56139,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968955517,"difficulty":0.0031044483}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alfred's card is shown to Alfred. Alfred's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Jason can now know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alfred","Jason"],"index":33984,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5581549406,"difficulty":0.4418450594}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether Maria's forehead is muddy. It is publicly announced that Travis knows whether Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Travis can now know whether Maria can know whether Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Maria","Travis"],"index":28831,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994240999,"difficulty":0.0005759001}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Richard. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Richard can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Richard","Donald"],"index":46419,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9865002036,"difficulty":0.0134997964}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether or not everyone is thirsty. It is publicly announced that Sean knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Sean can now know whether Justine can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Lora","Justine","Sean"],"index":40798,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994667172,"difficulty":0.0005332828}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Andrew can now know whether Patricia can know whether Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","John","Patricia","Andrew"],"index":28746,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994466901,"difficulty":0.0005533099}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether Ryan's forehead is muddy. It is publicly announced that Nadia's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Joe can now know whether Ryan can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joe","Ryan","Nadia"],"index":50210,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994582534,"difficulty":0.0005417466}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene does not know whether Eugene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Delores can now know that Yesenia can know whether Delores's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alex","Yesenia","Delores","Eugene"],"index":55308,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9975643158,"difficulty":0.0024356842}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henrietta's card is shown to Anna. Henrietta's card is shown to Kenneth. Anna's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Anna knows whether Henrietta picked a red card. It is publicly announced that Anna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Henrietta can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Henrietta","Anna","Kenneth"],"index":43982,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990025163,"difficulty":0.0009974837}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Otis knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Pauline can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Otis","Kurt","Pauline"],"index":32639,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994488358,"difficulty":0.0005511642}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra does not know whether Deborah is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sandra can now know that Brian is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Deborah","Sandra","Brian"],"index":4224,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998331964,"difficulty":0.001668036}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Valerie can now know that Douglas can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Douglas","Valerie"],"index":12360,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989979863,"difficulty":0.0010020137}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilfred's forehead is not muddy. It is publicly announced that Clayton knows whether Wilfred's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Stella can now know that Clayton can know that Clayton's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wilfred","Clayton","Stella"],"index":54103,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973496199,"difficulty":0.0026503801}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"William can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gary","Bobbie","William","Gwendolyn"],"index":38324,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989634752,"difficulty":0.0010365248}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tammy's card is shown to Betsy. Heather's card is shown to Betsy. Tammy's card is shown to Tammy. Heather's card is shown to Tammy. Betsy's card is shown to Mary. Mary's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Betsy can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betsy","Tammy","Mary","Heather"],"index":14235,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991868138,"difficulty":0.0008131862}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Derek. Douglas's card is shown to Samantha. Samantha's card is shown to Samantha. Derek's card is shown to Brenna. It is publicly announced that someone picked a red card. It is publicly announced that Samantha picked a black card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Derek","Douglas","Samantha","Brenna"],"index":10802,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6861740947,"difficulty":0.3138259053}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessica knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jessica can now know whether Michele can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Charles","Michele"],"index":36848,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994900227,"difficulty":0.0005099773}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Faye does not know whether Faye's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jason can now know that Faye can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Jason","Faye"],"index":55749,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9868936539,"difficulty":0.0131063461}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Donald can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Donald","Mary","Alma"],"index":36498,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988899827,"difficulty":0.0011100173}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether Maxie's forehead is muddy. It is publicly announced that Shirley knows whether Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Shirley can now know that Maxie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maxie","David","Robert","Shirley"],"index":20584,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989222288,"difficulty":0.0010777712}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geneva's card is shown to Betty. Betty's card is shown to Geneva. Geneva's card is shown to Geneva. Betty's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether Betty picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Betty can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Geneva","Jennifer"],"index":29000,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9911541939,"difficulty":0.0088458061}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Penny knows whether Roosevelt's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Penny can now know whether Roosevelt can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Penny","Mary","Roosevelt","Jeff"],"index":42663,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.809691608,"difficulty":0.190308392}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether Sandra's forehead is muddy. It is publicly announced that Sandra knows whether Sandra's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know that John can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Janice","Sandra","Dan"],"index":37805,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Joyce can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joyce","Sharon","Michael"],"index":19651,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986844659,"difficulty":0.0013155341}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Alice. Alice's card is shown to Evelyn. Evelyn's card is shown to Eric. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alice can now know that Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alice","Evelyn","Eric"],"index":62149,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932444692,"difficulty":0.0067555308}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynn does not know whether Bradley is thirsty. It is publicly announced that James does not know whether Lynn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"James can now know whether Jo can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lynn","Jo","Bradley","James"],"index":22000,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993706346,"difficulty":0.0006293654}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Lillian can now know that Deborah can know that Kellie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lillian","Deborah","Kellie"],"index":40688,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.990506351,"difficulty":0.009493649}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether or not everyone's forehead is muddy. It is publicly announced that Paul knows whether or not nobody's forehead is muddy. It is publicly announced that Heidi knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Heidi can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Paul","Heidi"],"index":65593,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988747239,"difficulty":0.0011252761}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darryl does not know whether Larry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Larry can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rene","Jeffrey","Darryl","Larry"],"index":19327,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994601607,"difficulty":0.0005398393}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Domenic knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Hilton can now know that Domenic can know whether Hilton is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hilton","Domenic"],"index":8274,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6240416765,"difficulty":1.6240416765}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Claudia's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Claudia can now know that Krista can know that Krista's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Claudia","Krista"],"index":61208,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9982119799,"difficulty":1.9982119799}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille knows whether or not nobody's forehead is muddy. It is publicly announced that Lucille knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Marcia can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marcia","James","Paul","Lucille"],"index":29069,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990320206,"difficulty":0.0009679794}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Karen knows whether Karen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Karen can now know whether Juana can know whether Karen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Juana","Mildred","Karen"],"index":40850,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989193678,"difficulty":0.0010806322}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jon can now know that Stephanie can know that Jon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jon","William","Stephanie"],"index":57453,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996643424,"difficulty":0.003356576}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geraldine's card is shown to Geraldine. Mary's card is shown to Geraldine. Geraldine's card is shown to Mary. Mary's card is shown to Mary. David's card is shown to Mary. Mary's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Geraldine","Mary","David"],"index":24343,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993997812,"difficulty":0.0006002188}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Herman knows whether Herman is thirsty. It is publicly announced that Tina knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Herman can now know that Tina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tina","Herman"],"index":21781,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9439637065,"difficulty":0.0560362935}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellen knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Ellen can now know whether Ashley can know whether Marion is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marion","Ellen","Ashley"],"index":30223,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991256595,"difficulty":0.0008743405}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"John can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Jesus","Anna"],"index":12857,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992884398,"difficulty":0.0007115602}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that Shirley does not know whether Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Shirley can now know whether David can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Shirley","Dale"],"index":31467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9692935944,"difficulty":0.0307064056}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Michael knows whether Michael is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Julian can now know whether Michael can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Julian","Michael"],"index":66024,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994425178,"difficulty":0.0005574822}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Maribel. Patricia's card is shown to Laura. Maribel's card is shown to Patricia. Maribel's card is shown to Tobias. Laura's card is shown to Tobias. Patricia's card is shown to Tobias. It is publicly announced that someone picked a red card. It is publicly announced that Tobias knows whether Laura picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Laura can now know whether Tobias can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maribel","Laura","Patricia","Tobias"],"index":19510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5538856387,"difficulty":0.4461143613}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether Gary's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gary can now know that Gary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Denise","Karen","Gary"],"index":63832,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9484754205,"difficulty":0.0515245795}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Chris","Dwain"],"index":10351,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.995875299,"difficulty":0.004124701}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jean does not know whether Roger is thirsty. It is publicly announced that Roger is not thirsty. It is publicly announced that Roger does not know whether Jean is thirsty. It is publicly announced that Jean knows whether Roger is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Roger can now know whether Jean can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jean","Roger","Madeline"],"index":20656,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993339181,"difficulty":0.0006660819}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Kimberly. Johnnie's card is shown to Johnnie. It is publicly announced that someone picked a red card. It is publicly announced that Johnnie does not know whether Kimberly picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kimberly can now know whether Johnnie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kimberly","Johnnie"],"index":31707,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9520741105,"difficulty":1.9520741105}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobby's card is shown to Bobby. Bobby's card is shown to Alfred. Alfred's card is shown to Alfred. Alfred's card is shown to Dawn. Hazel's card is shown to Dawn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alfred can now know that Hazel can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bobby","Alfred","Hazel","Dawn"],"index":59273,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988133907,"difficulty":0.0011866093}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alton's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Mary can now know whether Alton can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shelby","Mary","Alton"],"index":50952,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999435246,"difficulty":0.000564754}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Marvin. Jae's card is shown to Kathleen. Kathleen's card is shown to Jae. Jae's card is shown to Jae. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathleen can now know whether Jae can know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marvin","Kathleen","Jae"],"index":37601,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6700843573,"difficulty":1.6700843573}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether Amber's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Amber can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amber","Laura","George","Chrystal"],"index":15797,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990670085,"difficulty":0.0009329915}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kerri can now know that Joan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Keven","Jerome","Kerri","Joan"],"index":32193,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9911417961,"difficulty":0.0088582039}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Augusta does not know whether Augusta's forehead is muddy. It is publicly announced that Rene's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Augusta can now know whether Rene can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Augusta","Rene"],"index":52636,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9854297638,"difficulty":1.9854297638}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melvin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Melvin can now know that Joel can know that Joel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joel","Melvin","Daniel"],"index":31815,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998070538,"difficulty":0.001929462}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patrick is thirsty. It is publicly announced that Eddie knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Eddie can now know whether Alexandra can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alexandra","Eddie","Patrick"],"index":19334,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9962406158,"difficulty":0.0037593842}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Darrell can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","James","Darrell","William"],"index":31332,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976392984,"difficulty":0.0023607016}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Kimberly can now know whether Kyle can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","Jong","Kyle"],"index":8685,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9899508357,"difficulty":0.0100491643}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Jimmie's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Jerry can now know that Jimmie can know that Jimmie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jimmie","Jerry","Melvin","Christopher"],"index":33408,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968981743,"difficulty":0.0031018257}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodora's card is shown to Lucille. Lucille's card is shown to Theodora. It is publicly announced that someone picked a red card. It is publicly announced that Lucille does not know whether Susan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Susan can now know that Theodora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lucille","Susan","Theodora"],"index":2184,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971290231,"difficulty":0.0028709769}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether or not nobody's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentd knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Mark can now know that Rebecca can know whether Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christine","Thomas","Rebecca","Mark"],"index":17179,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994282126,"difficulty":0.0005717874}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Homer's card is shown to Kelley. Homer's card is shown to Homer. John's card is shown to John. Homer's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Linda can know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelley","Homer","John","Linda"],"index":42753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8450784683,"difficulty":0.1549215317}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sonya knows whether Sonya's forehead is muddy. It is publicly announced that Sarah knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Sarah can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Delora","Sonya","Sarah"],"index":18076,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9964706898,"difficulty":0.0035293102}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Sarah. Jane's card is shown to Jane. John's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Sarah does not know whether Jane picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Sarah can now know whether Jane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Jane","John"],"index":63131,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9358451366,"difficulty":1.9358451366}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elisa's card is shown to Ellen. Elisa's card is shown to Perry. Jennifer's card is shown to Elisa. Ellen's card is shown to Jennifer. Elisa's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Perry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Ellen can now know that Perry can know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ellen","Perry","Elisa","Jennifer"],"index":31539,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5250677466,"difficulty":0.4749322534}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa does not know whether Theresa's forehead is muddy. It is publicly announced that Daniel knows whether or not everyone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Daniel can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Theresa","Daniel"],"index":51602,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990642667,"difficulty":0.0009357333}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Cynthia. Gina's card is shown to Gina. Mattie's card is shown to Frances. Cynthia's card is shown to Frances. Gina's card is shown to Frances. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mattie can now know that Cynthia can know that Frances picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mattie","Cynthia","Gina","Frances"],"index":33308,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982476234,"difficulty":0.0017523766}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Daniel. Daniel's card is shown to Lora. Daniel's card is shown to Anne. It is publicly announced that someone picked a red card. It is publicly announced that Lora does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know that Anne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","Lora","Anne"],"index":1642,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8055976629,"difficulty":0.1944023371}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia does not know whether Josefa is thirsty. It is publicly announced that Josefa is not thirsty. It is publicly announced that Josefa does not know whether Virginia is thirsty. It is publicly announced that Virginia knows whether Josefa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Virginia can now know that Minh can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Virginia","Josefa","Minh"],"index":64303,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.939219296,"difficulty":1.939219296}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Andrea's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Angela can now know that Sharon can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Sharon","Andrea","Angela"],"index":20576,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993920326,"difficulty":0.0006079674}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know that Carl is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Nancy","Cindy","Carl"],"index":41120,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.959954679,"difficulty":0.040045321}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Stan can now know whether Mary can know whether Christi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christi","Stan","Mary"],"index":52805,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990781546,"difficulty":0.0009218454}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know whether Bruce can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bruce","Erica","Elizabeth","Arthur"],"index":37089,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991680384,"difficulty":0.0008319616}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jean knows whether Jean is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jean can now know whether Edward can know that Melissa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jean","Melissa","Edward"],"index":14117,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.995216608,"difficulty":0.004783392}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billy's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Billy can now know that Bessie can know that Billy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bessie","Billy"],"index":53308,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970881343,"difficulty":0.0029118657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy is thirsty. It is publicly announced that Leon does not know whether or not everyone is thirsty. It is publicly announced that Leon does not know whether Maryanna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Leon can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Courtney","Maryanna","Amy","Leon"],"index":4283,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986525774,"difficulty":0.0013474226}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leona does not know whether Leona's forehead is muddy. It is publicly announced that Horace's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Horace can now know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leona","Charles","Richard","Horace"],"index":2694,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983147383,"difficulty":0.0016852617}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn knows whether or not everyone's forehead is muddy. It is publicly announced that Shawn knows whether Shawn's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ronald can now know that Shawn can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ronald","Shawn"],"index":61447,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980182648,"difficulty":0.0019817352}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether or not everyone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know that Donna can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bobbie","Angela","Donna","David"],"index":9412,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998996675,"difficulty":0.001003325}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether Clemmie is thirsty. It is publicly announced that Elizabeth knows whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Clemmie can now know whether George can know whether Bernard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Clemmie","Bernard","Elizabeth"],"index":24004,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992421865,"difficulty":0.0007578135}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrea knows whether or not nobody's forehead is muddy. It is publicly announced that Andrea does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Andrea can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marie","Andrea"],"index":42427,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970507622,"difficulty":0.0029492378}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allan knows whether someone's forehead is muddy. It is publicly announced that Allan knows whether Justin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentd knows that (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Allan can now know that Thomas can know that Allan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Justin","Cornell","Allan"],"index":47548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982529283,"difficulty":0.0017470717}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Stephen can now know that Betty can know that Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephen","Andrew","Betty"],"index":42796,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976871014,"difficulty":0.0023128986}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that Charles can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Carolyn","Dee","Charles"],"index":66051,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994600415,"difficulty":0.0005399585}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felicita does not know whether Felicita's forehead is muddy. It is publicly announced that Felicita does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Felicita can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Felicita"],"index":58980,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994212389,"difficulty":0.0005787611}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mercedes can now know that Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mercedes","Samantha","Jean"],"index":61975,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7376451492,"difficulty":1.7376451492}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan knows whether or not nobody's forehead is muddy. It is publicly announced that Josefina's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentd knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Margaret can now know that Jonathan can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charlotte","Josefina","Jonathan","Margaret"],"index":63875,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993078709,"difficulty":0.0006921291}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Philip is thirsty. It is publicly announced that James does not know whether Philip is thirsty. It is publicly announced that James does not know whether Philip is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Philip can now know whether Philip is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Philip"],"index":35503,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9968841672,"difficulty":0.0031158328}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louise does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Suzette can now know whether Kimberly is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Louise","Kimberly","Sherri","Suzette"],"index":53969,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9889380932,"difficulty":0.0110619068}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joyce does not know whether or not everyone is thirsty. It is publicly announced that Joyce does not know whether James is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Joyce can now know whether James can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joyce","James"],"index":28295,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.935824573,"difficulty":1.935824573}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joe's card is shown to Joe. Joe's card is shown to Charles. Joe's card is shown to Anthony. Charles's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether Anthony picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Anthony can now know whether Charles can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Charles","Anthony","Michael"],"index":52824,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5101395249,"difficulty":1.5101395249}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Bryan can now know that Tom can know that Tom's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bryan","Roger","Robert","Tom"],"index":54739,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980231524,"difficulty":0.0019768476}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Sue does not know whether Sue's forehead is muddy. It is publicly announced that Craig knows whether Sue's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jessica can now know that Jessica's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sue","Craig","Jessica","Daniel"],"index":52208,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965177774,"difficulty":0.0034822226}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmelita knows whether someone's forehead is muddy. It is publicly announced that Carmelita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] 0","hypothesis":"Carmelita can now know that Carmelita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carmelita","Lynda","Dennis"],"index":27395,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6057904959,"difficulty":0.3942095041}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Marie. Mark's card is shown to Diane. Marie's card is shown to Mark. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marie","Diane","Mark"],"index":7223,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994501472,"difficulty":0.0005498528}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joann knows whether Dorthy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Dorthy can now know that Courtney's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorthy","Joann","Courtney"],"index":11252,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977686405,"difficulty":0.0022313595}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlotte's forehead is muddy. It is publicly announced that Shannon knows whether Charlotte's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Shannon can now know whether Shirley can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Brenda","Charlotte","Shannon"],"index":34588,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993404746,"difficulty":0.0006595254}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tonya's card is shown to Janet. Jill's card is shown to Jill. Tonya's card is shown to Jill. Tonya's card is shown to Tonya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jill can now know that Janet can know whether Tonya picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janet","Jill","Tonya"],"index":19456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6526976824,"difficulty":0.3473023176}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia knows whether Hector is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Hector can now know whether Virginia can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hector","Virginia"],"index":19926,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994667172,"difficulty":0.0005332828}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marie can now know that William can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brandy","Marie","William"],"index":59567,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989880919,"difficulty":0.0010119081}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cynthia does not know whether or not everyone is thirsty. It is publicly announced that Sharon knows whether Cynthia is thirsty. It is publicly announced that Hugo does not know whether Sharon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Hugo can now know that Cynthia can know whether Hugo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Cynthia","Hugo"],"index":4665,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7870304585,"difficulty":0.2129695415}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"John can now know whether Diana can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Todd","John","Robert","Diana"],"index":12190,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993695617,"difficulty":0.0006304383}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Charles can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Charles","Summer","Edward"],"index":47599,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9784503579,"difficulty":0.0215496421}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patti knows whether or not nobody's forehead is muddy. It is publicly announced that Lucile's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Lucile can now know whether Lucile's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edward","Lucile","Patti"],"index":5030,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994632602,"difficulty":0.0005367398}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin does not know whether Erin's forehead is muddy. It is publicly announced that Harold knows whether someone's forehead is muddy. It is publicly announced that Harold knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Harold can now know whether Maria can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Erin","Harold","Maria"],"index":66184,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5093148351,"difficulty":0.4906851649}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernice's card is shown to Wilson. William's card is shown to Wilson. Wilson's card is shown to Bernice. Wilson's card is shown to William. Bernice's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Bernice does not know whether Bernice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wilson","Bernice","William","Dorothy"],"index":8766,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944403768,"difficulty":0.0055596232}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Shawna. Angela's card is shown to Jeffrey. Louis's card is shown to Angela. Jeffrey's card is shown to Angela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shawna can now know that Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shawna","Louis","Jeffrey","Angela"],"index":58990,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953477979,"difficulty":0.0046522021}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Lawrence. Joyce's card is shown to Lawrence. Tom's card is shown to Matthew. Matthew's card is shown to Matthew. Joyce's card is shown to Matthew. Lawrence's card is shown to Joyce. Tom's card is shown to Joyce. Joyce's card is shown to Joyce. It is publicly announced that someone picked a red card. It is publicly announced that Matthew picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3,4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Matthew can now know whether Tom can know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Tom","Matthew","Joyce"],"index":56358,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9577063918,"difficulty":0.0422936082}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynn does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Lynn can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Caleb","Robyn","Lynn"],"index":49410,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995123148,"difficulty":0.0004876852}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Sandra can now know that Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Clayton","Sandra","Thomas"],"index":5686,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982328415,"difficulty":0.0017671585}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Anna can now know that Joe can know that Harry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joe","Anna","Harry"],"index":44555,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970427155,"difficulty":0.0029572845}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Rosa is thirsty. It is publicly announced that Thomas does not know whether Rosa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"John can now know that Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Thomas","Rosa","June"],"index":48173,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969472289,"difficulty":0.0030527711}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Courtney's card is shown to Neal. Neal's card is shown to Courtney. It is publicly announced that someone picked a red card. It is publicly announced that Courtney does not know whether or not everyone picked a red card. It is publicly announced that Neal knows whether Neal picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Courtney can now know that Neal can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Neal","Courtney"],"index":30016,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971336126,"difficulty":0.0028663874}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"John can now know that Ann can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vicky","Eleonore","Ann","John"],"index":16801,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993122816,"difficulty":0.0006877184}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Julie. Ana's card is shown to Julie. Kim's card is shown to Kim. Julie's card is shown to Jesus. Ana's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Julie does not know whether or not everyone picked a red card. It is publicly announced that Ana does not know whether Jesus picked a red card. It is publicly announced that Ana does not know whether Jesus picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Julie can now know that Ana can know whether Jesus picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Kim","Ana","Jesus"],"index":48812,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9001788497,"difficulty":1.9001788497}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francisco's card is shown to John. Francisco's card is shown to Stephani. Jane's card is shown to Stephani. Jane's card is shown to Francisco. John's card is shown to Jane. Stephani's card is shown to Jane. Francisco's card is shown to Jane. Jane's card is shown to Jane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Stephani","Francisco","Jane"],"index":50990,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993959665,"difficulty":0.0006040335}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia does not know whether or not everyone's forehead is muddy. It is publicly announced that Kari knows whether Virginia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Calvin can now know whether Virginia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kari","Melanie","Calvin","Virginia"],"index":11084,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9713518023,"difficulty":0.0286481977}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Rodolfo's card is shown to William. William's card is shown to Roy. Roy's card is shown to Roy. Roy's card is shown to Timothy. Roy's card is shown to Rodolfo. Timothy's card is shown to Rodolfo. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Timothy can now know whether Rodolfo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Roy","Timothy","Rodolfo"],"index":17600,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9835631847,"difficulty":1.9835631847}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Leona can now know that John can know that Leona's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Leona","Kenneth"],"index":38176,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967933297,"difficulty":0.0032066703}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melody can now know whether Bonnie can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Nancy","Melody","Bonnie"],"index":45491,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991443157,"difficulty":0.0008556843}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gayle does not know whether or not everyone is thirsty. It is publicly announced that Gayle does not know whether Amy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gayle can now know whether Amy can know that Gayle is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gayle","Amy"],"index":46324,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9233554006,"difficulty":0.0766445994}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Warren is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Theresa can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Theresa","Robert","Warren"],"index":20102,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995085001,"difficulty":0.0004914999}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Lucy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"John can now know that Felicitas can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Felicitas","Lucy","John"],"index":14833,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989688396,"difficulty":0.0010311604}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Gail's forehead is muddy. It is publicly announced that Pauline knows whether Pauline's forehead is muddy. It is publicly announced that Pauline's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Pauline can now know that Thomas can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pauline","Anthony","Thomas","Gail"],"index":22926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985566735,"difficulty":0.0014433265}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Joyce can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joshua","Eric","Joyce"],"index":19486,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983990788,"difficulty":0.0016009212}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"William can now know that Gina can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Gina","Bessie","William"],"index":64984,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988546371,"difficulty":0.0011453629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether or not everyone's forehead is muddy. It is publicly announced that Patrick does not know whether Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Henry can now know that Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shawnna","Henry","David","Patrick"],"index":54157,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9464635849,"difficulty":0.0535364151}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Dorian. Nick's card is shown to Dorian. Kevin's card is shown to Kevin. Nick's card is shown to Kevin. Dorian's card is shown to Josie. Josie's card is shown to Nick. Nick's card is shown to Nick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Josie can now know whether Nick can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorian","Kevin","Josie","Nick"],"index":21297,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993915558,"difficulty":0.0006084442}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Thomas is thirsty. It is publicly announced that Alice does not know whether Thomas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Alice can now know that Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Crista","John","Alice"],"index":38870,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9929686189,"difficulty":0.0070313811}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Nicholas. Thomas's card is shown to Nicholas. It is publicly announced that someone picked a red card. It is publicly announced that Nicholas does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Nicholas can now know that Nicholas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nicholas","Wanda","Thomas"],"index":2293,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7230338454,"difficulty":0.2769661546}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cordell's card is shown to Cordell. David's card is shown to David. Cordell's card is shown to Michelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know that Michelle can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cordell","David","Michelle"],"index":59910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947249293,"difficulty":0.0052750707}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. Katie's card is shown to David. Katie's card is shown to Katie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","James","Katie"],"index":26445,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990180731,"difficulty":0.0009819269}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Apolonia is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Apolonia can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Fred","Apolonia","Earl"],"index":9101,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989848733,"difficulty":0.0010151267}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carla does not know whether Carla's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Carla can now know whether John can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Jeffrey","Carla"],"index":13698,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9652853012,"difficulty":0.0347146988}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerry knows whether or not nobody's forehead is muddy. It is publicly announced that Tommie's forehead is muddy. It is publicly announced that Carmen does not know whether or not everyone's forehead is muddy. It is publicly announced that Carmen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agenta knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Carmen can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carmen","Kerry","Tommie","Howard"],"index":1503,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994812608,"difficulty":0.0005187392}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fannie knows whether Fannie is thirsty. It is publicly announced that Louis does not know whether Fannie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Richard can now know whether Fannie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Fannie","Richard","Louis"],"index":23626,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7593559027,"difficulty":1.7593559027}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Yong can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Yong","Robert"],"index":59682,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994128942,"difficulty":0.0005871058}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Raymond can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Robert","Edith","Raymond"],"index":45744,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989572763,"difficulty":0.0010427237}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know that Monica can know whether Monica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Paul","Edward","Monica"],"index":55190,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9606811404,"difficulty":0.0393188596}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martin's card is shown to Martin. Bennett's card is shown to Martin. Luis's card is shown to Martin. Luis's card is shown to Bennett. Luis's card is shown to Luis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Luis can now know that Bennett can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martin","Bennett","Luis"],"index":53910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993878603,"difficulty":0.0006121397}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Melissa's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"David can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Melissa","David"],"index":30407,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7819077373,"difficulty":0.2180922627}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elsa does not know whether Audrey is thirsty. It is publicly announced that Juanita does not know whether Audrey is thirsty. It is publicly announced that Elsa is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(1) ] (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Roland can now know whether Audrey is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elsa","Roland","Juanita","Audrey"],"index":58563,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961333275,"difficulty":0.0038666725}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dora's card is shown to Regina. John's card is shown to John. Andy's card is shown to John. Andy's card is shown to Andy. Dora's card is shown to Andy. It is publicly announced that someone picked a red card. It is publicly announced that Andy picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Andy can now know whether Andy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Regina","John","Andy","Dora"],"index":31927,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.978679359,"difficulty":0.021320641}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Gloria can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gloria","Gary"],"index":17789,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995136261,"difficulty":0.0004863739}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antonia knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Evelyn can now know that Antonia can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Antonia","John","Evelyn"],"index":10617,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993906021,"difficulty":0.0006093979}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Houston can now know whether Houston's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steven","Houston","Fred"],"index":47705,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8069528341,"difficulty":0.1930471659}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mildred does not know whether Mike is thirsty. It is publicly announced that Mike does not know whether Jessie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jessie can now know that Mildred can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mildred","Jessie","Mike"],"index":61962,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993931055,"difficulty":0.0006068945}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is muddy. It is publicly announced that Deborah's forehead is not muddy. It is publicly announced that Brian knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Deborah can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Tonya","Deborah"],"index":66843,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990311861,"difficulty":0.0009688139}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Vernon knows whether Wilbert's forehead is muddy. It is publicly announced that Vernon knows whether someone's forehead is muddy. It is publicly announced that Vernon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Lee can now know that Vernon can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melinda","Vernon","Lee","Wilbert"],"index":39918,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994567037,"difficulty":0.0005432963}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mildred does not know whether Jason is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Gloria can now know that Kent can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Gloria","Kent","Mildred"],"index":6576,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999335587,"difficulty":0.000664413}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. James's card is shown to Brenda. Brenda's card is shown to Louis. Louis's card is shown to Delbert. Delbert's card is shown to Delbert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Brenda","Louis","Delbert"],"index":28597,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9876616001,"difficulty":0.0123383999}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Patty knows whether Patty's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Audrey can now know whether Patty can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Audrey","Patty","George"],"index":61724,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994064569,"difficulty":0.0005935431}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Janice can now know that Julie can know that Janice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steve","Janice","Julie"],"index":41345,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976231456,"difficulty":0.0023768544}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank does not know whether Sergio is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentd knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Lisa can now know that Sergio can know whether Frank is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sergio","James","Frank","Lisa"],"index":14310,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970107079,"difficulty":0.0029892921}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Billie can now know that Kirby can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kirby","Roberto","Billie"],"index":45077,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987251163,"difficulty":0.0012748837}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela's forehead is muddy. It is publicly announced that Irene knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Irene can now know whether Dawn can know whether Irene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kristi","Dawn","Angela","Irene"],"index":40773,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994370341,"difficulty":0.0005629659}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Faith knows whether someone is thirsty. It is publicly announced that Faith does not know whether Bill is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Faith can now know whether Bill can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bill","Faith"],"index":46625,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999209106,"difficulty":0.000790894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jared does not know whether Jared's forehead is muddy. It is publicly announced that Jean knows whether Steven's forehead is muddy. It is publicly announced that Jared does not know whether Jared's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Jean can know that Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jared","Jean","Michael","Steven"],"index":27970,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99037081,"difficulty":0.00962919}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Franklin's card is shown to Henry. Henry's card is shown to Franklin. Franklin's card is shown to Franklin. Franklin's card is shown to Roger. Roger's card is shown to Roger. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Roger can now know whether Henry can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Henry","Franklin","Roger"],"index":65774,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994169474,"difficulty":0.0005830526}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is muddy. It is publicly announced that Ismael knows whether someone's forehead is muddy. It is publicly announced that Ismael knows whether Erin's forehead is muddy. It is publicly announced that Ismael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ismael can now know that Erin can know that Erin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Erin","Ismael"],"index":49222,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9858215451,"difficulty":0.0141784549}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Kathryn. William's card is shown to Kathryn. Robert's card is shown to Robert. Kathryn's card is shown to William. William's card is shown to William. William's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kathryn can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathryn","Robert","William","Anthony"],"index":59197,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968473315,"difficulty":0.0031526685}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Harris. Amy's card is shown to Lazaro. Lazaro's card is shown to Lazaro. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Harris can now know that Amy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amy","Harris","Lazaro"],"index":1669,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988449812,"difficulty":0.0011550188}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Taylor can now know that Dan can know that Dan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dan","Evelyn","Taylor","Mable"],"index":52622,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966521859,"difficulty":0.0033478141}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jack knows whether Blanca is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jack can now know whether Blanca can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Blanca","Jack"],"index":53555,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994725585,"difficulty":0.0005274415}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Charles can now know whether Billy can know whether Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Kenneth","Billy"],"index":24074,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994576573,"difficulty":0.0005423427}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Samuel can now know that Jennifer can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carol","Samuel","Jennifer"],"index":19594,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992911816,"difficulty":0.0007088184}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Augustine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Mary can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mike","Debbie","Mary","Augustine"],"index":2541,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993502498,"difficulty":0.0006497502}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Steven's forehead is muddy. It is publicly announced that Todd's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Steven can now know that Todd can know whether Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Todd"],"index":17277,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994651675,"difficulty":0.0005348325}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jarrod is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Aaron can now know that Jarrod can know that Jarrod is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Aaron","Erika","Jarrod"],"index":45142,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9672864676,"difficulty":0.0327135324}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Leslie can now know that Willie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willie","Mary","Sheila","Leslie"],"index":41775,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978105426,"difficulty":0.0021894574}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Crystal's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Bobby knows whether Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Bobby can now know whether Nancy can know whether Bobby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Crystal","Bobby","Nancy","Mary"],"index":24940,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9868191481,"difficulty":0.0131808519}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cruz can now know that Phillip can know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cruz","Judy","Phillip","Barbara"],"index":12897,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978321195,"difficulty":0.0021678805}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dexter can now know whether Andrea can know whether Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jenifer","Andrea","Dexter","Thomas"],"index":8146,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993898869,"difficulty":0.0006101131}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Stephen can now know that Alexandra can know whether Alexandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephen","Alexandra","William"],"index":1509,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993323684,"difficulty":0.0006676316}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Kathy is thirsty. It is publicly announced that Eileen does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Eileen can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Enoch","Eileen","Kathy"],"index":58522,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987645149,"difficulty":0.0012354851}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristi knows whether Natalie's forehead is muddy. It is publicly announced that Kristi's forehead is not muddy. It is publicly announced that Stacy knows whether Kristi's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Natalie can now know that Natalie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristi","Natalie","Stacy"],"index":6579,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9949002862,"difficulty":0.0050997138}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"James can now know that Gloria can know whether Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Gloria","James"],"index":38914,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994553924,"difficulty":0.0005446076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Richard can now know that Mary can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Margery","Mary","Kimberly"],"index":44528,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994772077,"difficulty":0.0005227923}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Scott can now know that Lillie can know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lillie","Scott","Philip","Rafael"],"index":1719,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9954589605,"difficulty":0.0045410395}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dana's card is shown to James. Erica's card is shown to James. James's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dana can now know that James can know whether Dana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Dana","Erica","John"],"index":33076,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9855415225,"difficulty":1.9855415225}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Helen's card is shown to Alice. Thomas's card is shown to Helen. Helen's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Thomas can now know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Alice","Helen"],"index":17321,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8251351118,"difficulty":0.1748648882}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Jason. Donna's card is shown to Donna. Alan's card is shown to Donna. Jason's card is shown to Alan. Donna's card is shown to Alan. Alan's card is shown to Alan. It is publicly announced that someone picked a red card. It is publicly announced that Donna picked a red card. It is publicly announced that Donna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Alan can now know whether Donna can know that Alan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Donna","Alan"],"index":5236,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9200292826,"difficulty":0.0799707174}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Derek's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Michelle can now know that Edward can know that Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Edward","John","Derek"],"index":19243,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967041612,"difficulty":0.0032958388}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samuel knows whether Samuel is thirsty. It is publicly announced that Jennifer does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Samuel can now know that Antonio is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Antonio","Samuel","Hazel","Jennifer"],"index":64632,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.958966434,"difficulty":0.041033566}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Kellee. David's card is shown to Johnny. Johnny's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kellee can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Kellee","Johnny","Nancy"],"index":48115,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959152341,"difficulty":0.0040847659}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Terrell. Terrell's card is shown to Christi. Christi's card is shown to Daniel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Terrell can now know that Christi can know whether Christi picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Terrell","Christi","Daniel"],"index":21059,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.605471015,"difficulty":1.605471015}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annie does not know whether Annie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Annie can now know that Gary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gary","George","Annie"],"index":61213,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9885480404,"difficulty":0.0114519596}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sally knows whether or not everyone is thirsty. It is publicly announced that Roger knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Sally can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angelina","Elizabeth","Roger","Sally"],"index":61848,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999065578,"difficulty":0.000934422}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jan's card is shown to Aaron. Aaron's card is shown to Jan. Crystal's card is shown to Jan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jan can now know whether Aaron picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Aaron","Jan","Shelby","Crystal"],"index":64458,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9470906258,"difficulty":1.9470906258}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leon","Patricia","Amanda","James"],"index":62635,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992223978,"difficulty":0.0007776022}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie's forehead is muddy. It is publicly announced that Franklin knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Franklin can now know whether Marie can know that Franklin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kimberly","Marie","Franklin"],"index":16628,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9473562837,"difficulty":0.0526437163}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sharon can now know that Carolyn can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Willie","Sharon","James"],"index":39783,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980410933,"difficulty":0.0019589067}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Donald can now know that Kathryn can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathryn","Donald","Jennifer"],"index":26952,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999358356,"difficulty":0.000641644}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra does not know whether or not everyone's forehead is muddy. It is publicly announced that Mark knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Debra can now know that Mark can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","David","Debra"],"index":29654,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994788766,"difficulty":0.0005211234}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Latoya's card is shown to Peggy. Peggy's card is shown to Latoya. It is publicly announced that someone picked a red card. It is publicly announced that Alan does not know whether Peggy picked a red card. It is publicly announced that Alan does not know whether Alan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Alan can now know whether Peggy can know whether Latoya picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alan","Peggy","Latoya"],"index":40785,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983750582,"difficulty":0.0016249418}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luz's card is shown to Teresa. Carlos's card is shown to Teresa. Carlos's card is shown to Luz. Teresa's card is shown to Emanuel. Carlos's card is shown to Carlos. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Teresa can now know whether Teresa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Teresa","Luz","Emanuel","Carlos"],"index":61200,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8446986675,"difficulty":1.8446986675}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marine knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Elsie can now know that Marine can know that Elsie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Elsie","Marine"],"index":8846,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9634642601,"difficulty":0.0365357399}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Betty can now know that Karen can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Betty","Karen"],"index":47818,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989407659,"difficulty":0.0010592341}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sheila can now know whether Jeffrey can know that Josephine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sheila","Josephine","Dorothy","Jeffrey"],"index":64244,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9953174591,"difficulty":0.0046825409}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Leona can now know that Wanda can know whether Leona is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leona","David","Wanda","Cheryl"],"index":33020,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9643367529,"difficulty":0.0356632471}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa's forehead is not muddy. It is publicly announced that Christopher does not know whether Christopher's forehead is muddy. It is publicly announced that Christopher knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Theresa can now know whether Chandra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chandra","Theresa","Christopher"],"index":32662,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.617515564,"difficulty":0.382484436}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pablo's card is shown to Pablo. It is publicly announced that someone picked a red card. It is publicly announced that Pablo does not know whether Andrew picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Pablo can now know whether Pablo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pablo","Kathie","Andrew"],"index":7249,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6888724566,"difficulty":0.3111275434}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamela's card is shown to James. James's card is shown to Pamela. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"James can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Pamela"],"index":25072,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.593955636,"difficulty":1.593955636}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know whether Sheila can know whether Jerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Sheila","Roger","John"],"index":22670,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993777275,"difficulty":0.0006222725}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know that Jimmy can know that Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Matthew","Jimmy","Ruth","Anthony"],"index":56503,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977353811,"difficulty":0.0022646189}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy. It is publicly announced that Frank's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] Agentb knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Sonia can now know that Andrew can know whether Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frank","Sonia","Doris","Andrew"],"index":29925,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9599446654,"difficulty":0.0400553346}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tabitha does not know whether Patrice is thirsty. It is publicly announced that Tabitha does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Tabitha can now know that Jeanette can know that Patrice is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tabitha","Patrice","Jeanette","Rodney"],"index":10744,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9498606324,"difficulty":0.0501393676}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Holly can now know that Harry can know whether Olinda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Holly","Olinda","Bryan","Harry"],"index":16114,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993181229,"difficulty":0.0006818771}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antionette is thirsty. It is publicly announced that Christina does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Antionette can now know that Antionette is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christina","Antionette","Mary"],"index":62819,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7069829106,"difficulty":0.2930170894}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Elizabeth can now know whether Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Barbara","Elizabeth"],"index":3175,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9981246591,"difficulty":0.0018753409}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Edwin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Daniel can now know that Kim can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Edwin","Kim"],"index":49349,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984147549,"difficulty":0.0015852451}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that James knows whether Maurice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Maurice can now know that Hilton can know that Hilton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melissia","Maurice","Hilton","James"],"index":46347,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976654053,"difficulty":0.0023345947}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Greg does not know whether Donna is thirsty. It is publicly announced that Nick knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Donna can now know that Dominique can know whether Donna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dominique","Nick","Donna","Greg"],"index":6147,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9421836734,"difficulty":0.0578163266}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leo does not know whether Virginia is thirsty. It is publicly announced that Leo does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know that Michael can know whether Virginia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Leo","Michael","Virginia"],"index":56807,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9883784652,"difficulty":0.0116215348}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emily knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Anthony can now know that Emily's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Emily","Anthony","David"],"index":17341,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978389144,"difficulty":0.0021610856}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valerie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Albert can now know that Valerie can know that Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Valerie","Paul","Albert"],"index":2231,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937699437,"difficulty":0.0062300563}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pearl does not know whether Richard is thirsty. It is publicly announced that Richard does not know whether Pearl is thirsty. It is publicly announced that Pearl does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"George can now know that Richard can know that George is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Pearl","George","Ethel"],"index":43859,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9932966828,"difficulty":0.0067033172}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Branden's forehead is muddy. It is publicly announced that Branden's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] 0","hypothesis":"Robert can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Branden","Robert","John"],"index":49986,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993569255,"difficulty":0.0006430745}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Desmond can now know whether Desmond's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Desmond","James","Jeffery"],"index":52410,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.992985189,"difficulty":0.007014811}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Douglas can now know that Nancy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Douglas","Nancy"],"index":49793,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989394546,"difficulty":0.0010605454}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerald does not know whether Eva is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Gerald can now know that Jessica can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessica","Gerald","Mary","Eva"],"index":34383,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977756143,"difficulty":0.0022243857}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"George can now know that George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Judith","Jessie","George","Paul"],"index":47386,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6721472144,"difficulty":0.3278527856}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Christopher can now know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Kerry","Earl"],"index":329,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9898117185,"difficulty":0.0101882815}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virgil is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Virgil can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Virgil","Jacqulyn","Ronald"],"index":1229,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949394464,"difficulty":0.0050605536}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bonita does not know whether Tammy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Catherine can now know that Bonita can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Catherine","Tammy","Bonita"],"index":49025,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970999956,"difficulty":0.0029000044}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jasmine's card is shown to Jasmine. Inez's card is shown to Jasmine. Jasmine's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Maria can now know that Jasmine can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jasmine","Maria","Inez"],"index":2533,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994077682,"difficulty":0.0005922318}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Carolyn can now know that Dennis can know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dennis","Carolyn","Wanda","Robin"],"index":38525,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976165295,"difficulty":0.0023834705}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Trish does not know whether or not everyone is thirsty. It is publicly announced that Trish does not know whether Joe is thirsty. It is publicly announced that Seymour knows whether Seymour is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Joe can now know whether Trish is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Seymour","Vera","Joe","Trish"],"index":44684,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9135757685,"difficulty":1.9135757685}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether John is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Edward can now know whether John can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Edward"],"index":59977,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9944100976,"difficulty":0.0055899024}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lester's card is shown to Samuel. Samuel's card is shown to Lester. Lee's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lee can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lee","Samuel","Lester","James"],"index":33774,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960536957,"difficulty":0.0039463043}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Calvin knows whether someone is thirsty. It is publicly announced that Clifford does not know whether Calvin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Davina can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clifford","Lisa","Calvin","Davina"],"index":57513,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990007281,"difficulty":0.0009992719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terrence knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Margaret can now know whether Aldo can know whether Aldo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Aldo","Margaret","Adele","Terrence"],"index":54088,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9935777187,"difficulty":0.0064222813}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Melinda can now know that Melinda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Melinda","Richard"],"index":27101,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9808262587,"difficulty":0.0191737413}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha knows whether Martha is thirsty. It is publicly announced that Scott does not know whether Martha is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Scott can now know that Scott is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Martha","Scott"],"index":31980,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8753154874,"difficulty":1.8753154874}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Melvin. Melvin's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Melvin knows whether or not everyone picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Mary can now know whether Melvin can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melvin","Mary"],"index":5244,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998559773,"difficulty":0.001440227}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daisy does not know whether Daisy's forehead is muddy. It is publicly announced that Daisy does not know whether Daisy's forehead is muddy. It is publicly announced that Daisy's forehead is not muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Sarah can now know whether Daisy can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Daisy","Scott"],"index":20808,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994763732,"difficulty":0.0005236268}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Henry can now know whether Shirl can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Henry","Christine","Shirl","Lauryn"],"index":45544,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974718094,"difficulty":0.0025281906}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa's forehead is not muddy. It is publicly announced that Lisa does not know whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Teresa can now know that Dean can know that Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","Teresa","Dean"],"index":7411,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972129464,"difficulty":0.0027870536}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"John can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Barbara"],"index":20144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994794726,"difficulty":0.0005205274}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phillip knows whether Shannon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Phillip can now know that Blanca can know whether Phillip's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shannon","Blanca","Phillip"],"index":65724,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993774295,"difficulty":0.0006225705}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy's forehead is muddy. It is publicly announced that Samuel knows whether someone's forehead is muddy. It is publicly announced that Samuel knows whether Rodney's forehead is muddy. It is publicly announced that Samuel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know that Samuel can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Rodney","Samuel"],"index":17469,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994113445,"difficulty":0.0005886555}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond does not know whether Raymond's forehead is muddy. It is publicly announced that Allene knows whether Mary's forehead is muddy. It is publicly announced that Raymond does not know whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Raymond can now know that Allene can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Raymond","Allene","Samantha","Mary"],"index":45301,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998950839,"difficulty":0.001049161}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Harold can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vickie","Jerry","Harold"],"index":30839,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989134073,"difficulty":0.0010865927}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Victor. Ines's card is shown to Victor. Mary's card is shown to Mary. Steven's card is shown to Mary. Victor's card is shown to Ines. Ines's card is shown to Ines. Victor's card is shown to Steven. Ines's card is shown to Steven. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Ines picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1,3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1,3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Victor can now know that Ines can know that Victor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victor","Mary","Ines","Steven"],"index":5403,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955675006,"difficulty":0.0044324994}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Angel's card is shown to Angel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Angel can now know that James can know whether Cindy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Angel","Cindy"],"index":992,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972015619,"difficulty":0.0027984381}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Geraldine. Geraldine's card is shown to German. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Geraldine picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know whether Geraldine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geraldine","German","Robert"],"index":47884,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9918688536,"difficulty":0.0081311464}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Beatrice knows whether Beatrice is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lindsey can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Beatrice","Lindsey"],"index":66284,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999438107,"difficulty":0.000561893}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether or not everyone's forehead is muddy. It is publicly announced that Gilbert does not know whether Gilbert's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Jesus can now know whether Barbara can know that Jesus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesus","Gilbert","Dennis","Barbara"],"index":6897,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8442351222,"difficulty":0.1557648778}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie does not know whether Amy is thirsty. It is publicly announced that Amy is not thirsty. It is publicly announced that Sean does not know whether Willie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Sean can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Willie","Sean","Amy"],"index":35567,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995111227,"difficulty":0.0004888773}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Suzanne's card is shown to Natasha. Joyce's card is shown to Arthur. Suzanne's card is shown to Arthur. Natasha's card is shown to Joyce. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Joyce picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Natasha can now know that Arthur can know that Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Natasha","Arthur","Joyce","Suzanne"],"index":27790,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930480123,"difficulty":0.0069519877}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jermaine's card is shown to Jermaine. Robbie's card is shown to Robbie. Jermaine's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mary can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jermaine","Robbie","Mary"],"index":23177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990516305,"difficulty":0.0009483695}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myrna does not know whether Melvin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Myrna can now know that Myrna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Myrna","Melvin","Willie"],"index":24323,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9706680179,"difficulty":0.0293319821}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Carlos does not know whether Ida is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ida can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ida","Carlos","Geraldine"],"index":24413,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993696809,"difficulty":0.0006303191}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Andrew. John's card is shown to John. Paul's card is shown to John. Paul's card is shown to Wayne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Andrew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","John","Paul","Wayne"],"index":22717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994083643,"difficulty":0.0005916357}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Fred can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Fred","Maria"],"index":19389,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988915324,"difficulty":0.0011084676}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Shameka can now know whether Larry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dovie","Larry","Shameka"],"index":7712,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994194508,"difficulty":0.0005805492}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Francis can now know whether Douglas can know whether Francis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Douglas","Shelby","Alicia"],"index":60958,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9939568043,"difficulty":0.0060431957}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Anna can now know that Teresa can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Teresa","David","Patricia","Anna"],"index":37586,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989622831,"difficulty":0.0010377169}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis is not thirsty. It is publicly announced that James is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"James can now know that Arnold is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Dennis","Sandra","Arnold"],"index":60526,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9887328148,"difficulty":0.0112671852}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Whitney is thirsty. It is publicly announced that Elizabeth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Dale can now know that Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Whitney","Dale","Elizabeth"],"index":35490,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.960637331,"difficulty":0.039362669}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Larry. Wilmer's card is shown to Larry. Christopher's card is shown to Carey. Carey's card is shown to Wilmer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","Christopher","Carey","Wilmer"],"index":13043,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993745685,"difficulty":0.0006254315}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carlos can now know whether Corinne can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Corinne","Carlos","Jo"],"index":40163,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9862424135,"difficulty":0.0137575865}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly does not know whether Dave is thirsty. It is publicly announced that Kelly does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Kelly can now know that Kelly is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dave","Kelly"],"index":67550,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6133044362,"difficulty":1.6133044362}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Maurice can now know whether Vera's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maurice","Mark","Vera"],"index":16102,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994472861,"difficulty":0.0005527139}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Larry can now know that Marty can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Larry","Ann","Marty"],"index":33833,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994884729,"difficulty":0.0005115271}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Benjamin's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Benjamin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Michael can now know whether Christopher can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Benjamin","Michael","Christopher","Johnnie"],"index":57185,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993702769,"difficulty":0.0006297231}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scot does not know whether or not everyone is thirsty. It is publicly announced that Gary does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Mary can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diane","Mary","Scot","Gary"],"index":38211,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988333583,"difficulty":0.0011666417}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bethany does not know whether Chery is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Rolando does not know whether Bethany is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Madeline can now know that Bethany is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chery","Madeline","Rolando","Bethany"],"index":26407,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960967898,"difficulty":0.0039032102}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Micheal can now know that Virginia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Micheal","Virginia","Johnny"],"index":5507,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989105463,"difficulty":0.0010894537}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Wanda. Kathyrn's card is shown to Kathyrn. Luisa's card is shown to Kathyrn. Wanda's card is shown to Jefferson. Wanda's card is shown to Luisa. Luisa's card is shown to Luisa. It is publicly announced that someone picked a red card. It is publicly announced that Kathyrn does not know whether Wanda picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jefferson can now know whether Jefferson picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wanda","Kathyrn","Jefferson","Luisa"],"index":4261,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9781318903,"difficulty":0.0218681097}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Doris. Mathew's card is shown to Doris. Amy's card is shown to Amy. Doris's card is shown to Mathew. It is publicly announced that someone picked a red card. It is publicly announced that Doris does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Doris can now know whether Amy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Amy","Mathew"],"index":42402,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994394183,"difficulty":0.0005605817}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether or not everyone's forehead is muddy. It is publicly announced that Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] Agenta knows whether (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Jason can now know whether Conrad can know whether Conrad's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Linda","Douglas","Conrad"],"index":12862,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994351268,"difficulty":0.0005648732}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucy knows whether Gladys's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Robert can now know that Lucy can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Lucy","Michelle","Gladys"],"index":25834,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999364078,"difficulty":0.000635922}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Curtis's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Curtis can now know that Curtis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Curtis","Michael"],"index":8030,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.721221447,"difficulty":1.721221447}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gussie knows whether Gussie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Anthony can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rosa","Anthony","Derek","Gussie"],"index":28709,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989762306,"difficulty":0.0010237694}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Justine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Patricia can now know whether Justine can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anne","Avis","Justine","Patricia"],"index":28718,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993610978,"difficulty":0.0006389022}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Cindy can now know whether Jason can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jason","Cindy"],"index":17294,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993414283,"difficulty":0.0006585717}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Karen knows whether Alice's forehead is muddy. It is publicly announced that Karen knows whether someone's forehead is muddy. It is publicly announced that Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentb knows that (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentb knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Karen can now know that Bailey can know whether Bailey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bailey","Karen","Rhonda","Alice"],"index":10331,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.958129406,"difficulty":0.041870594}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Stanley can now know that Stanley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stanley","Tonya","Shari","Laurence"],"index":67431,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978082776,"difficulty":0.0021917224}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to George. George's card is shown to George. Brady's card is shown to George. George's card is shown to Brady. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know whether William can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Helen","George","Brady"],"index":4629,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9667068124,"difficulty":0.0332931876}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Terry can now know whether Mary can know whether Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Terry"],"index":51652,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958583713,"difficulty":0.0041416287}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tammy knows whether someone is thirsty. It is publicly announced that Adam does not know whether Rodrigo is thirsty. It is publicly announced that Titus is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Tammy can now know that Adam is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Titus","Tammy","Adam","Rodrigo"],"index":46515,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9889988303,"difficulty":0.0110011697}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucile does not know whether Jack is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Claude can now know whether Arlene can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arlene","Jack","Claude","Lucile"],"index":8963,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993821383,"difficulty":0.0006178617}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond does not know whether Raymond's forehead is muddy. It is publicly announced that Kenneth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Leon can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Leon","Jerry","Raymond"],"index":4151,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988415837,"difficulty":0.0011584163}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sally's card is shown to Pat. Sally's card is shown to Hazel. Jeremy's card is shown to Hazel. Hazel's card is shown to Sally. Hazel's card is shown to Jeremy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sally can now know that Sally picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pat","Hazel","Sally","Jeremy"],"index":3895,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9939272404,"difficulty":0.0060727596}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Loraine's card is shown to Thomas. Paula's card is shown to Thomas. Loraine's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Loraine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Thomas can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","James","Loraine","Paula"],"index":21708,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994737506,"difficulty":0.0005262494}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Russell can now know that Russell is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Russell","Robert"],"index":39607,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8576671481,"difficulty":0.1423328519}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Steven can now know whether Kim can know that Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Regina","Kim","Steven","Sandra"],"index":25452,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8842536807,"difficulty":0.1157463193}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda knows whether Amanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Amanda can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amanda","Donald","Jean","Joseph"],"index":41017,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989796281,"difficulty":0.0010203719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herb does not know whether Herb's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Herb can now know that Lenore can know whether Lenore's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Herb","Jerry","Lenore","Tony"],"index":9544,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9932619929,"difficulty":0.0067380071}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to Rhonda. Linda's card is shown to Rhonda. Rhonda's card is shown to Linda. Linda's card is shown to Linda. Roy's card is shown to Linda. Rhonda's card is shown to Roy. Linda's card is shown to Roy. Roy's card is shown to Roy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rhonda can now know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rhonda","Linda","Roy"],"index":36681,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9440453053,"difficulty":0.0559546947}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Edwin. Edwin's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Edwin can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edwin","Jesus"],"index":22967,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9933951497,"difficulty":0.0066048503}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mabel can now know that David can know that Myron is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Myron","David","Mabel"],"index":11937,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967978597,"difficulty":0.0032021403}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Michelle. Michelle's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Michelle knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Patricia can now know that Michelle can know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michelle","Patricia"],"index":60629,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6182066202,"difficulty":0.3817933798}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tomas's card is shown to Miquel. Marilyn's card is shown to Miquel. Miquel's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tomas can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tomas","Marilyn","Miquel","Michael"],"index":4332,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957478642,"difficulty":0.0042521358}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alex's card is shown to Alex. Tobias's card is shown to Jessie. Alex's card is shown to Tobias. It is publicly announced that someone picked a red card. It is publicly announced that Alex picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Jessie can now know that Alex picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alex","Jessie","Tobias"],"index":63227,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6065052152,"difficulty":1.6065052152}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Evelyn can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Barbara","Robert","Pauline"],"index":32381,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998388052,"difficulty":0.001611948}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irene is thirsty. It is publicly announced that Eleanor knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Irene can now know that Raymond can know that Raymond is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raymond","Eleanor","Irene"],"index":61735,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9873719215,"difficulty":0.0126280785}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill knows whether Ira's forehead is muddy. It is publicly announced that Bill knows whether Bill's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bill can now know that Doyle can know whether Ira's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ira","Bill","Doyle"],"index":5017,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993763566,"difficulty":0.0006236434}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Allen","Leonard"],"index":8860,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993641973,"difficulty":0.0006358027}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffany's card is shown to John. John's card is shown to Tiffany. Jessica's card is shown to Tiffany. Tiffany's card is shown to Tiffany. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Tiffany picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Jessica","Tiffany","Jeannette"],"index":22613,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932890534,"difficulty":0.0067109466}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Bobby can now know that Lynda can know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Bobby","Kathleen","Lynda"],"index":45335,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9959053993,"difficulty":0.0040946007}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darius's card is shown to Frankie. Darius's card is shown to Darius. Jennie's card is shown to Darius. Frankie's card is shown to Jennie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennie can now know that Darius can know that Frankie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frankie","Darius","Jennie"],"index":4106,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998110652,"difficulty":0.001889348}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lindsay can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joleen","Dolores","Edward","Lindsay"],"index":20123,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992559552,"difficulty":0.0007440448}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phyllis knows whether Betty is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Phyllis can now know that Betty can know whether Betty is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Betty","Phyllis"],"index":5250,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9917442203,"difficulty":0.0082557797}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that Andrew knows whether Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"William can now know that Andrew can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alfred","Andrew","William"],"index":44469,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.993093729,"difficulty":0.006906271}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clinton's card is shown to Clinton. Anita's card is shown to Clinton. Frederick's card is shown to Clinton. Anita's card is shown to Anita. Russell's card is shown to Anita. Frederick's card is shown to Frederick. Russell's card is shown to Frederick. Anita's card is shown to Russell. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clinton can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clinton","Anita","Frederick","Russell"],"index":25728,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994029999,"difficulty":0.0005970001}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Amy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Amy"],"index":21005,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990195036,"difficulty":0.0009804964}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Erik. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Erik does not know whether Erik picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Erik can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erik","John"],"index":57889,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990384579,"difficulty":0.0009615421}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Nancy can now know that Irene can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Holly","Nancy","Irene","James"],"index":17626,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995042086,"difficulty":0.0004957914}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shelly is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Thomas can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kristin","Thomas","Henry","Shelly"],"index":16720,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990339279,"difficulty":0.0009660721}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether Robert is thirsty. It is publicly announced that Corey does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Nancy can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Corey","Robert","Ashley"],"index":15557,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989104271,"difficulty":0.0010895729}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah knows whether or not nobody is thirsty. It is publicly announced that Deborah does not know whether Gene is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gene can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deborah","Gene","Christopher"],"index":64824,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994365573,"difficulty":0.0005634427}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Portia can now know whether Edith is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betty","Portia","Edith"],"index":3423,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970443845,"difficulty":0.0029556155}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Pearl can now know that Heather can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Diane","Pearl","Heather"],"index":20255,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9904124141,"difficulty":0.0095875859}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Joseph can now know whether Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dawn","Maria","Joseph"],"index":64957,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9927454591,"difficulty":0.0072545409}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rick does not know whether Cheryl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Rick can now know whether Cheryl can know whether Cheryl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rick","Francisca","Stephen","Cheryl"],"index":65271,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985250831,"difficulty":0.0014749169}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Temeka knows whether Samantha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Samantha can now know whether Jessica can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ouida","Temeka","Samantha","Jessica"],"index":49194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9590758681,"difficulty":0.0409241319}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Brett can now know that Charisse can know whether Brett's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Brett","Alice","Charisse"],"index":3612,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994295239,"difficulty":0.0005704761}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judy does not know whether Shirley is thirsty. It is publicly announced that William does not know whether Judy is thirsty. It is publicly announced that Shirley does not know whether or not everyone is thirsty. It is publicly announced that John does not know whether Judy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"John can now know whether William can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judy","William","John","Shirley"],"index":54869,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9747689366,"difficulty":0.0252310634}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda is thirsty. It is publicly announced that William is not thirsty. It is publicly announced that Nathaniel does not know whether Frances is thirsty. It is publicly announced that Linda does not know whether Nathaniel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentd knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"William can now know that Linda can know that Linda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Nathaniel","Frances","William"],"index":52929,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.985434413,"difficulty":1.985434413}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ramona's card is shown to David. David's card is shown to Ramona. Ramona's card is shown to Ramona. David's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Ramona knows whether Ramona picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"James can now know whether Ramona can know that Ramona picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Ramona","James"],"index":1134,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9786711335,"difficulty":1.9786711335}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenny does not know whether Lisa is thirsty. It is publicly announced that Kenny does not know whether Gwen is thirsty. It is publicly announced that Lisa does not know whether Gwen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"David can now know that Gwen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gwen","David","Kenny","Lisa"],"index":64316,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960415363,"difficulty":0.0039584637}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Grace can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jamie","Stephanie","Grace","Floyd"],"index":24477,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989491105,"difficulty":0.0010508895}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Susan. Vilma's card is shown to Susan. Andrew's card is shown to Andrew. Susan's card is shown to Vilma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Andrew can now know that Vilma can know whether Andrew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Andrew","Vilma"],"index":37265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7679641247,"difficulty":0.2320358753}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Alta. Alta's card is shown to Alice. Antwan's card is shown to Alice. Antwan's card is shown to Antwan. Daniel's card is shown to Antwan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Antwan can now know whether Alta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alta","Alice","Antwan","Daniel"],"index":3011,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9673164487,"difficulty":0.0326835513}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marquita knows whether Marquita's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Tina can now know that Marquita can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tina","Marquita"],"index":43516,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994755387,"difficulty":0.0005244613}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Denise's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Carmen can now know that Denise can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carmen","Denise","Anthony"],"index":40132,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9896472096,"difficulty":0.0103527904}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that Annice does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"William can now know that Natasha can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Annice","Natasha"],"index":67371,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994515777,"difficulty":0.0005484223}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy does not know whether Gay is thirsty. It is publicly announced that Andrew knows whether Andrew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Andrew can now know that Gay can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amy","Gay","Maudie","Andrew"],"index":38598,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989554882,"difficulty":0.0010445118}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether or not everyone is thirsty. It is publicly announced that George does not know whether Antonia is thirsty. It is publicly announced that George does not know whether Maria is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Courtney can now know that Antonia can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Antonia","Courtney","Maria"],"index":8806,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953733087,"difficulty":0.0046266913}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jake knows whether Jake's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jake can now know whether Kendra can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","John","Jake","Kendra"],"index":54777,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991793036,"difficulty":0.0008206964}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Henry. Frances's card is shown to Henry. Guadalupe's card is shown to Karl. Frances's card is shown to Karl. Frances's card is shown to Guadalupe. Henry's card is shown to Frances. It is publicly announced that someone picked a red card. It is publicly announced that Karl knows whether Guadalupe picked a red card. It is publicly announced that Karl knows whether someone picked a red card. It is publicly announced that Karl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentb knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Karl can now know whether Henry can know whether Karl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Henry","Karl","Guadalupe","Frances"],"index":4516,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9969338179,"difficulty":0.0030661821}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is muddy. It is publicly announced that Andres knows whether someone's forehead is muddy. It is publicly announced that Andres knows whether Daniel's forehead is muddy. It is publicly announced that Andres knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know whether Andres can know that Andres's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Daniel","Andres"],"index":20446,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993095398,"difficulty":0.0006904602}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hazel knows whether Ruby's forehead is muddy. It is publicly announced that Ruby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"Ruby can now know whether Hyun can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hyun","Dorothy","Ruby","Hazel"],"index":11826,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994664788,"difficulty":0.0005335212}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leo's card is shown to Leo. Manuel's card is shown to Manuel. Malinda's card is shown to Malinda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leo can now know that Malinda can know that Manuel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leo","Manuel","Malinda"],"index":30048,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974396229,"difficulty":0.0025603771}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacy does not know whether Stacy's forehead is muddy. It is publicly announced that Stacy does not know whether Stacy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Stacy can now know that Sandra can know whether Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sandra","Stacy"],"index":26392,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9555118084,"difficulty":1.9555118084}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Debra. Debra's card is shown to Alice. Alice's card is shown to Ronald. Ronald's card is shown to Ronald. Debra's card is shown to Anna. Anna's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Debra does not know whether or not everyone picked a red card. It is publicly announced that Debra picked a red card. It is publicly announced that Debra does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Debra can now know whether Ronald can know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Alice","Ronald","Anna"],"index":66504,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987081289,"difficulty":0.0012918711}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Ronnie can now know that Timothy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ronnie","Timothy"],"index":23219,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998671174,"difficulty":0.001328826}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Ruth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ruth","Henry"],"index":17071,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986020923,"difficulty":0.0013979077}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether George's forehead is muddy. It is publicly announced that George does not know whether or not everyone's forehead is muddy. It is publicly announced that Roy knows whether Walter's forehead is muddy. It is publicly announced that Roy knows whether Jonathon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"George can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roy","Walter","Jonathon","George"],"index":36438,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994722009,"difficulty":0.0005277991}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laquita's card is shown to Laquita. Carol's card is shown to Laquita. Laquita's card is shown to Carol. Nyla's card is shown to Carol. Nyla's card is shown to Nyla. It is publicly announced that someone picked a red card. It is publicly announced that Carol knows whether someone picked a red card. It is publicly announced that Nyla picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Carol can now know that Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laquita","Carol","Nyla"],"index":9951,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.602624774,"difficulty":0.397375226}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Ernest can now know that Terry can know whether Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ernest","Terry"],"index":15118,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964836836,"difficulty":0.0035163164}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alma knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Gabriel can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gabriel","Alma"],"index":61389,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9891839027,"difficulty":0.0108160973}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Charla. Cole's card is shown to Cole. Charla's card is shown to Kari. Charla's card is shown to Laura. Cole's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know whether Cole can know that Laura picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charla","Cole","Kari","Laura"],"index":47517,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8383974433,"difficulty":0.1616025567}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas knows whether Stephanie's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Nicholas can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Nicholas","Stephanie"],"index":7050,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985663295,"difficulty":0.0014336705}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Bernard can now know whether Lauren's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lauren","Bernard","Elizabeth","John"],"index":46090,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994012117,"difficulty":0.0005987883}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tommy's card is shown to Tommy. Henry's card is shown to Tommy. Tommy's card is shown to Margaret. Tommy's card is shown to Henry. Margaret's card is shown to Henry. It is publicly announced that someone picked a red card. It is publicly announced that Tommy does not know whether Margaret picked a red card. It is publicly announced that Margaret knows whether or not everyone picked a red card. It is publicly announced that Henry knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Margaret can now know whether Tommy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tommy","Margaret","Henry"],"index":62760,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999432981,"difficulty":0.000567019}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Daniel. Paul's card is shown to Paul. Rufus's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that Daniel can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Paul","Rufus"],"index":49361,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993769526,"difficulty":0.0006230474}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clarence does not know whether Andrea is thirsty. It is publicly announced that Andrea does not know whether Julie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Andrea can now know that Vera can know that Julie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vera","Clarence","Julie","Andrea"],"index":20053,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983274341,"difficulty":0.0016725659}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether Jocelyn's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Charles can now know that Ryan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jocelyn","Ryan","Robert","Charles"],"index":5900,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9304586649,"difficulty":0.0695413351}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leon","Whitney","John","Joanne"],"index":67548,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981620908,"difficulty":0.0018379092}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael knows whether Michael is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Theodore can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Theodore"],"index":42144,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990449548,"difficulty":0.0009550452}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] 0","hypothesis":"Andreas can now know whether Andreas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Scott","Andreas","Thomas"],"index":7567,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974077344,"difficulty":0.0025922656}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Monica can now know that Stacy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Monica","Stacy","Donald"],"index":25234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949856997,"difficulty":0.0050143003}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rene does not know whether David is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Rene can now know whether David can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Rene","Emily","Michael"],"index":17332,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993251562,"difficulty":0.0006748438}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dora knows whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Tiffany can now know whether Rose can know whether Rose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tiffany","Rose","Dora"],"index":29064,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9869177938,"difficulty":1.9869177938}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Dale's card is shown to Dale. Michael's card is shown to Dale. Michael's card is shown to Michael. Patricia's card is shown to Tony. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Dale","Michael","Tony"],"index":65108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993958473,"difficulty":0.0006041527}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Ivory is thirsty. It is publicly announced that William does not know whether Susan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Susan can now know that Susan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ivory","Don","Susan","William"],"index":2340,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9809961319,"difficulty":0.0190038681}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Rhoda is thirsty. It is publicly announced that Kevin does not know whether Brian is thirsty. It is publicly announced that Rhoda does not know whether Brian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Larry can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Larry","Kevin","Rhoda"],"index":29433,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964369535,"difficulty":0.0035630465}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Sonny. Sonny's card is shown to Bryan. Bryan's card is shown to Kimberly. Steve's card is shown to Steve. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sonny can now know whether Bryan can know whether Steve picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sonny","Bryan","Kimberly","Steve"],"index":38577,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986932874,"difficulty":0.0013067126}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to William. William's card is shown to William. William's card is shown to Colette. Colette's card is shown to Colette. April's card is shown to Colette. William's card is shown to April. It is publicly announced that someone picked a red card. It is publicly announced that Ryan does not know whether Colette picked a red card. It is publicly announced that Colette does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ryan can now know that William can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ryan","William","Colette","April"],"index":1586,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989192486,"difficulty":0.0010807514}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephanie's card is shown to Samantha. Archie's card is shown to Samantha. Ernest's card is shown to Stephanie. Archie's card is shown to Archie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Samantha can now know whether Archie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samantha","Stephanie","Archie","Ernest"],"index":18750,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993620515,"difficulty":0.0006379485}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kimberly can now know whether Eileen can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eileen","Ralph","Kimberly","Barbara"],"index":20982,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992488027,"difficulty":0.0007511973}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leigh knows whether Leigh's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Raymond can now know whether Linnie can know whether Gloria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leigh","Linnie","Raymond","Gloria"],"index":28449,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994024038,"difficulty":0.0005975962}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann does not know whether Ann's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Charles can now know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Ann","Joseph","Dawn"],"index":45294,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5385531187,"difficulty":0.4614468813}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Wanda's card is shown to Patricia. Patricia's card is shown to Wanda. Wanda's card is shown to Wanda. Patricia's card is shown to Suzanne. Daniel's card is shown to Suzanne. Suzanne's card is shown to Daniel. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that Wanda can know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Wanda","Suzanne","Daniel"],"index":35993,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981697798,"difficulty":0.0018302202}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellis does not know whether Ellis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Norman can now know that Rhonda can know that Ellis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rhonda","Leone","Ellis","Norman"],"index":24182,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967983365,"difficulty":0.0032016635}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Kimberley is thirsty. It is publicly announced that William knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Kimberley can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kimberley","William"],"index":24832,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990164042,"difficulty":0.0009835958}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Blanche knows whether Edmund's forehead is muddy. It is publicly announced that Blanche's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Edmund can now know whether Blanche can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edmund","Blanche"],"index":29480,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994326234,"difficulty":0.0005673766}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Neil's card is shown to Cara. Evelyn's card is shown to Mary. Evelyn's card is shown to Evelyn. Mary's card is shown to Neil. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn does not know whether or not everyone picked a red card. It is publicly announced that Cara picked a black card. It is publicly announced that Evelyn does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Neil can now know that Evelyn can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cara","Mary","Evelyn","Neil"],"index":11035,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7308681607,"difficulty":1.7308681607}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gloria can now know whether Amy can know whether Amy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Michael","Angela","Amy"],"index":39261,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993921518,"difficulty":0.0006078482}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether Tara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Raymond can now know whether Tara can know that Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tara","Riley","Raymond","Jose"],"index":51330,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994503856,"difficulty":0.0005496144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gail does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Joshua can now know that Randy can know that Joshua's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","John","Joshua","Gail"],"index":11721,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9577550888,"difficulty":0.0422449112}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Davis can now know that Jeffrey can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Craig","Davis","Jeffrey","Victoria"],"index":55757,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998990953,"difficulty":0.001009047}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Michael. Michael's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether Margaret picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Margaret knows whether Michael picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] (Agentb knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Margaret can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Margaret"],"index":31623,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994530082,"difficulty":0.0005469918}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcia does not know whether Marcia's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Jerry can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amos","Marcia","Jerry"],"index":58646,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993758798,"difficulty":0.0006241202}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gabriel does not know whether Gabriel's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Shelby can now know whether Joseph can know that Shelby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shelby","Joseph","Gabriel"],"index":7942,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8922371268,"difficulty":1.8922371268}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lois can now know that Benny is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Benny","Orval","Lois"],"index":15341,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975734353,"difficulty":0.0024265647}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether Brett's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Anthony can now know that Shelly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Shelly","Brett"],"index":12086,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983950257,"difficulty":0.0016049743}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that Corey's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agenta knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"James can now know whether Corey can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Robert","Corey"],"index":65465,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9964074492,"difficulty":0.0035925508}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Elisabeth can now know that Heather can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tara","Elisabeth","Heather","Gertrude"],"index":9229,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994744658,"difficulty":0.0005255342}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robyn does not know whether David is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Robyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","John","Robyn","Terri"],"index":15112,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9938999414,"difficulty":0.0061000586}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darlene knows whether Darlene is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Keith can now know whether Darlene can know whether Darlene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Keith","Darlene"],"index":40460,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987088442,"difficulty":0.0012911558}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana knows whether Matthew's forehead is muddy. It is publicly announced that Diana's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Diana can now know that Diana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Raymond","Diana","Matthew","Stephen"],"index":29285,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.6270263195,"difficulty":1.6270263195}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edmund does not know whether Edmund's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Johnathan can now know whether Nancy can know whether Edmund's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Johnathan","Edmund","Daniel"],"index":23110,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987516403,"difficulty":0.0012483597}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catharine knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michael can now know that John can know that Marvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","John","Catharine","Marvin"],"index":57804,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972905517,"difficulty":0.0027094483}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know whether Robert can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Carlton","Elizabeth","Sandra"],"index":48759,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993304014,"difficulty":0.0006695986}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] Agenta knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Richard can now know that Steven can know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Bonnie","Margaret","Steven"],"index":60994,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9936959147,"difficulty":0.0063040853}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Holly does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Joan can now know that Kevin can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Joan","Holly","Kevin"],"index":58594,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994743466,"difficulty":0.0005256534}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie knows whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Pearlie can now know that Leslie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leslie","Laura","Pearlie"],"index":60472,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990028739,"difficulty":0.0009971261}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Stacy knows whether Stacy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Benjamin can now know that Mary can know whether Stacy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Benjamin","Stacy"],"index":55531,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991105199,"difficulty":0.0008894801}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Tyrone. Tyrone's card is shown to Debra. Stella's card is shown to Debra. Tyrone's card is shown to Stella. Debra's card is shown to Stella. It is publicly announced that someone picked a red card. It is publicly announced that Tyrone knows whether or not nobody picked a red card. It is publicly announced that Stella does not know whether Stella picked a red card. It is publicly announced that Stella does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Debra can now know that Tyrone can know that Tyrone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tyrone","Debra","Stella","Tracy"],"index":61719,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6802810431,"difficulty":1.6802810431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barry does not know whether Annika is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Annika can now know that Barry can know that Lisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barry","Joshua","Annika","Lisa"],"index":33117,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983690381,"difficulty":0.0016309619}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacey's card is shown to Ellen. Ellen's card is shown to Stacey. Stacey's card is shown to Stacey. Stacey's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Stacey does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Donna can now know whether Ellen can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellen","Stacey","Donna"],"index":64317,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Salvador does not know whether Jeremy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Edith can now know whether Salvador can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annie","Salvador","Edith","Jeremy"],"index":10984,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994171858,"difficulty":0.0005828142}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Susan. Susan's card is shown to Anthony. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Susan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Susan","Anthony","Doris"],"index":17775,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994159937,"difficulty":0.0005840063}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey's forehead is muddy. It is publicly announced that Jeffrey knows whether someone's forehead is muddy. It is publicly announced that Tina knows whether Robert's forehead is muddy. It is publicly announced that Justin does not know whether Justin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Justin can now know whether Tina can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Tina","Justin","Jeffrey"],"index":24031,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994449019,"difficulty":0.0005550981}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Laraine's forehead is not muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agenta knows that (Agentb knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Thomas can now know that Laraine can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Laraine"],"index":7235,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993733764,"difficulty":0.0006266236}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ricky does not know whether or not everyone is thirsty. It is publicly announced that Jeniffer knows whether Ricky is thirsty. It is publicly announced that Robert does not know whether Jeniffer is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Ricky can now know that Robert can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeniffer","Ricky","Robert"],"index":18835,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9937026501,"difficulty":0.0062973499}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know whether Michael can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Herbert","Michael","Valerie","Carl"],"index":32869,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991377592,"difficulty":0.0008622408}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shanice knows whether Janet's forehead is muddy. It is publicly announced that Janet's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Janet can now know that Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shanice","Janet"],"index":37612,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.5911502838,"difficulty":0.4088497162}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Teresa. Denise's card is shown to Teresa. Denise's card is shown to Rodney. Billy's card is shown to Billy. Rodney's card is shown to Denise. Denise's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Billy knows whether someone picked a red card. It is publicly announced that Teresa picked a red card. It is publicly announced that Rodney does not know whether Billy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Denise can now know whether Billy can know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Teresa","Rodney","Billy","Denise"],"index":64470,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985673428,"difficulty":0.0014326572}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emely does not know whether Jose is thirsty. It is publicly announced that Emely does not know whether or not everyone is thirsty. It is publicly announced that Emely does not know whether Jose is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Emely can now know that Beatriz can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beatriz","Jose","Elizabeth","Emely"],"index":66910,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9753342271,"difficulty":0.0246657729}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irma is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Paul can now know whether Irma can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michele","Irma","Paul"],"index":54827,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995011091,"difficulty":0.0004988909}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Marianne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marianne can now know that Damon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Linda","Damon","Marianne"],"index":52540,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9872447848,"difficulty":0.0127552152}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Craig. Tony's card is shown to Tony. Dorine's card is shown to Dorine. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether Dorine picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Tony does not know whether Dorine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Dorine can now know whether Craig can know whether Dorine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Craig","Tony","Dorine"],"index":48197,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987508059,"difficulty":0.0012491941}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. David's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether John picked a red card. It is publicly announced that John knows whether or not nobody picked a red card. It is publicly announced that David picked a black card. It is publicly announced that John knows whether David picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"John can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","John"],"index":12044,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5088337064,"difficulty":0.4911662936}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Manuela does not know whether Brenda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Brenda can now know that Manuela can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Manuela","Brenda","Armando"],"index":15477,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994390607,"difficulty":0.0005609393}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramona knows whether Zachariah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Zachariah can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ramona","Bobby","Zachariah"],"index":40463,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990513921,"difficulty":0.0009486079}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know whether Esther can know whether Esther's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Esther","Bradly","Amy"],"index":33995,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994607568,"difficulty":0.0005392432}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ron knows whether or not nobody's forehead is muddy. It is publicly announced that Ron does not know whether Ron's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ron can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Susan","Ron"],"index":13473,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998941958,"difficulty":0.001058042}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa knows whether Theresa's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"Linda can now know that Theresa can know whether Jake's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Theresa","Jake","Linda","Benjamin"],"index":55096,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999453485,"difficulty":0.000546515}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Bonnie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Bonnie can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Bonnie","Peter"],"index":5553,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9966267347,"difficulty":0.0033732653}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"June can now know whether Sharon can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Celia","June","Sharon"],"index":38068,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993515611,"difficulty":0.0006484389}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Dustin. Lucy's card is shown to Kelly. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kelly can now know that Dustin can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dustin","Kelly","Lucy","Patricia"],"index":14266,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990159273,"difficulty":0.0009840727}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Eusebia can now know that Gerald can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gerald","Victor","Eusebia","William"],"index":61997,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9917767048,"difficulty":0.0082232952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Tracy is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Michael is thirsty. It is publicly announced that Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] (Agentd knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Joseph can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Tracy","Barbara","Joseph"],"index":1595,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994965792,"difficulty":0.0005034208}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Linda can now know that Wendy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wendy","Linda","Evelyn","Lucy"],"index":53478,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9827350974,"difficulty":0.0172649026}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Courtney's card is shown to Courtney. Jerry's card is shown to Courtney. Heather's card is shown to Joan. Courtney's card is shown to Jerry. Joan's card is shown to Heather. Jerry's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know whether Heather can know whether Courtney picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Courtney","Joan","Jerry","Heather"],"index":32202,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986521602,"difficulty":0.0013478398}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elsie does not know whether Robert is thirsty. It is publicly announced that Robert knows whether or not everyone is thirsty. It is publicly announced that Phoebe knows whether or not everyone is thirsty. It is publicly announced that Phoebe does not know whether Elsie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Phoebe can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Phoebe","Elsie","Robert"],"index":21552,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988014698,"difficulty":0.0011985302}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Joseph knows whether Joseph is thirsty. It is publicly announced that Joseph knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Joseph can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathryn","Patrick","Joseph"],"index":35205,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993756413,"difficulty":0.0006243587}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Lawrence. Robert's card is shown to Lawrence. Joseph's card is shown to Lawrence. Joseph's card is shown to Marie. Lawrence's card is shown to Robert. Marie's card is shown to Joseph. Robert's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Joseph can now know that Robert can know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lawrence","Marie","Robert","Joseph"],"index":47813,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.986586988,"difficulty":0.013413012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula does not know whether or not everyone is thirsty. It is publicly announced that Paula does not know whether Pauline is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Andrew knows whether Andrew is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Paula can now know whether Pauline can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Pauline","Paula"],"index":8208,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999438107,"difficulty":0.000561893}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Melissa. Pete's card is shown to Melissa. Melissa's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Melissa's card is shown to Pete. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know that Pete picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melissa","Elizabeth","Pete"],"index":45604,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979935884,"difficulty":0.0020064116}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] 0","hypothesis":"Timothy can now know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Betty","Timothy"],"index":48761,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9871844649,"difficulty":0.0128155351}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether Ashley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Salvador can now know that Scott can know that Salvador's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Juan","Ashley","Salvador"],"index":19378,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9946755171,"difficulty":0.0053244829}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Marilyn can now know whether Janice can know that Janice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","James","Marilyn","Janice"],"index":40981,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999348104,"difficulty":0.000651896}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Martha's card is shown to Leonard. Martha's card is shown to Jason. Leonard's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether or not everyone picked a red card. It is publicly announced that Martha knows whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Michael can now know that Jason picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Martha","Michael","Leonard","Jason"],"index":16610,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9811313152,"difficulty":0.0188686848}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vicki's card is shown to Flora. Thomas's card is shown to Florence. Flora's card is shown to Florence. Florence's card is shown to Florence. Vicki's card is shown to Florence. Flora's card is shown to Vicki. Vicki's card is shown to Vicki. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Flora can now know whether Thomas can know whether Flora picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Flora","Florence","Vicki"],"index":5439,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984574318,"difficulty":0.0015425682}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Alice can now know whether Jessica can know whether Jessica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Terry","Jessica","Alice"],"index":44756,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9750493765,"difficulty":0.0249506235}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"George can now know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","William","Danielle","Edward"],"index":51728,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973512888,"difficulty":0.0026487112}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vincent does not know whether or not everyone is thirsty. It is publicly announced that Jessica is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Jessica can now know that Jennifer can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vincent","Jennifer","Barbara","Jessica"],"index":27469,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994897842,"difficulty":0.0005102158}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dora's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Dora can now know that David can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cathy","David","Dora"],"index":10448,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981695414,"difficulty":0.0018304586}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria's forehead is not muddy. It is publicly announced that Maria's forehead is not muddy. It is publicly announced that Mary knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Mary can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Patricia","Maria"],"index":57823,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.988740623,"difficulty":0.011259377}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nina knows whether Jared's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Warren can now know that Terri's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jared","Nina","Warren","Terri"],"index":31768,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974666834,"difficulty":0.0025333166}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hee does not know whether Debbie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Debbie can now know whether David can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Hee","Debbie","David"],"index":32203,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9710653424,"difficulty":0.0289346576}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emma knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Nicole can now know that John can know that Nadine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nadine","Nicole","Emma","John"],"index":27763,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996760428,"difficulty":0.003239572}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Dwight. Alejandro's card is shown to Dwight. Dwight's card is shown to Gary. Alejandro's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know that Alejandro picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dwight","Gary","Ronald","Alejandro"],"index":41005,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970107079,"difficulty":0.0029892921}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Lawrence's card is shown to Linda. Tracy's card is shown to Lawrence. Tracy's card is shown to Tracy. Tracy's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Lawrence does not know whether Brenda picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Tracy can now know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Lawrence","Tracy","Brenda"],"index":32538,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5557581782,"difficulty":1.5557581782}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Guadalupe does not know whether Jimmie is thirsty. It is publicly announced that Angela does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Angela can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Angela","Jimmie","Guadalupe"],"index":6736,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994680285,"difficulty":0.0005319715}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erik knows whether Crystal's forehead is muddy. It is publicly announced that Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Erik can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erik","Crystal"],"index":33330,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998971343,"difficulty":0.001028657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Philip does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Maureen can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Philip","Allison","Maureen","Steven"],"index":8876,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995090961,"difficulty":0.0004909039}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theodore is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Theodore can now know whether Frank is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Manuel","Patricia","Theodore"],"index":6171,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960771203,"difficulty":0.0039228797}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clifford's card is shown to Scott. Mary's card is shown to Clifford. Peter's card is shown to Clifford. Mary's card is shown to Mary. Peter's card is shown to Mary. Clifford's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Clifford picked a red card. It is publicly announced that Mary does not know whether Clifford picked a red card. It is publicly announced that Peter does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Clifford can now know whether Mary can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Clifford","Mary","Peter"],"index":46135,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8015115857,"difficulty":0.1984884143}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Joseph can now know that Fernando can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Joseph","Fernando"],"index":45199,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988628626,"difficulty":0.0011371374}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather does not know whether Barbara is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Heather can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Heather","Carmen","Clay"],"index":8272,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962246418,"difficulty":0.0037753582}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Garry can now know that Donald can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Garry","Sean","Donald","Robert"],"index":48044,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998922348,"difficulty":0.001077652}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jay does not know whether Emily is thirsty. It is publicly announced that Bill does not know whether Emily is thirsty. It is publicly announced that Bill knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Jay can now know that Bill can know whether Bill is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emily","Jay","Bill"],"index":20219,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9826782346,"difficulty":0.0173217654}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Jared. Dorothy's card is shown to Vasiliki. Vasiliki's card is shown to Vasiliki. Vasiliki's card is shown to Helen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vasiliki can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jared","Dorothy","Vasiliki","Helen"],"index":13058,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953149557,"difficulty":0.0046850443}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Matthew. Ernestine's card is shown to Matthew. Marcos's card is shown to Matthew. Ernestine's card is shown to Larry. Marcos's card is shown to Ernestine. It is publicly announced that someone picked a red card. It is publicly announced that Ernestine knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Matthew can now know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Larry","Ernestine","Marcos"],"index":231,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9606522918,"difficulty":0.0393477082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymonde does not know whether Raymonde's forehead is muddy. It is publicly announced that Julius does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Larry can now know that Julius's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julius","Ignacio","Larry","Raymonde"],"index":43458,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5647521615,"difficulty":0.4352478385}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kim is thirsty. It is publicly announced that Paulette knows whether Kim is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Lester can now know whether Paulette is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paulette","Lester","Kim"],"index":6414,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5690946579,"difficulty":1.5690946579}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ileana's card is shown to Edna. Christopher's card is shown to Edna. Warren's card is shown to Christopher. Christopher's card is shown to Warren. It is publicly announced that someone picked a red card. It is publicly announced that Edna does not know whether Edna picked a red card. It is publicly announced that Edna picked a black card. It is publicly announced that Ileana does not know whether Ileana picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Christopher can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edna","Ileana","Christopher","Warren"],"index":468,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9233108759,"difficulty":0.0766891241}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Abigail is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Patricia can now know whether Abigail can know whether Abigail is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Abigail","Patricia","Dorothy"],"index":5101,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997851491,"difficulty":0.002148509}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah knows whether Helen is thirsty. It is publicly announced that Helen is thirsty. It is publicly announced that Helen knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Sarah can now know that Helen can know that Sarah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sarah","Helen"],"index":634,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5197581649,"difficulty":0.4802418351}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kevin can now know that Sheldon can know that Sheldon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sheldon","Larry","Joyce","Kevin"],"index":36191,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947952628,"difficulty":0.0052047372}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myrna knows whether Myrna is thirsty. It is publicly announced that Russell knows whether Russell is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Russell can now know whether Myrna can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Myrna","Russell"],"index":36412,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994624257,"difficulty":0.0005375743}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis's forehead is not muddy. It is publicly announced that Jonathan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Dennis can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonathan","Dennis","Elsie"],"index":25436,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993084669,"difficulty":0.0006915331}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Theresa can now know that Raymond can know that Adam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Adam","Raymond","Sarah","Theresa"],"index":37946,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9955394864,"difficulty":0.0044605136}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"James can now know that Jeff can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeff","Larry","James"],"index":5073,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937909245,"difficulty":0.0062090755}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maxine does not know whether Michelle is thirsty. It is publicly announced that Maxine does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Michelle can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maxine","Michelle"],"index":25844,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986304045,"difficulty":0.0013695955}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Caitlyn knows whether Caitlyn is thirsty. It is publicly announced that Brenda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Caitlyn can now know whether Lori can know whether Lori is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Caitlyn","Brenda","Lori"],"index":4355,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9526433945,"difficulty":0.0473566055}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Tina can now know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tina","Wesley","Patricia"],"index":35749,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7535540462,"difficulty":0.2464459538}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth does not know whether Vickey is thirsty. It is publicly announced that Sandra does not know whether Ruth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Vickey can now know whether Ruth can know whether Ruth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Dora","Vickey","Sandra"],"index":47213,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989539385,"difficulty":0.0010460615}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynn knows whether Lynn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"William can now know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","William","Lynn"],"index":16216,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989491105,"difficulty":0.0010508895}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Amanda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Amanda can now know that Miranda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Amanda","Miranda"],"index":62836,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9983172417,"difficulty":0.0016827583}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Linda can now know that Allen can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","Barbara","Allen","Linda"],"index":23123,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993218184,"difficulty":0.0006781816}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bobby can now know that Bobby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Esther","Bobby"],"index":58614,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978784323,"difficulty":0.0021215677}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Tara. John's card is shown to John. John's card is shown to Karen. Karen's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that John picked a black card. It is publicly announced that Karen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 3 ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 3 ] 0","hypothesis":"John can now know that Tara can know whether Tara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tara","John","Karen"],"index":37047,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7354037762,"difficulty":0.2645962238}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerome does not know whether Jerome's forehead is muddy. It is publicly announced that Irvin does not know whether Irvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Virginia can now know that Irvin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virginia","Jerome","Irvin"],"index":10282,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9935386777,"difficulty":0.0064613223}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen does not know whether or not everyone's forehead is muddy. It is publicly announced that Patricia knows whether or not nobody's forehead is muddy. It is publicly announced that Kathleen does not know whether Kathleen's forehead is muddy. It is publicly announced that Patricia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Kathleen can now know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kathleen","Patricia"],"index":56211,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9882525802,"difficulty":0.0117474198}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sang does not know whether Hazel is thirsty. It is publicly announced that Sang does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Sang is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agenta knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Hazel can now know that Rosita can know that Hazel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Hazel","Rosita","Sang"],"index":8473,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.912491858,"difficulty":0.087508142}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aleta does not know whether Louise is thirsty. It is publicly announced that Freddie is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Freddie can now know that Louise can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aleta","Freddie","Louise","Jean"],"index":32172,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994787574,"difficulty":0.0005212426}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fidel knows whether or not nobody's forehead is muddy. It is publicly announced that Fidel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] 0","hypothesis":"Fidel can now know that Arthur's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Fidel","Arthur","Karen"],"index":30313,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994112432,"difficulty":0.005887568}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that Lauren knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Lauren can now know whether Mark can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lauren","Mark","David","Lisa"],"index":23748,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994683862,"difficulty":0.0005316138}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aurelia does not know whether Frank is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Frank can now know that Frank is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Aurelia","Frank"],"index":20978,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9934222102,"difficulty":0.0065777898}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Hong. Charles's card is shown to Roy. Roy's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Roy knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Roy can now know that Hong picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hong","Roy","Charles"],"index":39415,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983817339,"difficulty":0.0016182661}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Brett is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brett","Robert"],"index":47556,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9858112335,"difficulty":0.0141887665}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julio knows whether or not nobody is thirsty. It is publicly announced that Betty does not know whether Julio is thirsty. It is publicly announced that Julio is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Julio can now know whether Kim can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Kim","Michael","Julio"],"index":57799,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994817376,"difficulty":0.0005182624}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jewel can now know that David can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["David","Jewel"],"index":22690,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7460587025,"difficulty":0.2539412975}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know that Tonya can know that Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tonya","Sarah","Richard","Lorena"],"index":25596,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985505939,"difficulty":0.0014494061}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rena's card is shown to Rena. Rena's card is shown to Marie. Marie's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Marie knows whether Marie picked a red card. It is publicly announced that Rena does not know whether Marie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Rena can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rena","Marie"],"index":1493,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994570613,"difficulty":0.0005429387}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael knows whether Michael is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Connie can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Connie","Michael"],"index":33079,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994988441,"difficulty":0.0005011559}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymond can now know that Norma can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Virginia","Norma","Raymond"],"index":22642,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988874793,"difficulty":0.0011125207}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramona knows whether Ramona's forehead is muddy. It is publicly announced that Amy knows whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Frances can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Ramona","Frances","Amy"],"index":23158,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989855886,"difficulty":0.0010144114}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Jaqueline. George's card is shown to George. Joseph's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether Jaqueline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jaqueline","George","Joseph","James"],"index":54708,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.989395678,"difficulty":0.010604322}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Christopher can now know that Nathanael can know that Nathanael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nathanael","Christopher"],"index":28004,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977547526,"difficulty":0.0022452474}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francesca knows whether Trina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Trina can now know whether Francesca can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Francesca","Trina","Richard"],"index":15609,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9734438062,"difficulty":0.0265561938}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Juan's forehead is muddy. It is publicly announced that Clayton knows whether Juan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Steven can now know whether Lawrence can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clayton","Steven","Juan","Lawrence"],"index":59239,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993840456,"difficulty":0.0006159544}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor does not know whether Victor's forehead is muddy. It is publicly announced that Victor does not know whether or not everyone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] 0","hypothesis":"Larry can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Victor","Dorothy","Larry"],"index":29242,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988563061,"difficulty":0.0011436939}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether Lillian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Lillian can now know whether Cynthia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverly","Lillian","Sarah","Cynthia"],"index":50155,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994188547,"difficulty":0.0005811453}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy. It is publicly announced that Jimmy knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Marcella can now know that Marcella's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Joseph","Marcella","Jimmy"],"index":40814,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.983684063,"difficulty":0.016315937}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that George knows whether or not nobody's forehead is muddy. It is publicly announced that Rebecca knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"George can now know whether Charles can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","George","Charles","Rebecca"],"index":42920,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992765784,"difficulty":0.0007234216}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that April does not know whether William is thirsty. It is publicly announced that William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 1 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"William can now know whether Santiago is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Santiago","April"],"index":32333,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9946315289,"difficulty":0.0053684711}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita's forehead is not muddy. It is publicly announced that Stacey knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Amanda can now know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rita","Stacey","Amanda"],"index":17031,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984223843,"difficulty":0.0015776157}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Penny does not know whether David is thirsty. It is publicly announced that Raymond is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] 0","hypothesis":"Raymond can now know that Richard can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Richard","David","Penny"],"index":15835,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994418025,"difficulty":0.0005581975}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Pilar's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Charles","William","Pilar"],"index":19687,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968242645,"difficulty":0.0031757355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Dwayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Dwayne can now know whether Alicia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Alicia","Joseph","Dwayne"],"index":58945,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9948813915,"difficulty":0.0051186085}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Susan knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Susan can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","John","Susan"],"index":45829,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989608526,"difficulty":0.0010391474}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia knows whether Virginia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Virginia can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Allen","Christian","Michael","Virginia"],"index":61660,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989722967,"difficulty":0.0010277033}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"William can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Heidi","Jerry","William"],"index":2789,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9906630516,"difficulty":0.0093369484}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Marlene knows whether or not everyone's forehead is muddy. It is publicly announced that Marlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"John can now know that Marlene can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Marlene","Steven","Lonnie"],"index":5887,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9877877831,"difficulty":0.0122122169}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Mandy can now know that Roy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mandy","Roy"],"index":35403,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991650581,"difficulty":0.0008349419}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to Rhonda. James's card is shown to Rhonda. James's card is shown to James. Rhonda's card is shown to Joseph. James's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rhonda","James","Joseph"],"index":62701,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989529848,"difficulty":0.0010470152}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"John can now know whether David can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Rodrick","Shannon","David"],"index":41477,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992823005,"difficulty":0.0007176995}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know whether Elizabeth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacquelyn","James","Joseph","Elizabeth"],"index":62131,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9707843661,"difficulty":0.0292156339}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher knows whether someone is thirsty. It is publicly announced that Patricia knows whether Patricia is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Christopher can now know whether Patricia can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Christopher"],"index":60750,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994578958,"difficulty":0.0005421042}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Margaret can now know whether Annemarie can know that Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Annemarie","Ronda","Madeline","Margaret"],"index":48314,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9902932644,"difficulty":0.0097067356}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Pauline can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","Darryl","Joseph","Michael"],"index":52748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998883307,"difficulty":0.001116693}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa is not thirsty. It is publicly announced that John knows whether Teresa is thirsty. It is publicly announced that Teresa does not know whether Chiquita is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Teresa can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Charles","Chiquita","Teresa"],"index":18765,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9849618673,"difficulty":0.0150381327}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ina's card is shown to Yolanda. Caleb's card is shown to Yolanda. Yolanda's card is shown to Page. Page's card is shown to Page. Ina's card is shown to Page. Ina's card is shown to Ina. Yolanda's card is shown to Caleb. Ina's card is shown to Caleb. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Yolanda can now know that Ina can know that Caleb picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Yolanda","Page","Ina","Caleb"],"index":13599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975036979,"difficulty":0.0024963021}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Betty can now know whether Kelley can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Betty","Kelley"],"index":37932,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993275404,"difficulty":0.0006724596}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Johnnie does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Bernice can now know that Shanna can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnnie","Bernice","Michael","Shanna"],"index":55484,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992291927,"difficulty":0.0007708073}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristen can now know that James can know that Kristen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kristen","Richard","Michelle","James"],"index":15267,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984180927,"difficulty":0.0015819073}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina knows whether Pearle's forehead is muddy. It is publicly announced that Christina knows whether Christina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Shantel can now know whether Pearle can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pearle","Christina","Shantel"],"index":43266,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994372725,"difficulty":0.0005627275}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Toney is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Maureen can now know that Toney can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maureen","Toney"],"index":41604,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9614562988,"difficulty":0.0385437012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Donald can now know whether Dorothy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Donald","Aisha"],"index":40149,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994651675,"difficulty":0.0005348325}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Margaret can now know that William can know that Marianne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Margaret","Marianne"],"index":30391,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971398115,"difficulty":0.0028601885}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Kenneth. Debbie's card is shown to Kenneth. Debbie's card is shown to Gary. Debbie's card is shown to Debbie. It is publicly announced that someone picked a red card. It is publicly announced that Gary does not know whether or not everyone picked a red card. It is publicly announced that Debbie does not know whether Gary picked a red card. It is publicly announced that Debbie does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] (Agentb knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Gary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kenneth","Gary","Debbie"],"index":12907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994354844,"difficulty":0.0005645156}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sabrina's card is shown to Gregory. Michael's card is shown to Gregory. Sabrina's card is shown to Sabrina. Sabrina's card is shown to Sally. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sabrina can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Sabrina","Sally","Michael"],"index":54912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988849759,"difficulty":0.0011150241}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that Peggy's forehead is muddy. It is publicly announced that Peggy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"David can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Peggy","David"],"index":14605,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983831644,"difficulty":0.0016168356}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is muddy. It is publicly announced that Keri knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Keri can now know that Nancy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edgar","Nancy","Keri"],"index":2169,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990390539,"difficulty":0.0009609461}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kathrine can now know that Ruth can know that Kathrine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gerald","Claude","Ruth","Kathrine"],"index":51119,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9926356673,"difficulty":0.0073643327}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Vera can now know whether Vernon can know that Vernon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Russell","Vernon","Juana","Vera"],"index":14027,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992590547,"difficulty":0.0007409453}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Armando's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentd knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Donald can now know whether James can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Armando","Caridad","Donald"],"index":53838,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992899895,"difficulty":0.0007100105}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Richard's card is shown to Robert. Kenneth's card is shown to Richard. Robert's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Anthony's card is shown to Kenneth. Kenneth's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know whether Anthony can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Richard","Kenneth","Anthony"],"index":7000,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990763664,"difficulty":0.0009236336}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Inez is not thirsty. It is publicly announced that Inez is not thirsty. It is publicly announced that Jane does not know whether Willis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jane can now know that Inez can know that Inez is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Willis","Jane","Shirley","Inez"],"index":60795,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8434568048,"difficulty":0.1565431952}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Roland. Donnie's card is shown to Roland. Roland's card is shown to Donnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Roland","Donnie","Edward"],"index":67478,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993430972,"difficulty":0.0006569028}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Richard can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Robert","Gaynelle","Lillie"],"index":24095,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994507432,"difficulty":0.0005492568}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffry is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Ann can now know whether Ann is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffry","Hope","Ann"],"index":44770,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988049269,"difficulty":0.0011950731}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruby knows whether Frankie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Frankie can now know that Ruby can know that Alfred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alfred","Frankie","Ruby"],"index":63992,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9945350885,"difficulty":0.0054649115}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmie's card is shown to Cheryl. Debbie's card is shown to Cheryl. Walter's card is shown to Jimmie. Debbie's card is shown to Debbie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jimmie can now know whether Cheryl can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Walter","Jimmie","Debbie"],"index":46580,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993799925,"difficulty":0.0006200075}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Ronald can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherry","Ronald","Robert"],"index":28118,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.990799129,"difficulty":0.009200871}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kurt does not know whether or not everyone is thirsty. It is publicly announced that Fred does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kurt can now know that Fred can know that Kurt is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steve","Kurt","Fred"],"index":45230,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9036684632,"difficulty":1.9036684632}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Judith can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Judith"],"index":18399,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984753728,"difficulty":0.0015246272}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Raymond's forehead is muddy. It is publicly announced that Ashley does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ashley can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Raymond","John","Ashley","Robert"],"index":47642,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992939234,"difficulty":0.0007060766}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pamela does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Emily can now know whether Emily is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Pamela","Emily","Mary"],"index":31103,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9915130734,"difficulty":0.0084869266}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Alec knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Alec can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donald","Michael","Alton","Alec"],"index":62978,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994310737,"difficulty":0.0005689263}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Frank can now know whether John can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janet","Frank","John"],"index":12040,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994440675,"difficulty":0.0005559325}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Virginia can now know that Sheila can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sheila","Virginia","Leo"],"index":48155,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989687204,"difficulty":0.0010312796}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Caitlin does not know whether Sabrina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Doug can now know whether Sabrina can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Caitlin","Doug","Sabrina"],"index":38931,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994273186,"difficulty":0.0005726814}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Era's card is shown to Jeffrey. Jeffrey's card is shown to Michael. Michael's card is shown to Michael. Terry's card is shown to Michael. Jeffrey's card is shown to Era. Terry's card is shown to Era. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Terry can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Michael","Terry","Era"],"index":28387,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990516305,"difficulty":0.0009483695}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Antonio","Carol","Robert"],"index":35501,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5877984762,"difficulty":1.5877984762}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Darrell. Yvonne's card is shown to Darrell. Yvonne's card is shown to Bret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Yvonne can now know that Darrell can know whether Bret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darrell","Yvonne","Bret"],"index":66394,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981045723,"difficulty":0.0018954277}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ethel's card is shown to Ethel. Glenn's card is shown to Glenn. Glenn's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Glenn can now know that Ethel can know whether Glenn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ethel","Glenn","Donna"],"index":64324,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.729606688,"difficulty":1.729606688}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lola does not know whether Lola's forehead is muddy. It is publicly announced that Ricky knows whether Barbara's forehead is muddy. It is publicly announced that Lola does not know whether Lola's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"David can now know whether Lola can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lola","Ricky","David","Barbara"],"index":7829,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5514051318,"difficulty":0.4485948682}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Douglas. Thomas's card is shown to Thomas. Rex's card is shown to Thomas. Douglas's card is shown to Charles. Charles's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rex can now know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Douglas","Thomas","Rex","Charles"],"index":24709,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5304313898,"difficulty":1.5304313898}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Eric. Eric's card is shown to Eric. Eric's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Daniel can now know whether Eric can know whether Randy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Eric","Randy"],"index":61836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984200001,"difficulty":0.0015799999}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that April knows whether Ryan's forehead is muddy. It is publicly announced that April's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"April can now know that Ryan can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ryan","April"],"index":33467,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99827075,"difficulty":0.00172925}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Merrill's card is shown to Merrill. Larry's card is shown to Larry. Doris's card is shown to Doris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know whether Merrill picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Merrill","Larry","Shelley","Doris"],"index":43756,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6438894868,"difficulty":0.3561105132}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Craig knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Craig can now know that Eric can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Craig","Billy","Eric"],"index":19576,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9592400789,"difficulty":0.0407599211}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shawn is not thirsty. It is publicly announced that Shawn does not know whether Betty is thirsty. It is publicly announced that David does not know whether Betty is thirsty. It is publicly announced that David knows whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Shawn can now know whether Julio can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shawn","David","Betty","Julio"],"index":32073,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9899716377,"difficulty":0.0100283623}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy knows whether or not everyone's forehead is muddy. It is publicly announced that Gladys knows whether Jeremy's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Jeremy can now know that Gladys can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeremy","Gladys"],"index":24966,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988403916,"difficulty":0.0011596084}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Ida can now know whether Kenneth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samuel","Catherine","Ida","Kenneth"],"index":18504,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994445443,"difficulty":0.0005554557}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Thomas can now know that Helen can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Henry","Helen","Thomas","Jason"],"index":58613,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994279742,"difficulty":0.0005720258}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Daniel's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Paul can now know whether Robin can know whether Robin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robin","Daniel","Paul"],"index":31936,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989138842,"difficulty":0.0010861158}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shane does not know whether Shane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lisa can now know that Barbra can know that Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Barbra","Shane","Lisa"],"index":41101,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969702959,"difficulty":0.0030297041}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elliot does not know whether Mohamed is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Mohamed can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elliot","Mohamed"],"index":36649,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9928574562,"difficulty":0.0071425438}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Tim can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lawrence","Tim","Jeffrey"],"index":65142,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995136261,"difficulty":0.0004863739}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Tanya's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tanya","Gary","Michael"],"index":64641,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993240833,"difficulty":0.0006759167}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether Gary is thirsty. It is publicly announced that Katrina does not know whether Anthony is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Anthony can now know that Katrina can know whether Gary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Katrina","Gary","Grace"],"index":51999,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976559877,"difficulty":0.0023440123}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Willie can now know that Hazel can know that Willie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hazel","George","Willie","Colin"],"index":65800,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997294724,"difficulty":0.002705276}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jane's card is shown to Jane. Truman's card is shown to Jane. Jane's card is shown to Truman. It is publicly announced that someone picked a red card. It is publicly announced that Jane knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jane can now know whether Jane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jane","Truman"],"index":15569,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9535514712,"difficulty":0.0464485288}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ronnie can now know whether David can know whether Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Ronnie","David"],"index":21870,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993681312,"difficulty":0.0006318688}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Sandra can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Carl","Christine"],"index":56705,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989816546,"difficulty":0.0010183454}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elmer's card is shown to Elmer. Dorothy's card is shown to Elmer. Elmer's card is shown to Dorothy. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy knows whether someone picked a red card. It is publicly announced that Dorothy knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Dorothy can now know that Elmer can know whether Elmer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elmer","Dorothy"],"index":47921,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6662372351,"difficulty":1.6662372351}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilyn does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Judith can now know that Michael can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judith","Michael","Marilyn","Eve"],"index":25287,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5466572642,"difficulty":0.4533427358}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Christopher. Christopher's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Walter can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christopher","Walter"],"index":65257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994095564,"difficulty":0.0005904436}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janelle knows whether Janelle's forehead is muddy. It is publicly announced that Cortez's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Janelle can now know that Cortez can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Cortez","Janelle"],"index":25653,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940496683,"difficulty":0.0059503317}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Brandon's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Orlando can now know that Brandon can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brandon","Orlando","Hector"],"index":57529,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993426204,"difficulty":0.0006573796}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Marta knows whether Marta is thirsty. It is publicly announced that Marta knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Sharon can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sharon","Carol","Marta"],"index":18648,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994120598,"difficulty":0.0005879402}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Sharon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Donna can now know that Donna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Mary","Sharon"],"index":20380,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951879978,"difficulty":0.0048120022}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annie does not know whether Judy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Kay can now know whether Judy can know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Judy","Kay","Annie"],"index":62497,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9933524132,"difficulty":0.0066475868}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Pam does not know whether Jacques is thirsty. It is publicly announced that Virginia does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Pam can now know that Virginia can know whether Jacques is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Virginia","Pam","Jacques","Mary"],"index":59324,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981629252,"difficulty":0.0018370748}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Eloise can now know that Stefanie can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kristofer","Stefanie","Eloise"],"index":17873,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994290471,"difficulty":0.0005709529}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kimberly can now know whether Mary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Mary","Kimberly"],"index":67161,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.994969666,"difficulty":0.005030334}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorraine knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lorraine can now know whether David can know that Kim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lorraine","David","Timothy","Kim"],"index":60426,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994377494,"difficulty":0.0005622506}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to George. Dalila's card is shown to George. Velvet's card is shown to Velvet. Velvet's card is shown to Dalila. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"George can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Velvet","Dalila"],"index":17649,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944463968,"difficulty":0.0055536032}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Susan. Jesse's card is shown to Jesse. Mark's card is shown to Jesse. Susan's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Jesse picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Susan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Jesse","Mark"],"index":64369,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7927910686,"difficulty":1.7927910686}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pete does not know whether Pete's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Pete can now know that Linda can know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pete","Linda"],"index":1232,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.858982265,"difficulty":1.858982265}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Francis. Jerry's card is shown to Francis. Jerry's card is shown to Jerry. Gerald's card is shown to Jerry. Francis's card is shown to Gerald. Jerry's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that Gerald knows whether Jerry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Gerald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francis","Jerry","Gerald"],"index":4051,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990465045,"difficulty":0.0009534955}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Louise. Louise's card is shown to Terry. Terry's card is shown to Terry. Yvette's card is shown to Terry. Louise's card is shown to Yvette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Louise can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Louise","Terry","Yvette"],"index":41532,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989797473,"difficulty":0.0010202527}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Misty does not know whether Buddy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Henry can now know that Misty can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Buddy","Misty","Henry"],"index":42633,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962894917,"difficulty":0.0037105083}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Steven can now know that Kimberly can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Steven","Kimberly"],"index":51935,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993543029,"difficulty":0.0006456971}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Ronald can now know whether Elizabeth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Elizabeth","Glayds","Christie"],"index":62817,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7011601329,"difficulty":0.2988398671}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lesli's card is shown to Harold. April's card is shown to Harold. Harold's card is shown to Anthony. Lesli's card is shown to Anthony. Lesli's card is shown to Lesli. Anthony's card is shown to April. It is publicly announced that someone picked a red card. It is publicly announced that April picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Anthony can now know whether Harold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harold","Anthony","Lesli","April"],"index":15710,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8483694196,"difficulty":0.1516305804}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristy's card is shown to Inez. Ingrid's card is shown to Ingrid. Wayne's card is shown to Ingrid. Kristy's card is shown to Ingrid. Ingrid's card is shown to Wayne. Wayne's card is shown to Kristy. It is publicly announced that someone picked a red card. It is publicly announced that Kristy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Wayne can now know that Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Inez","Ingrid","Wayne","Kristy"],"index":63554,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9024978876,"difficulty":1.9024978876}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Pauline. Wayne's card is shown to Pauline. Pauline's card is shown to Wayne. It is publicly announced that someone picked a red card. It is publicly announced that Wayne does not know whether Wayne picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Wayne can now know whether Pauline can know that Wayne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pauline","Wayne"],"index":27324,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7458900809,"difficulty":1.7458900809}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Julie. Jeanette's card is shown to Julie. Julie's card is shown to John. John's card is shown to John. Linda's card is shown to John. Jeanette's card is shown to John. Julie's card is shown to Linda. John's card is shown to Jeanette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Julie can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","John","Linda","Jeanette"],"index":48086,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7222588658,"difficulty":0.2777411342}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Darlene can now know that Luke can know that Luke's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Deborah","Luke","Darlene"],"index":42476,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977706671,"difficulty":0.0022293329}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Tanya's card is shown to Robert. Gary's card is shown to Robert. Katherine's card is shown to Robert. Robert's card is shown to Tanya. Tanya's card is shown to Tanya. Gary's card is shown to Tanya. Tanya's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether Katherine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Tanya can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Tanya","Gary","Katherine"],"index":20258,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990416169,"difficulty":0.0009583831}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tammy's card is shown to Tammy. Rosa's card is shown to Tammy. Rosa's card is shown to Rosa. It is publicly announced that someone picked a red card. It is publicly announced that Tammy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Tammy can now know that Rosa can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tammy","Rosa","James"],"index":67673,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9566821456,"difficulty":0.0433178544}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Toni knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Toni can now know whether Shayla can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shayla","Dale","Louise","Toni"],"index":17859,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9869508147,"difficulty":0.0130491853}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Miriam. Miriam's card is shown to Beverly. Beverly's card is shown to Beverly. Beverly's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Beverly does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know that Miriam can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Miriam","Beverly","Karen"],"index":61664,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989362359,"difficulty":0.0010637641}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Jane. Jane's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"William can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jane","William"],"index":25562,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994508624,"difficulty":0.0005491376}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"April can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["April","Roxanne","William","Jimmy"],"index":15303,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987737536,"difficulty":0.0012262464}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christina can now know that Marie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christina","Stuart","Marie","William"],"index":21414,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9936705828,"difficulty":0.0063294172}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heidi's card is shown to Heidi. Ranae's card is shown to Ranae. Heidi's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Heidi","Ranae","Thomas"],"index":30002,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993531108,"difficulty":0.0006468892}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Su knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Su can now know whether Raymond can know that Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Raymond","Bert","Su"],"index":1464,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992759824,"difficulty":0.0007240176}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Justin","Brenda"],"index":22766,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985494018,"difficulty":0.0014505982}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dolly can now know that Julie can know that Bruce's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bruce","Julie","Dolly"],"index":567,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978366494,"difficulty":0.0021633506}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that George does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brandon can now know whether Brandon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Brandon","Joan"],"index":23918,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8820154071,"difficulty":0.1179845929}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emily's card is shown to Maria. Maria's card is shown to Emily. Dorene's card is shown to Dorene. It is publicly announced that someone picked a red card. It is publicly announced that Dorene knows whether Dorene picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Maria can now know whether Dorene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Emily","Dorene"],"index":4371,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9359275103,"difficulty":1.9359275103}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tristan knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Margaret can now know that Lucas can know whether Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucas","Margaret","Dorothy","Tristan"],"index":40198,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993909597,"difficulty":0.0006090403}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alta is not thirsty. It is publicly announced that Alfred knows whether or not everyone is thirsty. It is publicly announced that Alta knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alfred can now know whether Dorothy can know whether Dorothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfred","Dorothy","Alta","Paul"],"index":21057,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9451129436,"difficulty":0.0548870564}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether or not everyone's forehead is muddy. It is publicly announced that Gerald does not know whether Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Jessica can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","June","Kathleen","Gerald"],"index":56733,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5165361762,"difficulty":1.5165361762}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darryl does not know whether Don is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Darryl can now know whether Don is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Don","Darryl","Dallas"],"index":22006,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974130988,"difficulty":0.0025869012}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geneva does not know whether or not everyone's forehead is muddy. It is publicly announced that Geneva knows whether Eric's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows whether (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Eric can now know whether Sandy can know that Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geneva","Gayle","Sandy","Eric"],"index":60532,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6265974045,"difficulty":0.3734025955}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Doug can now know that Mary can know that Nicole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Nicole","Doug"],"index":45446,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9892087579,"difficulty":0.0107912421}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Christopher can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elena","Christopher","Mary"],"index":26471,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979945421,"difficulty":0.0020054579}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nathaniel can now know that Richard can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Abel","Nathaniel","Richard"],"index":10316,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9913357496,"difficulty":0.0086642504}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eduardo knows whether Eduardo is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Richard can now know whether Jaime can know whether Eduardo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Eduardo","Jaime"],"index":21992,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991346002,"difficulty":0.0008653998}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernice does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"John can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Bernice","John","Victoria"],"index":53981,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989855886,"difficulty":0.0010144114}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Jessica can now know that Sheila can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sheila","Jessica","Donald","Doris"],"index":46560,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993748069,"difficulty":0.0006251931}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Belinda does not know whether John is thirsty. It is publicly announced that Belinda does not know whether Steven is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Dustin can now know that Belinda can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Dustin","Steven","Belinda"],"index":58455,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951744676,"difficulty":0.0048255324}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sadie knows whether someone's forehead is muddy. It is publicly announced that Lori does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Sadie can now know that Lori can know that Sadie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sadie","Cora","Lori"],"index":37688,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8195564747,"difficulty":0.1804435253}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Myron can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Myron","Robert"],"index":34936,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994626641,"difficulty":0.0005373359}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Seth's card is shown to Seth. Seth's card is shown to Matthew. Matthew's card is shown to Matthew. Tammy's card is shown to Matthew. Matthew's card is shown to Tammy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Seth can now know whether Tammy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Seth","Matthew","Tammy"],"index":19226,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9221842289,"difficulty":0.0778157711}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen does not know whether or not everyone's forehead is muddy. It is publicly announced that Lynne knows whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Karen can now know that Melissa can know that Karen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Lynne","Jennifer","Melissa"],"index":13584,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7445039153,"difficulty":1.7445039153}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ryan can now know that Amanda can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ryan","Amanda","Charles"],"index":24961,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988823533,"difficulty":0.0011176467}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michele knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jenny can now know that Michele can know that Michele's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michele","Jenny"],"index":61978,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951928854,"difficulty":0.0048071146}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence knows whether or not everyone's forehead is muddy. It is publicly announced that Clarence knows whether Justin's forehead is muddy. It is publicly announced that Clarence knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Clarence can now know that Justin can know that Justin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Clarence","Justin"],"index":1026,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9950386882,"difficulty":0.0049613118}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gretchen's card is shown to Benjamin. Benjamin's card is shown to Kenneth. Kenneth's card is shown to Kristen. Gretchen's card is shown to Kristen. Kristen's card is shown to Gretchen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristen can now know whether Kenneth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Benjamin","Kenneth","Kristen","Gretchen"],"index":7627,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993919134,"difficulty":0.0006080866}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Verla's card is shown to Robert. Juan's card is shown to Verla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Juan can now know whether Robert can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Juan","Robert","Verla"],"index":11315,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9580473304,"difficulty":0.0419526696}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Clayton knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Kevin can now know whether Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clayton","Richard","Kevin"],"index":36477,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9245730639,"difficulty":0.0754269361}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan knows whether Clara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Alan can now know whether Alan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alan","Alicia","Clara"],"index":44991,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994161129,"difficulty":0.0005838871}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank's forehead is not muddy. It is publicly announced that Frank knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Frank can now know that Martha can know whether Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carol","Martha","Frank"],"index":65555,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9735941887,"difficulty":0.0264058113}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Amanda can now know that Pauline can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amanda","Pauline","Albert"],"index":62684,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989708662,"difficulty":0.0010291338}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony knows whether Tony's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Charles can now know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tony","Charles"],"index":58463,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978634715,"difficulty":0.0021365285}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susana does not know whether Susana's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Susana can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","Susana","Mary"],"index":59539,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994402528,"difficulty":0.0005597472}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark's forehead is muddy. It is publicly announced that Mark knows whether Joseph's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Robert can now know whether Mark can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Robert","Mark"],"index":18859,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992565513,"difficulty":0.0007434487}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Rose's card is shown to Rose. Barbara's card is shown to Daniel. Rose's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Rose picked a red card. It is publicly announced that Anthony knows whether Rose picked a red card. It is publicly announced that Barbara does not know whether Daniel picked a red card. It is publicly announced that Rose knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows whether (Agentd knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Rose can now know whether Anthony can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Rose","Daniel","Anthony"],"index":27720,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9118089676,"difficulty":1.9118089676}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Ann","William","Joseph"],"index":29190,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7073409557,"difficulty":0.2926590443}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hubert's card is shown to Adela. Adela's card is shown to Hubert. Hubert's card is shown to Nettie. It is publicly announced that someone picked a red card. It is publicly announced that Adela picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Nettie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Adela can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Harry","Adela","Hubert","Nettie"],"index":8523,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990031123,"difficulty":0.0009968877}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alberta knows whether or not everyone's forehead is muddy. It is publicly announced that Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Douglas can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Douglas","Yolanda","Alberta","Miguel"],"index":49424,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linette does not know whether Linette's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linette knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Linette can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linette","James","Mary"],"index":40050,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9559815526,"difficulty":0.0440184474}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Mattie can now know that Seth can know that Sam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Seth","Sam","Betty","Mattie"],"index":35947,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9914016128,"difficulty":0.0085983872}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Judy can now know whether Larry can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Rosa","Judy","Karin"],"index":63611,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9382839799,"difficulty":1.9382839799}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Pauline. William's card is shown to William. Clyde's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","William","Clyde","Richard"],"index":40208,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989131689,"difficulty":0.0010868311}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Dennis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Virginia","Dennis"],"index":16176,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987975359,"difficulty":0.0012024641}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antoinette knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Ellen can now know whether Antoinette can know that Thelma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Antoinette","Thelma","Ellen"],"index":4831,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994378686,"difficulty":0.0005621314}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kimberly","Jason","Mary"],"index":36527,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998506248,"difficulty":0.001493752}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Frank can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Frank","Tammy","Victor"],"index":36050,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991080165,"difficulty":0.0008919835}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to William. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Paul"],"index":58670,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993497014,"difficulty":0.006502986}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerry does not know whether Lillie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jerry can now know whether Lillie can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jerry","Lillie"],"index":57118,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992591739,"difficulty":0.0007408261}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janet can now know that Carlos can know whether Jordan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carlos","Shay","Jordan","Janet"],"index":13857,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983002543,"difficulty":0.0016997457}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether Jacob's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacob's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Helen can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Richard","John","Jacob"],"index":54908,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989945292,"difficulty":0.0010054708}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jerry can now know that Charles can know whether Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Jerry","Aimee","Charles"],"index":3938,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.941691637,"difficulty":0.058308363}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carolyn can now know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Jason","Carolyn","Luis"],"index":40845,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976812601,"difficulty":0.0023187399}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luke does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Bernard is thirsty. It is publicly announced that Bernard knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Luke can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Luke","Bernard"],"index":58065,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994720817,"difficulty":0.0005279183}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kacy knows whether Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Crystal can now know whether Kacy can know whether Kacy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Kacy","Richard"],"index":48596,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994021654,"difficulty":0.0005978346}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Carrie can now know whether John can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carrie","Charles","John"],"index":8646,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994500279,"difficulty":0.0005499721}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether Chad can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Darlene","Chad","Charles"],"index":45177,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999275744,"difficulty":0.000724256}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lillie can now know whether Thomas can know that Lillie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lillie","Thomas"],"index":67230,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994285703,"difficulty":0.0005714297}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether someone's forehead is muddy. It is publicly announced that Larry knows whether someone's forehead is muddy. It is publicly announced that Larry knows whether someone's forehead is muddy. It is publicly announced that Larry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lindsey can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Lindsey","Michael"],"index":62591,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966345429,"difficulty":0.0033654571}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jamar is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Shirley can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jamar","Michael","Bettina","Shirley"],"index":64047,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995132685,"difficulty":0.0004867315}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tanya knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Warren can now know whether Tanya can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tanya","Warren"],"index":21573,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.83294034,"difficulty":0.16705966}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Thomas can now know whether Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Vickie","James","Jessica"],"index":3061,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994445443,"difficulty":0.0005554557}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Michelle can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Michelle","Robert"],"index":55940,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984052777,"difficulty":0.0015947223}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leanne knows whether Eleanor's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Leanne can now know that Eleanor can know that Freddy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Freddy","Leanne","Eleanor"],"index":33420,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979513288,"difficulty":0.0020486712}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tyrone does not know whether Raymond is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Raymond can now know that Tyrone can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Raymond","Tyrone"],"index":58084,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9900301695,"difficulty":0.0099698305}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether someone's forehead is muddy. It is publicly announced that Kermit does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Kermit","Isidro","Michael"],"index":3303,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999450624,"difficulty":0.000549376}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Nicole knows whether Judith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Victoria can now know whether Judith can know that Victoria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicole","Victoria","Judith"],"index":23938,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993312359,"difficulty":0.0006687641}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Jeffrey can now know that Clarence can know whether Clarence's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Jeffrey","Clarence","David"],"index":49521,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9927216172,"difficulty":0.0072783828}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Brett can now know that Kevin can know whether Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Martha","Samuel","Kevin","Brett"],"index":21435,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994211197,"difficulty":0.0005788803}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte does not know whether Chun is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Paulette knows whether someone is thirsty. It is publicly announced that Chun does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Chun can now know that Chun is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Paulette","Charlotte","Chun"],"index":3720,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7602504492,"difficulty":1.7602504492}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bryon can now know that Francisco's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francisco","Joseph","Bryon","Mark"],"index":51928,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977338314,"difficulty":0.0022661686}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shenna knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Charles knows whether Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Crystal can now know whether Charles can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Patricia","Shenna","Crystal"],"index":21368,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993620515,"difficulty":0.0006379485}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clayton does not know whether Clayton's forehead is muddy. It is publicly announced that Lauren knows whether Lauren's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lauren can now know that Clayton can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","Tina","Lauren","Clayton"],"index":22780,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.999063313,"difficulty":0.000936687}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harry's card is shown to Arthur. Don's card is shown to Louisa. Harry's card is shown to Don. It is publicly announced that someone picked a red card. It is publicly announced that Don does not know whether Arthur picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Arthur can now know whether Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Louisa","Don","Harry"],"index":40623,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8423227668,"difficulty":1.8423227668}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heidi's card is shown to Ronald. Ronald's card is shown to Bradley. Mandy's card is shown to Mandy. It is publicly announced that someone picked a red card. It is publicly announced that Heidi does not know whether Heidi picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Bradley can now know that Ronald can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Bradley","Heidi","Mandy"],"index":59553,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994168282,"difficulty":0.0005831718}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Maria can now know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Kathryn","Angelo","Amanda"],"index":19031,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928719401,"difficulty":0.0071280599}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lindsay's card is shown to Brooke. William's card is shown to Kathleen. Lindsay's card is shown to Kathleen. Brooke's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that William picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"William can now know that Brooke can know that Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brooke","Kathleen","William","Lindsay"],"index":25443,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957717061,"difficulty":0.0042282939}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jeanie can now know whether Carolyn can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Carl","Carolyn","Jeanie"],"index":64506,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993676543,"difficulty":0.0006323457}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miguel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Suzanne can now know that Miguel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Suzanne","Miguel"],"index":7019,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990239143,"difficulty":0.0009760857}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vera's card is shown to Vera. Valerie's card is shown to Juan. Juan's card is shown to Valerie. Valerie's card is shown to Valerie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Juan can now know whether Vera can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vera","Juan","Valerie"],"index":49088,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994058609,"difficulty":0.0005941391}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Richard can now know whether Micheal can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Micheal","Curtis","Richard","Kevin"],"index":26672,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992406368,"difficulty":0.0007593632}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hien knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ada can now know whether Michael can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Ada","Hien"],"index":64518,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993783236,"difficulty":0.0006216764}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Steven. Heather's card is shown to Steven. Larry's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know whether Heather can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Heather","Larry"],"index":21592,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994028807,"difficulty":0.0005971193}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Larry. Ron's card is shown to Larry. Ron's card is shown to Ron. Ron's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Larry can now know that Ron can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Larry","Ron","Michael"],"index":36392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9838584065,"difficulty":0.0161415935}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ralph can now know that Ralph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Julie","Ralph","Kimiko"],"index":37494,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973937273,"difficulty":0.0026062727}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobby's card is shown to Bobby. Theodore's card is shown to Bobby. Bobby's card is shown to Theodore. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Deanna can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deanna","Bobby","Theodore","Mary"],"index":27314,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980980754,"difficulty":0.0019019246}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Sandy's card is shown to Joseph. Sandy's card is shown to Sandy. Stanley's card is shown to Sandy. Stanley's card is shown to Stanley. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know that Stanley can know that Stanley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Sandy","Stanley"],"index":15283,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5780093074,"difficulty":1.5780093074}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mamie can now know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mamie","William","Kathleen"],"index":55402,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977510571,"difficulty":0.0022489429}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Matthew can know that Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Ruth","William","Matthew"],"index":45766,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977389574,"difficulty":0.0022610426}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra does not know whether Gertrude is thirsty. It is publicly announced that Timothy does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Gertrude does not know whether Sandra is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Gertrude can now know that Timothy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Gertrude","Sandra"],"index":14506,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993864298,"difficulty":0.0006135702}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Richard's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"John can now know whether Richard can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","John"],"index":49425,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994404912,"difficulty":0.0005595088}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Joanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Richard can now know whether Johnnie can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnnie","Richard","Joanne"],"index":64457,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994270802,"difficulty":0.0005729198}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cynthia does not know whether Christy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Francis can now know that John can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Francis","John","Christy","Cynthia"],"index":21393,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988684654,"difficulty":0.0011315346}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sylvia does not know whether Giselle is thirsty. It is publicly announced that Giselle does not know whether Carl is thirsty. It is publicly announced that Sylvia does not know whether Giselle is thirsty. It is publicly announced that Sylvia does not know whether Frieda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentc knows whether (Agentd knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Carl can now know whether Sylvia can know that Frieda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frieda","Giselle","Carl","Sylvia"],"index":47984,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9794537425,"difficulty":0.0205462575}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willard does not know whether Willard's forehead is muddy. It is publicly announced that Estell does not know whether Estell's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Estell can now know that Carolyn can know that Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Willard","Carolyn","Estell"],"index":55098,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9868311882,"difficulty":1.9868311882}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Faye's card is shown to Kerri. Robert's card is shown to Kerri. Kerri's card is shown to Faye. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Kerri does not know whether Rachel picked a red card. It is publicly announced that Rachel does not know whether Kerri picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Faye can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rachel","Kerri","Faye","Robert"],"index":63258,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8371124268,"difficulty":0.1628875732}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Thomas","Douglas"],"index":24598,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990270138,"difficulty":0.0009729862}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond does not know whether Juan is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Ashlee can now know that Raymond can know whether Juan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juan","Ashlee","Raymond"],"index":65262,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958155751,"difficulty":0.0041844249}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacqueline knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Jacqueline can now know that Nathan can know that Nathan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jacqueline","Nathan","Bernice"],"index":32399,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996068716,"difficulty":0.003931284}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lauren's card is shown to Lauren. Demetrius's card is shown to Lauren. Lauren's card is shown to Demetrius. It is publicly announced that someone picked a red card. It is publicly announced that Lauren does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Diana can now know that Lauren can know that Demetrius picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Diana","Lauren","Demetrius"],"index":14132,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7588365078,"difficulty":0.2411634922}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mary can now know whether David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Gregory","Mary"],"index":15399,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6030655503,"difficulty":0.3969344497}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lester's card is shown to Tara. Cecelia's card is shown to Tara. Lester's card is shown to Lester. Tara's card is shown to Cecelia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tara can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tara","Lester","Cecelia"],"index":2964,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992871881,"difficulty":0.0007128119}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lawrence does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Patricia can now know whether Lawrence can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Natalie","Lawrence","Patricia","Maynard"],"index":37853,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994180202,"difficulty":0.0005819798}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ralph does not know whether Julie is thirsty. It is publicly announced that Ralph knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Julie can now know that Ralph can know that Julie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ralph","Julie"],"index":51114,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9944458008,"difficulty":0.0055541992}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Melvin can now know whether Joyce can know that Melvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Barbara","Tiffany","Melvin"],"index":33653,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9951381087,"difficulty":0.0048618913}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that April does not know whether April's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"April can now know whether Catherine can know that April's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Catherine","April","Frances"],"index":44771,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9754123688,"difficulty":0.0245876312}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Tawana is thirsty. It is publicly announced that Tawana does not know whether Elizabeth is thirsty. It is publicly announced that Elizabeth does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Joseph can now know that Elizabeth can know whether Kathryn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathryn","Joseph","Elizabeth","Tawana"],"index":29392,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976171851,"difficulty":0.0023828149}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jill does not know whether Laurence is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jill can now know that Donna can know whether Laurence is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donna","Laurence","Jill"],"index":48727,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977270961,"difficulty":0.0022729039}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jaime knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jaime can now know whether Gilbert can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jaime","Gilbert"],"index":29752,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994583726,"difficulty":0.0005416274}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virgil does not know whether Susan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Virgil can now know whether Susan can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Alan","Virgil","Suzanne"],"index":5971,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99920398,"difficulty":0.00079602}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angie's card is shown to James. Gerald's card is shown to James. Angie's card is shown to Angie. Milda's card is shown to Angie. James's card is shown to Milda. Angie's card is shown to Gerald. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Milda picked a red card. It is publicly announced that Angie picked a black card. It is publicly announced that James does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Angie can now know that Milda can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Angie","Milda","Gerald"],"index":4116,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.978982091,"difficulty":0.021017909}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilber's card is shown to Wilber. Rickey's card is shown to Wilber. Jill's card is shown to Jill. Jill's card is shown to Rickey. Rickey's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Rickey does not know whether or not everyone picked a red card. It is publicly announced that Rickey does not know whether Rickey picked a red card. It is publicly announced that Wilber knows whether Rickey picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jill can now know that Rickey can know whether Rickey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wilber","Jill","Rickey","Douglas"],"index":50840,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8148599863,"difficulty":1.8148599863}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Megan does not know whether Megan's forehead is muddy. It is publicly announced that Megan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Marilyn can now know whether Tristan can know whether Beverly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Megan","Tristan","Beverly","Marilyn"],"index":53171,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993075132,"difficulty":0.0006924868}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aaron does not know whether Kathryn is thirsty. It is publicly announced that Kathryn knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Kathryn can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brett","Eula","Kathryn","Aaron"],"index":25988,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989792705,"difficulty":0.0010207295}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Judith can now know that Charles can know whether Judith is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Justin","Charles","Judith"],"index":37994,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941719174,"difficulty":0.0058280826}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know that Edward can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","John","Edward","Donald"],"index":57881,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994229078,"difficulty":0.0005770922}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Phylicia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Phylicia can now know that Warren can know whether Phylicia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Warren","Phylicia"],"index":38200,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9902584553,"difficulty":0.0097415447}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"David can now know that Matt's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Eddie","Matt","Joan"],"index":37356,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979319572,"difficulty":0.0020680428}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know that Vesta can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Teresa","Vesta","Michelle","David"],"index":46871,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994718432,"difficulty":0.0005281568}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nan knows whether Larhonda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"David can now know whether Earl can know whether Nan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nan","Earl","David","Larhonda"],"index":32723,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993946552,"difficulty":0.0006053448}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Derrick does not know whether Derrick's forehead is muddy. It is publicly announced that Demarcus does not know whether Demarcus's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Demarcus can now know that Derrick can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Demarcus","Irma","Derrick"],"index":47520,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994120598,"difficulty":0.0005879402}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Thad. George's card is shown to Thad. Thad's card is shown to Alan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harriet can now know whether Harriet picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thad","Harriet","Alan","George"],"index":19816,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9608873725,"difficulty":0.0391126275}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Travis's card is shown to Travis. Mario's card is shown to Travis. Tayna's card is shown to Travis. Mario's card is shown to Mario. Tayna's card is shown to Tayna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tayna can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Travis","Mario","Tayna"],"index":10820,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989816546,"difficulty":0.0010183454}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry knows whether someone's forehead is muddy. It is publicly announced that Sherry knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agenta knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"John can now know whether Sherry can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Michael","Judith","Sherry"],"index":23209,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994057417,"difficulty":0.0005942583}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Stewart's card is shown to Melissa. Melissa's card is shown to Stewart. It is publicly announced that someone picked a red card. It is publicly announced that Stewart knows whether Stewart picked a red card. It is publicly announced that Stewart picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! 2 ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! 2 ] 0","hypothesis":"Melissa can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Melissa","Stewart"],"index":55790,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9260044694,"difficulty":0.0739955306}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie's forehead is muddy. It is publicly announced that Melanie knows whether Patricia's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Patricia can now know that Melanie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Mark","Melanie"],"index":41334,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989461303,"difficulty":0.0010538697}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know whether Lisa can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","James","Ronald","Jeffrey"],"index":58899,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993801117,"difficulty":0.0006198883}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Victoria does not know whether Kelly is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kelly can now know whether Cheryl can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Victoria","Michael","Kelly"],"index":52583,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994644523,"difficulty":0.0005355477}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] 0","hypothesis":"Jamie can now know that Kevin can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jamie","Mark","Robert","Kevin"],"index":59607,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998729527,"difficulty":0.001270473}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sonya knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Charles can now know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mathew","Charles","Sonya","Christina"],"index":55072,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99765414,"difficulty":0.00234586}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosetta knows whether Daniel's forehead is muddy. It is publicly announced that Rosetta knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Clara can now know whether Rosetta's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Clara","Daniel","Rosetta"],"index":37225,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994235039,"difficulty":0.0005764961}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Esther does not know whether or not everyone is thirsty. It is publicly announced that Esther does not know whether Geri is thirsty. It is publicly announced that Geri knows whether Esther is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Geri can now know whether Esther can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Geri","Esther"],"index":10694,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.996712327,"difficulty":0.003287673}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loretta knows whether or not nobody's forehead is muddy. It is publicly announced that Jesse's forehead is not muddy. It is publicly announced that Loretta's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] Agentc knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"Anthony can now know that Jesse can know that Jesse's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jesse","Elbert","Anthony","Loretta"],"index":52156,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8257001042,"difficulty":0.1742998958}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joel's card is shown to Joel. Joel's card is shown to Grace. Grace's card is shown to Grace. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Grace picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Grace picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Grace can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joel","Grace"],"index":57795,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9928145409,"difficulty":0.0071854591}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cory knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Cory can now know whether Judith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christopher","Cory","Judith"],"index":65022,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994507432,"difficulty":0.0005492568}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wanda does not know whether Ronald is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Ronald can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janette","Ronald","Wanda"],"index":43842,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994638562,"difficulty":0.0005361438}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether Lottie's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia knows whether Lottie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Lottie can now know whether Virginia can know whether Virginia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lottie","Arthur","Virginia","William"],"index":20977,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994029999,"difficulty":0.0005970001}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Mark. Gregory's card is shown to Mark. Mark's card is shown to Gregory. Mark's card is shown to Joshua. Judy's card is shown to Joshua. Gregory's card is shown to Joshua. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Gregory can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","Judy","Gregory","Joshua"],"index":43855,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994294047,"difficulty":0.0005705953}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Joseph can now know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vida","Joseph","Cindy"],"index":16377,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957256317,"difficulty":0.0042743683}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Sara. Judith's card is shown to Judith. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eleanor can now know that Judith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eleanor","Sara","Judith","Michael"],"index":40350,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944850802,"difficulty":0.0055149198}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith does not know whether or not everyone's forehead is muddy. It is publicly announced that Ethelene's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] 0","hypothesis":"Ethelene can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edith","Stuart","Ethelene"],"index":3442,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969962835,"difficulty":0.0030037165}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda knows whether someone is thirsty. It is publicly announced that Eva knows whether Eva is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Brenda can now know whether Eva can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eva","Brenda"],"index":52828,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9897015095,"difficulty":0.0102984905}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether Ernest's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Anna can now know whether Rosa can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anna","Henry","Ernest","Rosa"],"index":63939,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993448853,"difficulty":0.0006551147}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhoda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Rhoda can now know whether Donnie can know whether Donnie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donnie","Joseph","Rhoda","Amber"],"index":56086,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9933534861,"difficulty":1.9933534861}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessica does not know whether Jerome is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Jessica can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jessica","Jerome"],"index":59352,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9928342104,"difficulty":0.0071657896}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Alice. Susan's card is shown to Judith. Carol's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Alice picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alice can now know that Susan can know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Susan","Judith","Carol"],"index":39894,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7707189322,"difficulty":0.2292810678}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sheila knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Kathy can now know that Sheila can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sheila","Kathy","Heath"],"index":32287,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9921781421,"difficulty":0.0078218579}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey does not know whether or not everyone is thirsty. It is publicly announced that Jeffrey does not know whether or not everyone is thirsty. It is publicly announced that Jeffrey does not know whether or not everyone is thirsty. It is publicly announced that Jeffrey does not know whether Antonio is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jeffrey can now know that Antonio can know whether Antonio is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeffrey","Antonio"],"index":39851,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9814658165,"difficulty":0.0185341835}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marlene does not know whether Edna is thirsty. It is publicly announced that Marlene does not know whether Cindy is thirsty. It is publicly announced that Cindy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] Agentc knows whether (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] 0","hypothesis":"Marlene can now know whether Jessie can know whether Cindy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessie","Edna","Marlene","Cindy"],"index":37736,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991543293,"difficulty":0.0008456707}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Joe can now know that Phyliss can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phyliss","Tracie","Joe"],"index":21547,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993410707,"difficulty":0.0006589293}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Scott can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ronald","Scott","Elton"],"index":6837,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9941792488,"difficulty":0.0058207512}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Thomas. Thomas's card is shown to Barbara. Bryan's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Bryan knows whether Bryan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Bryan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Barbara","Bryan"],"index":39810,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8959762454,"difficulty":0.1040237546}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Viola can now know whether Nora can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nora","Viola","Robert"],"index":29737,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994089603,"difficulty":0.0005910397}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debbie's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Debbie knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Debbie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debbie","Thomas"],"index":31989,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994340539,"difficulty":0.0005659461}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Joan. Lindsy's card is shown to Leslie. Lindsy's card is shown to Rhonda. Leslie's card is shown to Rhonda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joan can now know whether Leslie can know whether Rhonda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lindsy","Joan","Leslie","Rhonda"],"index":7561,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985741377,"difficulty":0.0014258623}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Kevin is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Christopher does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Kevin can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kevin","Perry","Christopher","William"],"index":61533,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993921518,"difficulty":0.0006078482}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dan knows whether Christina's forehead is muddy. It is publicly announced that Dan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 1 ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 1 ] 0","hypothesis":"Christina can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dan","Christina"],"index":43575,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994634986,"difficulty":0.0005365014}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jennie can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jennie","Norman","Eileen","Thomas"],"index":2740,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993550181,"difficulty":0.0006449819}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynn knows whether or not everyone's forehead is muddy. It is publicly announced that Lynn does not know whether Lynn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lynn can now know that Everett can know that Leon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lynn","Leon","Everett"],"index":26587,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9862006307,"difficulty":0.0137993693}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Belinda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Belinda can now know that Louis can know that Belinda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicolas","Louis","Belinda"],"index":29558,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979193807,"difficulty":0.0020806193}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rita's card is shown to Rita. Mary's card is shown to Rita. Rita's card is shown to Mary. Courtney's card is shown to Mary. Zachary's card is shown to Courtney. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Zachary can now know whether Zachary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Zachary","Rita","Mary","Courtney"],"index":3139,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7825571895,"difficulty":0.2174428105}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michele knows whether or not everyone's forehead is muddy. It is publicly announced that Michele's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 1 ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Michele can now know whether Kelly can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michele","Kelly"],"index":20725,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994248152,"difficulty":0.0005751848}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maynard knows whether James is thirsty. It is publicly announced that Maynard knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"James can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Maynard"],"index":46888,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979967475,"difficulty":0.0020032525}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Thelma. Trenton's card is shown to Thelma. Thelma's card is shown to Trenton. Thelma's card is shown to Kim. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Trenton can now know that Thelma can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thelma","Trenton","Kim"],"index":26866,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9861102104,"difficulty":0.0138897896}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Jeffrey. Robert's card is shown to Jeffrey. Sarah's card is shown to Jeffrey. Sarah's card is shown to Alice. Alice's card is shown to Sarah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffrey","Robert","Alice","Sarah"],"index":57551,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993414283,"difficulty":0.0006585717}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donny knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Carol can now know that Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","Carol","Donny","Alicia"],"index":8926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975630045,"difficulty":0.0024369955}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Harold. Harold's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that David does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"David can now know whether Harold can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Harold","Lisa"],"index":37842,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9976664782,"difficulty":0.0023335218}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Oliver knows whether or not everyone is thirsty. It is publicly announced that Mary is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Oliver can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Celeste","Oliver","Mary"],"index":28968,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977432489,"difficulty":0.0022567511}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricky's card is shown to Ricky. Danny's card is shown to Ricky. Billy's card is shown to Ricky. Danny's card is shown to Danny. Billy's card is shown to Danny. Danny's card is shown to Ahmad. Ricky's card is shown to Billy. Danny's card is shown to Billy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Billy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ricky","Danny","Ahmad","Billy"],"index":44210,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989739656,"difficulty":0.0010260344}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Tracy's card is shown to Barbara. Dora's card is shown to Tracy. Dora's card is shown to Dora. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Tracy","Dora","Michael"],"index":42325,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989307523,"difficulty":0.0010692477}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristie knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Dennis can now know that Kristie can know whether Kristie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dennis","Kristie"],"index":61194,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9915314317,"difficulty":0.0084685683}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Idella's card is shown to Stefanie. Jill's card is shown to Stefanie. Idella's card is shown to Jill. Stefanie's card is shown to Jill. It is publicly announced that someone picked a red card. It is publicly announced that Stefanie knows whether or not everyone picked a red card. It is publicly announced that Stefanie does not know whether Jill picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Stefanie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Idella","Stefanie","Jill"],"index":50089,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994663596,"difficulty":0.0005336404}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Trudy can now know whether Jessica can know that Helen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Jessica","Trudy"],"index":53043,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9904279709,"difficulty":0.0095720291}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard knows whether or not nobody is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Richard can now know whether Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Richard","Tammy"],"index":43751,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977288842,"difficulty":0.0022711158}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Tamica does not know whether Leola is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Tamica can now know that Tamica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katrina","Tamica","Leola"],"index":52750,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9554586411,"difficulty":0.0445413589}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bernice can now know whether Leo can know whether Leo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Bernice","Leo","Audrey"],"index":28973,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993841648,"difficulty":0.0006158352}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Darrell. Darcie's card is shown to Gregory. Darcie's card is shown to Matthew. Gregory's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Darrell knows whether or not everyone picked a red card. It is publicly announced that Darcie knows whether Darrell picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Darcie can now know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darcie","Darrell","Gregory","Matthew"],"index":47937,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8153125644,"difficulty":0.1846874356}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie does not know whether Stephanie's forehead is muddy. It is publicly announced that George knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Stephanie can now know that George can know whether Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["George","Stephanie"],"index":65065,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9333162308,"difficulty":0.0666837692}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ivory knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Nellie can now know that Ruth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nellie","Ivory","Denise","Ruth"],"index":47909,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989245534,"difficulty":0.0010754466}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Todd. Lisa's card is shown to Janet. Lisa's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Todd picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Janet picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Lisa can now know whether Janet can know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Todd","Janet","Lisa"],"index":27729,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9698556066,"difficulty":0.0301443934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hilario does not know whether Jeffrey is thirsty. It is publicly announced that Hilario does not know whether Carmen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Hilario can now know whether Yolanda can know that Jeffrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hilario","Carmen","Jeffrey","Yolanda"],"index":3923,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9852172732,"difficulty":0.0147827268}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Stephanie. Carl's card is shown to Margaret. Bryan's card is shown to Margaret. Bryan's card is shown to Bryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Carl","Margaret","Bryan"],"index":60333,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989777803,"difficulty":0.0010222197}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen does not know whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Karen can now know that Evan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Milly","Evan"],"index":60121,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989233613,"difficulty":0.0010766387}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Darrell. Anthony's card is shown to Darrell. Darrell's card is shown to Anthony. Anthony's card is shown to Anthony. Darrell's card is shown to Jeremy. William's card is shown to Jeremy. Jeremy's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darrell can now know whether Jeremy can know whether William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrell","Anthony","Jeremy","William"],"index":21325,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988476038,"difficulty":0.0011523962}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nichole knows whether Daniel's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Nichole can now know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Daniel","Nichole"],"index":40071,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9885564446,"difficulty":0.0114435554}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Yolanda. Robert's card is shown to Robert. Kathryn's card is shown to Robert. Robert's card is shown to Kathryn. Yolanda's card is shown to Ronald. Robert's card is shown to Ronald. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Ronald picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Kathryn can now know that Ronald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Yolanda","Robert","Kathryn","Ronald"],"index":29962,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7902139425,"difficulty":1.7902139425}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. John's card is shown to Jessica. Marvin's card is shown to Jessica. Jessica's card is shown to John. Marvin's card is shown to John. Jessica's card is shown to Marvin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Helen","John","Marvin"],"index":59379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946152568,"difficulty":0.0053847432}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Terri knows whether Terri is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Katherine can now know whether Katherine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Terri","Katherine"],"index":44187,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9894176126,"difficulty":0.0105823874}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linwood's card is shown to Dodie. Paul's card is shown to Dodie. Dodie's card is shown to Linwood. Linwood's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Linwood can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dodie","Linwood","Paul"],"index":16459,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993366599,"difficulty":0.0006633401}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janet does not know whether Tammy is thirsty. It is publicly announced that Tammy does not know whether Melody is thirsty. It is publicly announced that Melody does not know whether Janet is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Melody can now know that Tammy can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Enrique","Janet","Melody","Tammy"],"index":33453,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999091506,"difficulty":0.000908494}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry does not know whether Sherry's forehead is muddy. It is publicly announced that Sherry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Pamela can now know whether Alfred can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sherry","Pamela","Alfred","Elsie"],"index":13069,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9661099315,"difficulty":0.0338900685}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Victoria can now know that Ernest can know whether Ernest is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ernest","Jeffrey","Victoria","Charles"],"index":23197,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9723987579,"difficulty":0.0276012421}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Ora's card is shown to Charles. Anna's card is shown to Charles. Charles's card is shown to Justin. Justin's card is shown to Justin. Justin's card is shown to Anna. Anna's card is shown to Anna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ora can now know that Justin can know that Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Ora","Justin","Anna"],"index":7824,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972184896,"difficulty":0.0027815104}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentc knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jack can now know whether Jarvis can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jarvis","Antonio","Jack","James"],"index":63970,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994421601,"difficulty":0.0005578399}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myra does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nathaniel can now know whether Henry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Myra","James","Nathaniel","Henry"],"index":33509,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970549345,"difficulty":0.0029450655}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alec's card is shown to Kyle. Christina's card is shown to Kyle. Alec's card is shown to Alec. Alec's card is shown to Wendy. Kyle's card is shown to Christina. Wendy's card is shown to Christina. It is publicly announced that someone picked a red card. It is publicly announced that Kyle does not know whether Wendy picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Wendy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Kyle can now know whether Alec picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kyle","Alec","Wendy","Christina"],"index":12633,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7687187791,"difficulty":1.7687187791}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia knows whether Julia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Julia can now know that Tillie can know that Dominic's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dominic","Julia","Tillie","Tyrone"],"index":18971,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960772395,"difficulty":0.0039227605}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Carol can now know whether Johnathan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Johnathan","Carol"],"index":37623,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997191608,"difficulty":0.002808392}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Katherine can now know whether Gregory can know that Katherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Katherine","Mark","Gregory"],"index":13974,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960397482,"difficulty":0.0039602518}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Katherine knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Floyd can now know that Floyd's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Katherine","Floyd"],"index":24704,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9950544834,"difficulty":0.0049455166}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Christian's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Guadalupe can now know that Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Timothy","Guadalupe","Christian"],"index":46832,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973025322,"difficulty":0.0026974678}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felisha's card is shown to Felisha. Cassandra's card is shown to Felisha. Mary's card is shown to Cassandra. Mary's card is shown to Violet. Cassandra's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Felisha","Cassandra","Violet","Mary"],"index":16243,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993380904,"difficulty":0.0006619096}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Bruce knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Dorothea can now know that Bruce can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bruce","Dorothea"],"index":3308,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999412179,"difficulty":0.000587821}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janette's card is shown to Teri. Gregory's card is shown to Shirley. Janette's card is shown to Shirley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Janette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Teri","Shirley","Janette"],"index":9200,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970538616,"difficulty":0.0029461384}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Alice can now know that Nancy can know whether Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Carl","Nancy","Oscar"],"index":39597,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9694752097,"difficulty":0.0305247903}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Wilbert can now know that Richard can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wilbert","Richard","Helen"],"index":53669,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989488721,"difficulty":0.0010511279}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether Paige's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Paige's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jennifer can now know that Daniel can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paige","Maria","Daniel","Jennifer"],"index":10965,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996851027,"difficulty":0.003148973}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] 0","hypothesis":"James can now know whether William can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","William"],"index":52082,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9977935553,"difficulty":0.0022064447}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Peggy can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julissa","Nancy","Peggy","Janet"],"index":11785,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991073012,"difficulty":0.0008926988}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clifton's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Clifton can now know that Charles can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clifton","Joyce","Charles"],"index":29827,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987559319,"difficulty":0.0012440681}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kevin can now know that Kathy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kevin","Kathy","William","David"],"index":58734,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9221491218,"difficulty":1.9221491218}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lindsay's card is shown to Lois. Lois's card is shown to Lindsay. Scott's card is shown to Lindsay. Randal's card is shown to Scott. Lois's card is shown to Randal. Lindsay's card is shown to Randal. It is publicly announced that someone picked a red card. It is publicly announced that Lois does not know whether Randal picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Lindsay can now know that Randal picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lois","Lindsay","Scott","Randal"],"index":20364,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971012473,"difficulty":0.0028987527}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nolan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Nolan can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alfonso","Michael","Nolan"],"index":18325,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989883304,"difficulty":0.0010116696}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether Marilyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Marilyn can now know that Christine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marilyn","Christine","Diane"],"index":22568,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982308745,"difficulty":0.0017691255}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether Edna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Gladys can now know whether Terry can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Terry","Edna","Gladys"],"index":25940,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993768334,"difficulty":0.0006231666}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgann's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Georgann can now know that Terry can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Terry","Georgann"],"index":55655,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993332028,"difficulty":0.0006667972}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fabian is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Judy can now know that Fabian is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Fabian","Judy"],"index":65939,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9769336581,"difficulty":0.0230663419}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa does not know whether Lisa's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Dawn can now know whether Lisa can know whether Dawn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dawn","Lisa"],"index":60952,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985353947,"difficulty":0.0014646053}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa's forehead is not muddy. It is publicly announced that Charlie knows whether Vera's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Charlie can now know that Patricia can know that Vera's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlie","Vera","Lisa","Patricia"],"index":58590,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980778694,"difficulty":0.0019221306}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Gerald's card is shown to Michael. Michael's card is shown to Barbara. Roslyn's card is shown to Gerald. Michael's card is shown to Roslyn. Barbara's card is shown to Roslyn. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Barbara picked a red card. It is publicly announced that Barbara does not know whether Gerald picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Gerald can now know that Barbara can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Barbara","Gerald","Roslyn"],"index":45367,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9710581303,"difficulty":0.0289418697}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dianne does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Vena can now know whether Dianne can know whether Vena's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dianne","Kimberly","Vena"],"index":24737,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998090446,"difficulty":0.001909554}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Shirley. Kathleen's card is shown to Kathleen. Kathleen's card is shown to Kevin. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Shirley does not know whether Kevin picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Shirley can now know that Kathleen can know whether Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Kathleen","Kevin"],"index":48506,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5840291381,"difficulty":1.5840291381}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Mary. Florence's card is shown to Mary. Hannah's card is shown to Jessica. Mary's card is shown to Hannah. Hannah's card is shown to Hannah. Florence's card is shown to Florence. It is publicly announced that someone picked a red card. It is publicly announced that Florence knows whether or not everyone picked a red card. It is publicly announced that Jessica does not know whether Mary picked a red card. It is publicly announced that Florence knows whether someone picked a red card. It is publicly announced that Florence does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Hannah can now know that Mary can know that Hannah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Jessica","Hannah","Florence"],"index":38622,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9689721465,"difficulty":0.0310278535}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Edith. Edith's card is shown to Robert. Michelle's card is shown to Robert. Brian's card is shown to Michelle. Michelle's card is shown to Michelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edith can now know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edith","Brian","Robert","Michelle"],"index":30436,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9456396103,"difficulty":1.9456396103}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Emile can now know whether Ellen can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Ellen","Kelly","Emile"],"index":53210,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993602633,"difficulty":0.0006397367}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathleen does not know whether Jenna is thirsty. It is publicly announced that Kathleen does not know whether Tammy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Jenna can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","Jenna","Kathleen","Tammy"],"index":6264,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994168282,"difficulty":0.0005831718}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Glen can now know that Glen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Glen","Francesca","Bryant"],"index":24763,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9925171137,"difficulty":0.0074828863}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Patricia can now know that Michael can know that Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Alfreda","Michael"],"index":44272,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9536295533,"difficulty":0.0463704467}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paula knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Paula can now know whether Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clara","Paula","Sandra"],"index":66589,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994394183,"difficulty":0.0005605817}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jason can now know whether Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mui","Jason","Ronald"],"index":40914,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992833734,"difficulty":0.0007166266}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to David. David's card is shown to Anita. Martha's card is shown to Anita. Anita's card is shown to Anita. It is publicly announced that someone picked a red card. It is publicly announced that Martha knows whether Anita picked a red card. It is publicly announced that David does not know whether Anita picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Martha can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Martha","Anita"],"index":8247,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994064569,"difficulty":0.0005935431}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barton's card is shown to Barton. James's card is shown to Lewis. Lewis's card is shown to James. Barton's card is shown to Clarence. Lewis's card is shown to Clarence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barton can now know that James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barton","Lewis","James","Clarence"],"index":48274,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993768334,"difficulty":0.0006231666}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether Eva's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Eva can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Anna","Eva"],"index":30230,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990072846,"difficulty":0.0009927154}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matilde knows whether Michael's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Matilde can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Norma","Michael","Matilde"],"index":2304,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993021488,"difficulty":0.0006978512}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen does not know whether Paul is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Paul can now know that Lisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Joy","Karen","Paul"],"index":6344,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997841239,"difficulty":0.002158761}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Frank can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Claudia","Virginia","Frank","Emma"],"index":51241,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992903471,"difficulty":0.0007096529}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shelley is thirsty. It is publicly announced that Ray does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Ann can now know that Ann is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ray","Shelley","Ann","Mario"],"index":45981,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6193668842,"difficulty":0.3806331158}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Rosemarie can now know whether Audrey can know that Rosemarie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosemarie","Louisa","Audrey"],"index":2703,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9572345018,"difficulty":0.0427654982}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edwin is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jose can now know that Rolland can know whether Rolland is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annie","Rolland","Jose","Edwin"],"index":32858,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9097172022,"difficulty":0.0902827978}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Tammy does not know whether Cheryl is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Yvonne can now know that Tammy can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tammy","Cheryl","Yvonne"],"index":23678,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999391675,"difficulty":0.000608325}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly's forehead is not muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Josephine can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kimberly","David","Barbara","Josephine"],"index":54503,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990134239,"difficulty":0.0009865761}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wallace does not know whether Wallace's forehead is muddy. It is publicly announced that Wallace does not know whether Wallace's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Wallace can now know whether Scott can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Wallace","Scott"],"index":29404,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999442637,"difficulty":0.000557363}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether Cindi's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Shirley can now know whether Carol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cindi","Carol","Shirley"],"index":38607,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993773103,"difficulty":0.0006226897}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Lee can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donna","Lee","Jennifer","Robert"],"index":19574,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989671707,"difficulty":0.0010328293}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Martin","Steven","Douglas","John"],"index":18422,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978343844,"difficulty":0.0021656156}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Jerry's forehead is muddy. It is publicly announced that Jerry does not know whether Jerry's forehead is muddy. It is publicly announced that Jerry does not know whether Jerry's forehead is muddy. It is publicly announced that Jerry knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"John can now know that Jerry can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Jerry"],"index":41973,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988318086,"difficulty":0.0011681914}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Perry does not know whether Angela is thirsty. It is publicly announced that Nancy knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Nancy can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Perry","Angela","Nancy"],"index":62744,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960428476,"difficulty":0.0039571524}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know that Karen can know that Karen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elaine","Donald","Karen"],"index":25807,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9950246215,"difficulty":0.0049753785}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amber does not know whether or not everyone is thirsty. It is publicly announced that Amber does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Raymond can now know that April can know whether Amber is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amber","Raymond","April"],"index":53917,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8600028753,"difficulty":0.1399971247}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tricia's card is shown to Tricia. Brenda's card is shown to Tricia. Dewey's card is shown to Brenda. Rodney's card is shown to Dewey. Brenda's card is shown to Dewey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rodney can now know that Tricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tricia","Rodney","Brenda","Dewey"],"index":57247,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982361794,"difficulty":0.0017638206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna does not know whether Donna's forehead is muddy. It is publicly announced that Jeremy knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Barbara can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Barbara","Jeremy","Hilda"],"index":31867,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993958473,"difficulty":0.0006041527}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Harold knows whether or not nobody's forehead is muddy. It is publicly announced that Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! 2 ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! 2 ] 0","hypothesis":"Rose can now know that Frederick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harold","Rose","Frederick"],"index":44421,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9914903045,"difficulty":0.0085096955}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Rebecca can now know that Rebecca is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ronald","Rebecca"],"index":23386,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5146916509,"difficulty":0.4853083491}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hettie does not know whether Alfred is thirsty. It is publicly announced that Priscilla does not know whether Hettie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Hettie can now know that Hettie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alfred","Hettie","Priscilla"],"index":13534,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9794726372,"difficulty":0.0205273628}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allan's card is shown to Darlene. Jim's card is shown to Jim. Jim's card is shown to Allan. Darlene's card is shown to Billy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darlene can now know that Jim can know whether Allan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darlene","Jim","Allan","Billy"],"index":863,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9927143455,"difficulty":0.0072856545}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Barbara can now know whether Luke can know whether Luke's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barbara","Luke"],"index":27178,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9578831196,"difficulty":1.9578831196}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Omar does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Theresa can now know whether Angel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Omar","Theresa","Angel"],"index":42502,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990974665,"difficulty":0.0009025335}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Susan's forehead is muddy. It is publicly announced that Richard knows whether Zonia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kesha can now know that Susan can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Zonia","Richard","Kesha","Susan"],"index":43366,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966260195,"difficulty":0.0033739805}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Everett knows whether Robert's forehead is muddy. It is publicly announced that Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] 0","hypothesis":"Everett can now know whether Andrew can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Everett","Michael","Andrew","Robert"],"index":11377,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994494319,"difficulty":0.0005505681}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Michael. Emma's card is shown to Katherine. Katherine's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Katherine does not know whether or not everyone picked a red card. It is publicly announced that Katherine does not know whether or not everyone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Katherine","Steve","Emma"],"index":32606,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994503856,"difficulty":0.0005496144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Larry can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","Ingrid","Louis","Alan"],"index":32860,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992780089,"difficulty":0.0007219911}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adrian knows whether Crystal's forehead is muddy. It is publicly announced that Doyle knows whether Gladys's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Crystal can now know that Gladys's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gladys","Adrian","Crystal","Doyle"],"index":13327,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9933083057,"difficulty":0.0066916943}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"John can now know whether Johnny can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Johnny","John"],"index":38423,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9079985619,"difficulty":0.0920014381}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Benjamin. Lisa's card is shown to Lisa. Richard's card is shown to Lisa. Benjamin's card is shown to Richard. Lisa's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Benjamin can now know whether Lisa can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Benjamin","Lisa","Richard"],"index":60544,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.897993207,"difficulty":0.102006793}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Camille can now know that Pamela can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pamela","Camille","Charles"],"index":58922,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990723133,"difficulty":0.0009276867}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelley's card is shown to Alfredo. Shelley's card is shown to Jack. Alfredo's card is shown to Shelley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alfredo can now know whether Shelley can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alfredo","Jack","Shelley"],"index":34503,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992139339,"difficulty":0.0007860661}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Toby knows whether Elizabeth's forehead is muddy. It is publicly announced that Moises knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Moises can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Toby","Viola","Elizabeth","Moises"],"index":23582,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993002415,"difficulty":0.0006997585}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Sheri can now know that Robert can know that Amanda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Robert","Sheri","Amanda"],"index":64147,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975324869,"difficulty":0.0024675131}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Cora can now know whether Ryan can know whether Cora is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ryan","Jonathan","Cora","Jeffrey"],"index":47992,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989847541,"difficulty":0.0010152459}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Harry can now know that Linda can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Linda","Harry"],"index":20139,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983173609,"difficulty":0.0016826391}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Chad can now know that Larry can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Larry","Chad"],"index":25157,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993394017,"difficulty":0.0006605983}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Anthony can now know whether Kristopher can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Kristopher","Ronald"],"index":57937,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.98638165,"difficulty":0.01361835}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Albert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ronald can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marie","Ronald","Albert"],"index":25395,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992209673,"difficulty":0.0007790327}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Celia can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Celia","Edward","Martin","Karen"],"index":3611,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994699359,"difficulty":0.0005300641}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elmer knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jennifer can now know that Paul can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Elmer","Jennifer"],"index":29709,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992853999,"difficulty":0.0007146001}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Ann knows whether or not nobody's forehead is muddy. It is publicly announced that Irene knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Ann can now know whether Rebecca can know whether Irene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Ann","William","Irene"],"index":30923,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993271828,"difficulty":0.0006728172}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tracy can now know that Donna can know whether Tracy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","James","Tracy","Charles"],"index":10271,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993651509,"difficulty":0.0006348491}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tonya's card is shown to Tonya. Anne's card is shown to Tonya. Ruby's card is shown to Tonya. Allyson's card is shown to Allyson. Anne's card is shown to Anne. Allyson's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Allyson does not know whether Ruby picked a red card. It is publicly announced that Tonya knows whether Anne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Ruby can now know that Anne can know whether Ruby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tonya","Allyson","Anne","Ruby"],"index":28566,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7281122208,"difficulty":1.7281122208}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is muddy. It is publicly announced that Mary knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Christopher can now know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Christopher","Joe","Mary"],"index":67132,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993337989,"difficulty":0.0006662011}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Debra can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debra","Donald"],"index":3596,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9011991024,"difficulty":1.9011991024}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Gerald can now know that Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gerald","Brian","Virginia","Rebecca"],"index":59057,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983054399,"difficulty":0.0016945601}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurel knows whether Laurel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Doreen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Laurel","Doreen"],"index":42071,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989936948,"difficulty":0.0010063052}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Davis knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Davis can now know whether Anna can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Davis","Anna"],"index":29900,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993683696,"difficulty":0.0006316304}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myra does not know whether Myra's forehead is muddy. It is publicly announced that Myra does not know whether Myra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Myra can now know that Doreen can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doreen","Lori","Myra","Charlotte"],"index":12813,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994239807,"difficulty":0.0005760193}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Melvin can now know that Kevin can know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melvin","Kevin","Stephanie"],"index":28214,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9751082659,"difficulty":0.0248917341}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know whether John can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joy","Michael","James","John"],"index":33261,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964620471,"difficulty":0.0035379529}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Floyd knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Floyd can now know whether Julie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cheryl","Floyd","Charley","Julie"],"index":36991,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981353283,"difficulty":0.0018646717}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathrine knows whether or not everyone's forehead is muddy. It is publicly announced that Kathrine knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Ross can now know that Kathrine can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Peggy","Kathrine","Ross"],"index":50337,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994787574,"difficulty":0.0005212426}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheri knows whether Lola's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Lola can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lola","Emily","Cheri"],"index":42831,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990002513,"difficulty":0.0009997487}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Maria can now know that Fidel can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Maria","Fidel","James"],"index":65504,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9938246012,"difficulty":0.0061753988}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Brandon. Brian's card is shown to Brian. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Jeremy does not know whether Jeremy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Brandon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeremy","Brandon","Brian","Matthew"],"index":2215,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994014502,"difficulty":0.0005985498}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Mark. Mark's card is shown to Nicholas. Mark's card is shown to Isaac. Nicholas's card is shown to Isaac. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Isaac can now know that Nicholas can know that Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Nicholas","Isaac"],"index":5410,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979909658,"difficulty":0.0020090342}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myra knows whether or not everyone's forehead is muddy. It is publicly announced that Maria's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Elizabeth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Christina","Maria","Myra"],"index":11211,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989303946,"difficulty":0.0010696054}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Walter does not know whether or not everyone is thirsty. It is publicly announced that Walter knows whether Walter is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Warren can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Warren","Walter"],"index":6486,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983564019,"difficulty":0.0016435981}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luis's card is shown to Edgar. Edgar's card is shown to Luis. Luis's card is shown to Luis. Jodie's card is shown to Luis. Luis's card is shown to Jodie. Melissa's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Melissa picked a red card. It is publicly announced that Edgar picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Melissa can now know that Luis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edgar","Luis","Jodie","Melissa"],"index":8812,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9336034656,"difficulty":0.0663965344}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dominga can now know whether Terry can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Terry","Linda","Dominga"],"index":64254,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994618297,"difficulty":0.0005381703}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tony knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Tony can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kathleen","Tony"],"index":22250,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989315867,"difficulty":0.0010684133}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Ivana is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"William can now know that Ivana can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Ivana"],"index":24912,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7889984846,"difficulty":0.2110015154}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Vanessa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that Vanessa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Theresa","Vanessa"],"index":21971,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8912260532,"difficulty":0.1087739468}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Eduardo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Michael can now know that Eduardo can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Michael","Eduardo","Kent"],"index":52398,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989338517,"difficulty":0.0010661483}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elisabeth's forehead is not muddy. It is publicly announced that Joanne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] Agentc knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Irvin can now know whether Joanne can know that Irvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joanne","Elisabeth","Irvin"],"index":39395,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999435246,"difficulty":0.000564754}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Kevin. Kevin's card is shown to Carrie. Carrie's card is shown to Carrie. Kevin's card is shown to Mary. Carrie's card is shown to Tisha. Tisha's card is shown to Tisha. It is publicly announced that someone picked a red card. It is publicly announced that Tisha does not know whether Mary picked a red card. It is publicly announced that Kevin knows whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Kevin can now know whether Tisha can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Carrie","Mary","Tisha"],"index":60498,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9730038643,"difficulty":0.0269961357}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Michelle can now know whether Monica can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jamie","Michelle","Albert","Monica"],"index":65367,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993531108,"difficulty":0.0006468892}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is not muddy. It is publicly announced that Edward's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! ~(2) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Edward can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Edward"],"index":31837,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998324573,"difficulty":0.001675427}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Queen can now know that Audrey can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Queen","Audrey","Mary","Pablo"],"index":28773,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992417097,"difficulty":0.0007582903}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debbie knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"William can now know that Vickie can know whether Debbie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessie","William","Vickie","Debbie"],"index":9685,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978786707,"difficulty":0.0021213293}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Shawn can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Shawn"],"index":62069,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987620115,"difficulty":0.0012379885}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carlos knows whether Carlos is thirsty. It is publicly announced that Justin knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Carlos can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Justin","Jeffrey","Carlos"],"index":12460,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9922270775,"difficulty":0.0077729225}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Felicia can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brenda","Howard","Felicia"],"index":53219,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.912560463,"difficulty":1.912560463}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Cristina can now know that Joshua can know whether Joshua's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dennis","Cristina","Joshua","Elizabeth"],"index":31272,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993496537,"difficulty":0.0006503463}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ken does not know whether Felicia is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Ken knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Felicia can now know whether Ken is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amanda","Ken","Felicia","John"],"index":1314,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8673638701,"difficulty":0.1326361299}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Arturo can now know that Judi can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clifford","Judi","Mary","Arturo"],"index":60792,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994193316,"difficulty":0.0005806684}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Stefanie can now know whether Benjamin can know that Benjamin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Stefanie","Benjamin"],"index":30239,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6791554689,"difficulty":0.3208445311}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Gladys's card is shown to Joan. Joan's card is shown to Wallace. Joan's card is shown to Gladys. Gladys's card is shown to Gladys. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gladys can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joan","Wallace","Gladys"],"index":258,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994217157,"difficulty":0.0005782843}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether or not everyone is thirsty. It is publicly announced that Melissa does not know whether Martha is thirsty. It is publicly announced that Bryan does not know whether Martha is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Charlotte can now know whether Charlotte is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bryan","Martha","Charlotte","Melissa"],"index":8542,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9755896926,"difficulty":0.0244103074}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Lee is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jose","James","Lee"],"index":63878,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9730122089,"difficulty":0.0269877911}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julia does not know whether Gregory is thirsty. It is publicly announced that Gregory does not know whether Julia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Blanca can now know that Blanca is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregory","Blanca","Julia"],"index":44852,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9947104454,"difficulty":0.0052895546}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Pauline. Pauline's card is shown to Shirley. Shirley's card is shown to Shirley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pauline can now know that Pauline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pauline","Mary","Shirley"],"index":21753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9855750799,"difficulty":0.0144249201}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Harold can now know that Marjorie can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harold","Marjorie","Grace"],"index":5609,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993312359,"difficulty":0.0006687641}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Denise's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Brenda does not know whether Denise picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Brenda can now know that Denise can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brenda","Denise"],"index":40881,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999073863,"difficulty":0.000926137}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernard is not thirsty. It is publicly announced that Bernard knows whether Bernard is thirsty. It is publicly announced that Bernard does not know whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"James can now know that Charles can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bernard","Charles","James"],"index":66465,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989861846,"difficulty":0.0010138154}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terri's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Terri can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sabrina","Terri","William"],"index":41464,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986658096,"difficulty":0.0013341904}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy. It is publicly announced that Judy's forehead is not muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Pearl can now know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Pearl","Judy"],"index":18569,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6128575206,"difficulty":1.6128575206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Donald can now know whether Pauline is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","Donald","Maria","Jessie"],"index":1888,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953612685,"difficulty":0.0046387315}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheila's card is shown to Nina. Nina's card is shown to Sheila. Nina's card is shown to Timmy. It is publicly announced that someone picked a red card. It is publicly announced that Nina does not know whether or not everyone picked a red card. It is publicly announced that Nina does not know whether Nina picked a red card. It is publicly announced that Timmy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Timmy can now know whether Nina can know that Sheila picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nina","Sheila","Timmy"],"index":49418,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.955527246,"difficulty":0.044472754}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adina's card is shown to Gary. Paul's card is shown to Gary. Gary's card is shown to Michael. Adina's card is shown to Adina. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Michael","Adina","Paul"],"index":62186,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990455508,"difficulty":0.0009544492}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marilyn's card is shown to Angelia. Tony's card is shown to Tony. Tony's card is shown to Marilyn. Marilyn's card is shown to Marilyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tony can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Angelia","Tony","Marilyn"],"index":59813,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999368608,"difficulty":0.000631392}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith knows whether or not everyone's forehead is muddy. It is publicly announced that Phillip does not know whether Phillip's forehead is muddy. It is publicly announced that Daisy knows whether Kim's forehead is muddy. It is publicly announced that Phillip does not know whether Phillip's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] (Agentd knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Phillip can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kim","Daisy","Judith","Phillip"],"index":57134,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994881153,"difficulty":0.0005118847}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arturo knows whether someone's forehead is muddy. It is publicly announced that Don knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Charlene can now know that Don can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arturo","Don","Frank","Charlene"],"index":1,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980180264,"difficulty":0.0019819736}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Debbie. Gerald's card is shown to Gerald. Debbie's card is shown to Andrew. Andrew's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Andrew knows whether Debbie picked a red card. It is publicly announced that Gerald does not know whether Debbie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Debbie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debbie","Gerald","Andrew"],"index":29456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999381423,"difficulty":0.000618577}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emily's card is shown to John. Emily's card is shown to Leroy. John's card is shown to Rosemary. Rosemary's card is shown to Emily. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Leroy can know that Leroy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Leroy","Rosemary","Emily"],"index":32374,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9933850169,"difficulty":1.9933850169}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether Margaret's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Andrew can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Margaret","Andrew"],"index":3480,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9944065809,"difficulty":0.0055934191}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bettie is thirsty. It is publicly announced that Matthew knows whether Bettie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether 3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Bettie can now know that Matthew is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Rosa","Bettie"],"index":55277,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9570418596,"difficulty":0.0429581404}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lois","Paul","Paula","John"],"index":67392,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9966776371,"difficulty":0.0033223629}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Maria can now know that Nora can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nora","Maria","Cynthia"],"index":56323,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988431931,"difficulty":0.0011568069}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Cindy is thirsty. It is publicly announced that Cindy does not know whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Carrie can now know whether Linda can know whether Cindy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dena","Linda","Cindy","Carrie"],"index":62955,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990647435,"difficulty":0.0009352565}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Anthony. Anthony's card is shown to Marie. Marie's card is shown to Marie. Marie's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know whether Marie can know that Marie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Antonette","Anthony","Marie","Elizabeth"],"index":20693,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9495604634,"difficulty":0.0504395366}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold does not know whether Harold's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know that Harold can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","Harold","Patricia","John"],"index":21101,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989462495,"difficulty":0.0010537505}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bertie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Tuyet can now know whether Bertie can know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tuyet","Daniel","Bertie"],"index":53152,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990028739,"difficulty":0.0009971261}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francisco does not know whether or not everyone is thirsty. It is publicly announced that Francisco does not know whether Wendy is thirsty. It is publicly announced that Wendy knows whether or not everyone is thirsty. It is publicly announced that Francisco does not know whether Wendy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Francisco can now know whether Wendy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wendy","Francisco"],"index":8273,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.608959496,"difficulty":1.608959496}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jacob can now know that Robert can know whether Brandi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jacob","Robert","Brandi"],"index":8326,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980879426,"difficulty":0.0019120574}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josephine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Philip can now know that Betty can know whether Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Josephine","Philip"],"index":14143,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994820714,"difficulty":0.005179286}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Micah is not thirsty. It is publicly announced that Esther is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Esther can now know whether Rafael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Esther","Micah","Olivia","Rafael"],"index":33172,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997287035,"difficulty":0.002712965}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jorge's card is shown to Gladys. Gladys's card is shown to Jorge. Jorge's card is shown to Jorge. Jorge's card is shown to Herman. It is publicly announced that someone picked a red card. It is publicly announced that Gladys does not know whether Gladys picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gladys can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gladys","Jorge","Herman"],"index":45623,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9920347333,"difficulty":0.0079652667}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lenora knows whether someone is thirsty. It is publicly announced that Richard does not know whether Tabatha is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Lenora knows whether Lenora is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Tabatha can now know that Cynthia can know that Cynthia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tabatha","Cynthia","Lenora","Richard"],"index":43698,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967209697,"difficulty":0.0032790303}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phil knows whether Sabra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sabra can now know whether Phil can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phil","Sabra","John"],"index":1180,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994543195,"difficulty":0.0005456805}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell's forehead is muddy. It is publicly announced that Russell's forehead is muddy. It is publicly announced that Wayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Kelli can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kelli","Wayne","Russell"],"index":61371,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993346334,"difficulty":0.0006653666}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diana knows whether Sharon is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Sharon can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sharon","Diana"],"index":49276,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989846349,"difficulty":0.0010153651}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Joe can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lisa","Joe","Shawn"],"index":61070,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989715815,"difficulty":0.0010284185}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma knows whether Michael's forehead is muddy. It is publicly announced that John's forehead is not muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thelma","John","Michael"],"index":65873,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986923337,"difficulty":0.0013076663}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy. It is publicly announced that Ruby's forehead is not muddy. It is publicly announced that Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] Agentc knows whether (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] 0","hypothesis":"Ruby can now know whether Dorothy can know that Ruby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Ronald","Ruby"],"index":39065,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8646755815,"difficulty":0.1353244185}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isaac knows whether Mario's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario does not know whether Mario's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Isaac can now know that Isaac's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Isaac","David","Mario"],"index":43337,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9877053499,"difficulty":0.0122946501}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vera's card is shown to Vera. It is publicly announced that someone picked a red card. It is publicly announced that Vera picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Vera can now know that Cindy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vera","Shirley","Cindy"],"index":21135,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9912881255,"difficulty":0.0087118745}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathaniel's card is shown to Nathaniel. Josphine's card is shown to Nathaniel. Margaret's card is shown to Nathaniel. Margaret's card is shown to Josphine. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know that Josphine can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nathaniel","Josphine","Margaret"],"index":29215,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993218184,"difficulty":0.0006781816}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy. It is publicly announced that Angel knows whether Charles's forehead is muddy. It is publicly announced that Angel knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Everett can now know whether Ronald can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angel","Ronald","Charles","Everett"],"index":21608,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9251093864,"difficulty":0.0748906136}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Daniel can now know whether John can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daniel","John"],"index":11981,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8372118473,"difficulty":1.8372118473}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Daniel is thirsty. It is publicly announced that Richard does not know whether Daniel is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Richard can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Daniel","James","Richard"],"index":58514,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9793729186,"difficulty":0.0206270814}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Karon. Jean's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karon","David","Jean"],"index":23140,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994171858,"difficulty":0.0005828142}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agenta knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Mark can now know whether Wiley can know that Wiley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","James","Brian","Wiley"],"index":5747,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9057469368,"difficulty":1.9057469368}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rodney's card is shown to Jorge. Paul's card is shown to Jorge. Rodney's card is shown to Rodney. Rodney's card is shown to Paul. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Jorge does not know whether Jorge picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jorge can now know whether Rodney can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jorge","Rodney","Paul"],"index":50832,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9241300225,"difficulty":1.9241300225}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. William's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Maria can now know whether William can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maria","William"],"index":14129,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7471794486,"difficulty":0.2528205514}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Philip does not know whether Ellen is thirsty. It is publicly announced that Philip does not know whether or not everyone is thirsty. It is publicly announced that Margaret is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Philip can now know whether Ellen can know whether Ellen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellen","Philip","Margaret"],"index":49308,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983752966,"difficulty":0.0016247034}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime knows whether Colleen's forehead is muddy. It is publicly announced that Laura knows whether Laura's forehead is muddy. It is publicly announced that Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Richard can now know that Laura can know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Richard","Jaime","Colleen"],"index":28654,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.978823781,"difficulty":0.021176219}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nathaniel is thirsty. It is publicly announced that Amy knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Thomas can now know whether Amy can know whether Lois is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amy","Lois","Nathaniel","Thomas"],"index":16148,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992283583,"difficulty":0.0007716417}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ella knows whether someone's forehead is muddy. It is publicly announced that Ella knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Gladys can now know that Ella can know that Ella's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ella","Gladys"],"index":22703,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9955861568,"difficulty":0.0044138432}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold does not know whether Dora is thirsty. It is publicly announced that Mildred knows whether Mildred is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Cherie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dora","Mildred","Harold","Cherie"],"index":59515,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989493489,"difficulty":0.0010506511}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Suzanne does not know whether Rosemarie is thirsty. It is publicly announced that Phylis does not know whether Suzanne is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Rosemarie can now know that Suzanne can know that Rosemarie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosemarie","Phylis","Suzanne"],"index":63328,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9952157736,"difficulty":0.0047842264}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessie's card is shown to Eleanor. Linda's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Linda picked a red card. It is publicly announced that Eleanor picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Jessie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessie","Eleanor","Linda"],"index":46242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984205961,"difficulty":0.0015794039}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sherry does not know whether Joshua is thirsty. It is publicly announced that Jorge is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agentb knows that (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Sherry can now know that Joshua can know whether Sherry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jorge","Sherry","Victoria","Joshua"],"index":37677,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8466328979,"difficulty":1.8466328979}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Anna can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anna","David","Jason","John"],"index":15898,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994918108,"difficulty":0.0005081892}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Bobbi. Bobbi's card is shown to Charles. Ashley's card is shown to Ashley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bobbi can now know whether Ashley picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bobbi","Charles","Ashley"],"index":24697,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8810706735,"difficulty":0.1189293265}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Donald is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Donald knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Donald can now know that Matthew can know whether Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Matthew","Michael"],"index":45127,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9672027826,"difficulty":0.0327972174}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Darlene knows whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Flossie can now know whether Mathew can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","Mathew","Darlene","Flossie"],"index":34050,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992777705,"difficulty":0.0007222295}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Geoffrey can now know whether Robert can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geoffrey","Robert","Susan"],"index":19424,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994208813,"difficulty":0.0005791187}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bill's card is shown to Johnnie. It is publicly announced that someone picked a red card. It is publicly announced that Johnnie does not know whether Johnnie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Johnnie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Johnnie","Bill"],"index":38728,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994571805,"difficulty":0.0005428195}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Geraldine does not know whether Sabrina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Sabrina can now know that Gregory is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Geraldine","Sabrina","Gregory"],"index":47047,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980890155,"difficulty":0.0019109845}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine knows whether Christine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gregory can now know whether Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gregory","Paul","Christine"],"index":55629,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999432981,"difficulty":0.000567019}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marilyn knows whether Marilyn is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jennifer can now know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Marilyn","Jennifer","John"],"index":43614,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9944953322,"difficulty":0.0055046678}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ronald can now know whether Ronald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carmella","Ronald","Lisa"],"index":44636,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994302392,"difficulty":0.0005697608}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Todd can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Nathaniel","Brian","Todd"],"index":51519,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998550117,"difficulty":0.001449883}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether Ruth's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ann can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ruth","Ann","Jerrica","Gary"],"index":23671,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999337256,"difficulty":0.000662744}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Judy. Judy's card is shown to Amy. Amy's card is shown to Amy. Judy's card is shown to Peggy. Amy's card is shown to Peggy. Peggy's card is shown to Peggy. It is publicly announced that someone picked a red card. It is publicly announced that Peggy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Amy can now know that Peggy can know that Peggy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Judy","Amy","Peggy"],"index":9527,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9237998724,"difficulty":0.0762001276}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin is not thirsty. It is publicly announced that Christie does not know whether Craig is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] Agentd knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Theresa can now know that Justin can know whether Christie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christie","Craig","Justin","Theresa"],"index":32841,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.995377183,"difficulty":0.004622817}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Eileen knows whether Eileen is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Eileen can now know that Lucy can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lucy","Eileen"],"index":21702,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9907876849,"difficulty":0.0092123151}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander knows whether someone's forehead is muddy. It is publicly announced that Alexander knows whether Deidre's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Deidre can now know whether Christina can know whether Amber's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christina","Amber","Deidre","Alexander"],"index":56878,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990729094,"difficulty":0.0009270906}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Juan. William's card is shown to Juan. Gerald's card is shown to Gerald. Loyd's card is shown to Gerald. William's card is shown to Gerald. Juan's card is shown to Loyd. Loyd's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether or not nobody picked a red card. It is publicly announced that William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] Agentc knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Loyd can now know that William can know that Juan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juan","Gerald","Loyd","William"],"index":13488,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9735741615,"difficulty":0.0264258385}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Wayne. Patricia's card is shown to Wayne. John's card is shown to John. John's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Wayne picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"John can now know that Patricia can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wayne","John","Patricia"],"index":16659,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994071722,"difficulty":0.0005928278}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Colette's card is shown to Robert. Jarrett's card is shown to Jarrett. Colette's card is shown to Colette. It is publicly announced that someone picked a red card. It is publicly announced that Colette does not know whether Robert picked a red card. It is publicly announced that Jarrett does not know whether Jeanette picked a red card. It is publicly announced that Colette knows whether someone picked a red card. It is publicly announced that Colette does not know whether Jeanette picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] Agentb knows whether (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Jarrett can now know whether Colette can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Jarrett","Colette","Jeanette"],"index":31482,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9337193966,"difficulty":0.0662806034}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Russell can now know whether Amy can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amy","Jennifer","Russell"],"index":59497,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992438555,"difficulty":0.0007561445}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Carina. Kenneth's card is shown to Carina. Jerry's card is shown to Jerry. Carina's card is shown to Jacquelyn. Kenneth's card is shown to Jacquelyn. It is publicly announced that someone picked a red card. It is publicly announced that Carina does not know whether or not everyone picked a red card. It is publicly announced that Kenneth does not know whether Jacquelyn picked a red card. It is publicly announced that Kenneth does not know whether Jacquelyn picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kenneth can now know whether Jerry can know that Carina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carina","Jerry","Kenneth","Jacquelyn"],"index":3288,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8683428764,"difficulty":0.1316571236}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Christian can now know that Stuart can know that Carlos's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carlos","Christian","Stuart","David"],"index":13012,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981449842,"difficulty":0.0018550158}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Desiree's card is shown to Desiree. Stacy's card is shown to Timothy. Stacy's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Stacy picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Stacy can now know that Stacy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Desiree","Stacy","Timothy","Robert"],"index":33162,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6059550643,"difficulty":0.3940449357}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan knows whether or not nobody's forehead is muddy. It is publicly announced that Suzanne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Suzanne can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Howard","Suzanne","Juan"],"index":22111,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989668131,"difficulty":0.0010331869}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randolph's card is shown to William. William's card is shown to Ronald. Ronald's card is shown to Sharon. William's card is shown to Randolph. Randolph's card is shown to Randolph. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether Sharon picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Randolph can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Ronald","Sharon","Randolph"],"index":21539,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994167089,"difficulty":0.0005832911}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin does not know whether Donald is thirsty. It is publicly announced that Patrick is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agentc knows whether (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Justin can now know whether Patricia can know whether Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Patrick","Justin","Donald"],"index":56128,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992105961,"difficulty":0.0007894039}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Billy can now know whether Clinton can know that Carrie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carrie","Sherman","Clinton","Billy"],"index":16919,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9078919888,"difficulty":0.0921080112}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether Scott's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Scott can now know that Kathleen can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Scott","Lisa","Raymond"],"index":18709,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9301841259,"difficulty":0.0698158741}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne's forehead is not muddy. It is publicly announced that Danny knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Tyra can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danny","Anne","Tyra"],"index":5619,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989494681,"difficulty":0.0010505319}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Edward can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Amy","Edward"],"index":21403,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957928658,"difficulty":0.0042071342}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Michael. Laura's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Michael picked a red card. It is publicly announced that Laura does not know whether Michael picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Laura can now know whether Michael can know that Laura picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Laura"],"index":49359,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9893658161,"difficulty":0.0106341839}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Cindy's card is shown to Charles. Charles's card is shown to Cindy. Cindy's card is shown to Cindy. Kevin's card is shown to Cindy. Charles's card is shown to Kevin. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that Kevin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Cindy","Kevin"],"index":19148,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9603323936,"difficulty":0.0396676064}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Cameron","Bryan"],"index":7738,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979879856,"difficulty":0.0020120144}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Olga can now know that Jeffery can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffery","Nadine","Cynthia","Olga"],"index":11013,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9765981436,"difficulty":0.0234018564}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne knows whether Betsy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Yvonne can now know that Wendi can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Yvonne","Wendi","Betsy"],"index":64933,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989352822,"difficulty":0.0010647178}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Carlos knows whether Gracie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Carlos can now know that Donna can know that Carlos's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gracie","Joesph","Carlos","Donna"],"index":31684,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.994310379,"difficulty":0.005689621}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether Melanie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Paul can now know whether William can know that Melanie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Melanie","William","Janis"],"index":32509,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9888014793,"difficulty":0.0111985207}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Roxie's card is shown to Jennifer. Jennifer's card is shown to Roxie. Mary's card is shown to Roxie. Roxie's card is shown to Roxie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Mary","Roxie"],"index":57941,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994217157,"difficulty":0.0005782843}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Tammy can now know that David can know that Tammy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tammy","David","Viola"],"index":35198,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978379607,"difficulty":0.0021620393}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Christine. Christine's card is shown to Norma. Ashley's card is shown to Eric. Norma's card is shown to Eric. Eric's card is shown to Eric. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Norma can now know whether Norma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ashley","Christine","Norma","Eric"],"index":14955,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8984748721,"difficulty":1.8984748721}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ying knows whether Bertha's forehead is muddy. It is publicly announced that Bertha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bertha can now know whether Bertha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gail","Ying","Bertha"],"index":17334,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5952513218,"difficulty":0.4047486782}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Leon can now know whether Bernadette can know that Bernadette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leon","Bernadette","Sally"],"index":9888,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948484898,"difficulty":0.0051515102}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristen does not know whether Kristen's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Alan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alan","Kristen","Kevin"],"index":33351,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989724159,"difficulty":0.0010275841}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Julie. Ronald's card is shown to John. Julie's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that Ronald can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julie","John","Ronald"],"index":64095,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988474846,"difficulty":0.0011525154}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Julia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","April","Julia"],"index":20788,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987597466,"difficulty":0.0012402534}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jan's card is shown to Marion. Deborah's card is shown to Marion. Marion's card is shown to Jan. Jan's card is shown to Deborah. Deborah's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Deborah picked a red card. It is publicly announced that Marion does not know whether or not everyone picked a red card. It is publicly announced that Marion knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jan can now know that Deborah can know that Jan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marion","Jan","Deborah"],"index":15644,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5796414614,"difficulty":0.4203585386}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Carla can now know that Angie can know that Tina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carla","Tina","Edward","Angie"],"index":52969,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970811009,"difficulty":0.0029188991}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl's forehead is not muddy. It is publicly announced that King does not know whether King's forehead is muddy. It is publicly announced that King knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Rudy can now know that Carl can know that King's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carl","King","Rudy"],"index":45221,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9925669432,"difficulty":0.0074330568}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. Tammy's card is shown to David. David's card is shown to Tammy. Tammy's card is shown to Tammy. It is publicly announced that someone picked a red card. It is publicly announced that Tammy knows whether someone picked a red card. It is publicly announced that Tammy knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Tammy can now know that David can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Tammy"],"index":29845,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993557334,"difficulty":0.0006442666}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Judy can now know that Gretchen can know that Fannie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fannie","Gretchen","Judy","Richard"],"index":5938,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9959129691,"difficulty":0.0040870309}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Louise can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ruth","Karen","Louise"],"index":26617,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983776808,"difficulty":0.0016223192}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cathy knows whether James's forehead is muddy. It is publicly announced that Cathy's forehead is not muddy. It is publicly announced that Melissa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know whether Melissa can know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melissa","James","Harold","Cathy"],"index":25642,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6041954756,"difficulty":0.3958045244}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Miriam does not know whether Joseph is thirsty. It is publicly announced that Joseph knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Vincent can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Vincent","Joseph","Miriam"],"index":9556,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993853569,"difficulty":0.0006146431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Helen can know that Helen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirley","Charles","John","Helen"],"index":28698,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8834527135,"difficulty":0.1165472865}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alex does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Jennifer can now know that Alex can know that Alex is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alex","Jennifer"],"index":14929,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6136885285,"difficulty":0.3863114715}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Doris. Doris's card is shown to John. Doris's card is shown to Michael. John's card is shown to Michael. Raymond's card is shown to Michael. John's card is shown to Raymond. Michael's card is shown to Raymond. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymond can now know whether John can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doris","John","Michael","Raymond"],"index":7946,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993801117,"difficulty":0.0006198883}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Alvin's card is shown to Melissa. Camille's card is shown to Melissa. Christina's card is shown to Alvin. Camille's card is shown to Alvin. Christina's card is shown to Camille. It is publicly announced that someone picked a red card. It is publicly announced that Alvin does not know whether Melissa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Melissa can now know whether Melissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Melissa","Christina","Alvin","Camille"],"index":58500,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6376388073,"difficulty":1.6376388073}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Rose. Michael's card is shown to Michael. Muriel's card is shown to Muriel. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rose can now know whether Max picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rose","Michael","Max","Muriel"],"index":45273,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9789392948,"difficulty":0.0210607052}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Daniel's card is shown to Brenda. Sheri's card is shown to Nancy. Brenda's card is shown to Daniel. Sheri's card is shown to Daniel. Nancy's card is shown to Sheri. It is publicly announced that someone picked a red card. It is publicly announced that Sheri does not know whether Brenda picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Sheri does not know whether Daniel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentc knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Daniel can now know whether Sheri can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Nancy","Daniel","Sheri"],"index":3335,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993915558,"difficulty":0.0006084442}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Jean. Jean's card is shown to Larae. Larae's card is shown to Larae. It is publicly announced that someone picked a red card. It is publicly announced that Jean does not know whether Larae picked a red card. It is publicly announced that Carl does not know whether Carl picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Carl can now know whether Jean can know whether Jean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jean","Carl","Larae"],"index":50954,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977243543,"difficulty":0.0022756457}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Melissa can now know that Donald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melissa","Alysia","Mary","Donald"],"index":54719,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989497066,"difficulty":0.0010502934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby knows whether or not nobody's forehead is muddy. It is publicly announced that Patricia's forehead is muddy. It is publicly announced that Gregory does not know whether or not everyone's forehead is muddy. It is publicly announced that Gregory's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Gregory can now know that Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Bobby","Patricia","Hermine"],"index":24026,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6197329164,"difficulty":1.6197329164}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rafael does not know whether Bradley is thirsty. It is publicly announced that Marvin does not know whether Rafael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Rafael can now know whether Marvin can know that Lillie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marvin","Lillie","Bradley","Rafael"],"index":16592,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9961512685,"difficulty":0.0038487315}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beula's card is shown to Beula. Bernice's card is shown to Anthony. Anthony's card is shown to Bernice. Bernice's card is shown to Bernice. It is publicly announced that someone picked a red card. It is publicly announced that Bernice knows whether or not nobody picked a red card. It is publicly announced that Bernice picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] 0","hypothesis":"Beula can now know that Anthony can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beula","Anthony","Bernice"],"index":25244,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994261265,"difficulty":0.0005738735}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Ericka. Page's card is shown to Ericka. Larry's card is shown to Larry. Marty's card is shown to Larry. Page's card is shown to Marty. Marty's card is shown to Page. It is publicly announced that someone picked a red card. It is publicly announced that Page does not know whether Larry picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Marty can now know whether Page can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ericka","Larry","Marty","Page"],"index":27457,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9778149724,"difficulty":0.0221850276}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Victor can now know that Brenda can know that Janis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victor","Brenda","Janis","Sarah"],"index":51357,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959522486,"difficulty":0.0040477514}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Richard can now know that Lan can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Richard","Gloria","Lan"],"index":24717,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9154410362,"difficulty":0.0845589638}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether or not everyone's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy. It is publicly announced that Steven does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Steven can now know that Ronald can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Ronald"],"index":50236,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994354844,"difficulty":0.0005645156}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Robert. Robert's card is shown to Ronald. Ronald's card is shown to Ronald. Thomas's card is shown to Ronald. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know that Thomas can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Ronald","Thomas","Kathy"],"index":19602,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989252687,"difficulty":0.0010747313}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antonia knows whether Antonia is thirsty. It is publicly announced that Antonia does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Antonia can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Issac","Antonia"],"index":45956,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999515295,"difficulty":0.000484705}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cruz knows whether Grace's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Tanya can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cruz","Jacob","Grace","Tanya"],"index":59043,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986686707,"difficulty":0.0013313293}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether Wallace is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"David can now know that Wallace can know that Wallace is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Wallace","David"],"index":32813,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9919474721,"difficulty":1.9919474721}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cleo knows whether Robert's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"Ben can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jean","Ben","Robert","Cleo"],"index":36965,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994870424,"difficulty":0.0005129576}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Deborah can now know whether John can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Henry","John","Nicholas"],"index":43030,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993595481,"difficulty":0.0006404519}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Harold can now know that Shari's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harold","Shari","Patricia"],"index":59834,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9878031611,"difficulty":0.0121968389}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christian knows whether Christian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Norman can now know whether Christian can know that Ann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Ann","Christian","Norman"],"index":9559,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994539618,"difficulty":0.0005460382}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Leigh can now know whether Matthew can know that Christy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leigh","Matthew","Christy"],"index":31953,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994938374,"difficulty":0.0005061626}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether someone's forehead is muddy. It is publicly announced that Jose knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Peter can now know that Donald can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Jose","Peter","Tony"],"index":64500,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994875193,"difficulty":0.0005124807}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lavinia does not know whether James is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Lavinia can now know that Luz can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lavinia","Luz","Sharon","James"],"index":18176,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.991863966,"difficulty":0.008136034}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Max's forehead is muddy. It is publicly announced that Max knows whether someone's forehead is muddy. It is publicly announced that Nancy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Nancy can now know whether Max can know whether Max's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Max"],"index":61841,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994571805,"difficulty":0.0005428195}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Saul can now know that Margaret can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Saul","Margaret","Barbara","Francine"],"index":58643,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984965324,"difficulty":0.0015034676}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether Mark can know whether Ronda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronda","Linda","Mark","Pauline"],"index":63354,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992188215,"difficulty":0.0007811785}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Grace can now know that Eric can know that Grace is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paula","Eric","Irma","Grace"],"index":38779,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9721263051,"difficulty":0.0278736949}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dona does not know whether or not everyone's forehead is muddy. It is publicly announced that Dona does not know whether Dona's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dona can now know whether Florence can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dona","Florence"],"index":14554,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994652867,"difficulty":0.0005347133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly's forehead is muddy. It is publicly announced that Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] Agenta knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Patti can now know that Mary can know whether Herbert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patti","Mary","Kimberly","Herbert"],"index":42779,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993987083,"difficulty":0.0006012917}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Ty can now know whether Emilia can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Emilia","Tomas","Ty"],"index":23377,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994601607,"difficulty":0.0005398393}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randy knows whether or not nobody is thirsty. It is publicly announced that Rina does not know whether Randy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Randy can now know that Jeff can know whether Rina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rina","Randy","Jeff"],"index":39291,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966682792,"difficulty":0.0033317208}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Johnnie can now know whether Johnnie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Johnnie","Rose"],"index":59997,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9694280028,"difficulty":0.0305719972}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhonda knows whether Rosemary's forehead is muddy. It is publicly announced that Charlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Rhonda can now know whether Charlene can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosemary","Margaret","Charlene","Rhonda"],"index":64964,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994390607,"difficulty":0.0005609393}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Jeanne can now know whether Natalie can know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Natalie","Timothy","Vera","Jeanne"],"index":46569,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993280172,"difficulty":0.0006719828}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherri's card is shown to Nicole. Sherri's card is shown to Kathleen. Dorothy's card is shown to Kathleen. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Kathleen knows whether Sherri picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kathleen can now know whether Nicole can know that Sherri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicole","Kathleen","Sherri","Dorothy"],"index":46850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9074974656,"difficulty":0.0925025344}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Frank can now know whether Sandra can know whether Francis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Frank","Francis","Su"],"index":6441,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993539453,"difficulty":0.0006460547}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Richard can now know that Dorothy can know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Marie","Dorothy","William"],"index":67682,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977757335,"difficulty":0.0022242665}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Maria. Rose's card is shown to Maria. Maria's card is shown to Rose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marvin can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maria","Marvin","Rose","Oscar"],"index":15387,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992631078,"difficulty":0.0007368922}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Michael can now know whether Deborah can know that Tammy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tammy","Michael","Deborah"],"index":43849,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9919923544,"difficulty":0.0080076456}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane does not know whether or not everyone's forehead is muddy. It is publicly announced that Ernest knows whether or not everyone's forehead is muddy. It is publicly announced that Jane does not know whether Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Carla can now know whether Richard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carla","Ernest","Richard","Jane"],"index":24494,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99927634,"difficulty":0.00072366}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Casey can now know whether Mary can know whether Julia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Casey","Julia","Sidney","Mary"],"index":25571,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992970228,"difficulty":0.0007029772}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kathy can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathy","Jose","Hilton"],"index":37401,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995127916,"difficulty":0.0004872084}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian knows whether someone is thirsty. It is publicly announced that Michael does not know whether William is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Brian knows whether Brian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Laura can now know whether Brian can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Laura","Brian","Michael"],"index":50450,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989551306,"difficulty":0.0010448694}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sue's forehead is muddy. It is publicly announced that Jessenia does not know whether or not everyone's forehead is muddy. It is publicly announced that Jessenia does not know whether Jessenia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Sue can now know that Jessenia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sue","Jessenia"],"index":32795,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994687438,"difficulty":0.0005312562}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Katie is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Joe is thirsty. It is publicly announced that Toni does not know whether Katie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Toni can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Toni","Joe","Katie"],"index":66705,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989522696,"difficulty":0.0010477304}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Blaine's card is shown to Blaine. Robert's card is shown to Blaine. Robert's card is shown to Robert. Max's card is shown to Robert. Robert's card is shown to Max. It is publicly announced that someone picked a red card. It is publicly announced that Max does not know whether Blaine picked a red card. It is publicly announced that Blaine does not know whether Max picked a red card. It is publicly announced that Max knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Max can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Blaine","Robert","Max"],"index":59578,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992909431,"difficulty":0.0007090569}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Mildred's card is shown to Richard. Richard's card is shown to Mildred. Mildred's card is shown to Albert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that Albert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Mildred","Albert"],"index":7891,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992743134,"difficulty":0.0007256866}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Refugio knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Refugio can now know whether Angela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Armando","Alicia","Refugio","Angela"],"index":66499,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993108511,"difficulty":0.0006891489}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether Alfonso's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Andrew can now know that William can know that Alfonso's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alfonso","William","Andrew","Michael"],"index":46188,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979106784,"difficulty":0.0020893216}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Renee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Renee","Sallie","James"],"index":30764,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9814476967,"difficulty":0.0185523033}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucille's card is shown to Lucille. Lucille's card is shown to Ryan. It is publicly announced that someone picked a red card. It is publicly announced that Lucille does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lucille can now know whether Ryan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucille","Ryan","Nicole"],"index":2306,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994354844,"difficulty":0.0005645156}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bertha knows whether or not nobody's forehead is muddy. It is publicly announced that Bryan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Bryan can now know whether Bertha can know that Bertha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bryan","Bertha"],"index":33000,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992951155,"difficulty":0.0007048845}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Tatum can now know that James can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Pamela","Tatum","Patricia"],"index":1286,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994109869,"difficulty":0.0005890131}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Ronald can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Randy","Ronald","Geri"],"index":7343,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993519187,"difficulty":0.0006480813}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janis does not know whether Janis's forehead is muddy. It is publicly announced that Janis does not know whether Janis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Eli can now know whether Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Sandi","Janis","Eli"],"index":43881,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9933863282,"difficulty":0.0066136718}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Prince does not know whether Barbara is thirsty. It is publicly announced that Prince knows whether or not nobody is thirsty. It is publicly announced that Prince does not know whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Barbara can now know that Laura can know that Prince is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Laura","Prince","Barbara"],"index":32691,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972182512,"difficulty":0.0027817488}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Carol. Carol's card is shown to Rachel. Arthur's card is shown to Arthur. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Arthur can now know whether Arthur picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Rachel","Arthur"],"index":58257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8809667826,"difficulty":0.1190332174}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joanne does not know whether James is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Josephine does not know whether Joanne is thirsty. It is publicly announced that Joanne does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Josephine can now know whether Anthony can know whether Anthony is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","James","Joanne","Josephine"],"index":62142,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9698053598,"difficulty":0.0301946402}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carissa does not know whether Carissa's forehead is muddy. It is publicly announced that Sal does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Carissa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sal","Eric","Carissa","Susan"],"index":8456,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974246025,"difficulty":0.0025753975}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Joanne. Walter's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Joanne does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Walter can now know whether Joanne can know whether Joanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joanne","Walter"],"index":49123,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9937108755,"difficulty":0.0062891245}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Joe can now know that Thomas can know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joe","Debra","Thomas"],"index":51867,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7120440602,"difficulty":1.7120440602}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Marie's card is shown to Angela. Angela's card is shown to Gerald. Gerald's card is shown to Gerald. Angela's card is shown to Diana. Angela's card is shown to Marie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gerald can now know that Angela can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Gerald","Diana","Marie"],"index":43864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9714354277,"difficulty":0.0285645723}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donnie does not know whether Phillip is thirsty. It is publicly announced that Donnie does not know whether Phillip is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Donnie can now know whether Phillip is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Howard","Phillip","Christopher","Donnie"],"index":39524,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9438129663,"difficulty":0.0561870337}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doris does not know whether or not everyone is thirsty. It is publicly announced that Doris does not know whether Eric is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Doris can now know whether Eric can know that Doris is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eric","Doris"],"index":46007,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9676863551,"difficulty":0.0323136449}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Tammy can now know that Jaime can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tammy","Jaime"],"index":38981,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989903569,"difficulty":0.0010096431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Troy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Ryan can now know that Donna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","Christopher","Donna","Troy"],"index":19583,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.988689363,"difficulty":0.011310637}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alejandro's card is shown to Helen. Alejandro's card is shown to Mark. Mark's card is shown to Alejandro. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether or not everyone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know that Helen can know whether Helen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","Mark","Alejandro"],"index":62643,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5171253085,"difficulty":1.5171253085}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy. It is publicly announced that Rosalie knows whether Joseph's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Linda can now know that Rosalie can know whether Rosalie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Rosalie","Elbert","Joseph"],"index":20777,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9825162888,"difficulty":0.0174837112}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Ronald can now know that Numbers's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ronald","Numbers"],"index":53439,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974392653,"difficulty":0.0025607347}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elsie does not know whether or not everyone is thirsty. It is publicly announced that Elsie does not know whether Tracy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Martin can now know that Elsie can know that Martin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elsie","Martin","Tracy"],"index":9415,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9428351521,"difficulty":0.0571648479}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry knows whether or not everyone's forehead is muddy. It is publicly announced that Byron's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Colleen can now know that Brian can know whether Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Colleen","Harry","Byron"],"index":45401,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994332194,"difficulty":0.0005667806}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ethel does not know whether Jennifer is thirsty. It is publicly announced that Sharon is thirsty. It is publicly announced that Jennifer knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Jennifer can now know that Ethel can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ethel","Sharon","Jennifer"],"index":67462,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990769625,"difficulty":0.0009230375}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jennifer can now know that Robert can know that Rachel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Jennifer","Rachel"],"index":20146,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970699549,"difficulty":0.0029300451}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Kimberly can now know that Jose can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jose","Kimberly"],"index":4984,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.987934351,"difficulty":0.012065649}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa does not know whether Sheldon is thirsty. It is publicly announced that Glenn does not know whether Lisa is thirsty. It is publicly announced that Sheldon does not know whether Glenn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Glenn can now know that Glenn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lisa","Glenn","Sheldon"],"index":23610,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9733343124,"difficulty":0.0266656876}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rafael's card is shown to Rafael. Rafael's card is shown to Mitzi. Mitzi's card is shown to Mitzi. Tyrone's card is shown to Tyrone. Rafael's card is shown to Richard. Tyrone's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rafael can now know that Mitzi picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rafael","Mitzi","Tyrone","Richard"],"index":18039,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978086352,"difficulty":0.0021913648}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Susan can now know whether Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martha","Chris","Diego","Susan"],"index":57789,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991936088,"difficulty":0.0008063912}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Natalie does not know whether or not everyone is thirsty. It is publicly announced that Angela does not know whether Robert is thirsty. It is publicly announced that Natalie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Angela can now know that Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Natalie","Angela"],"index":65657,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9856852293,"difficulty":0.0143147707}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Minnie's card is shown to Minnie. Rick's card is shown to Minnie. Leona's card is shown to Leona. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Minnie can now know that Leona picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Minnie","Leona","Rick"],"index":9209,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976862669,"difficulty":0.0023137331}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Michelle's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Michelle can now know that Pat can know that Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michelle","Virgil","Pat"],"index":67613,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9692668319,"difficulty":0.0307331681}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Charles can now know that Christopher can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Christopher","Anthony","Harry"],"index":59751,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9918588996,"difficulty":0.0081411004}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Forrest does not know whether Phillip is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Eric can now know that Gary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Phillip","Forrest","Eric","Gary"],"index":17019,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984092116,"difficulty":0.0015907884}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that Alice can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Ernest","Alice","John"],"index":16852,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989247918,"difficulty":0.0010752082}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heidi's card is shown to Heidi. Deena's card is shown to Michael. Linda's card is shown to Deena. Michael's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Heidi knows whether or not nobody picked a red card. It is publicly announced that Michael knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Linda can now know that Deena can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heidi","Michael","Deena","Linda"],"index":40097,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5469205379,"difficulty":0.4530794621}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesse knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jesse","Robert","Earnestine"],"index":62063,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975086451,"difficulty":0.0024913549}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"James can now know that Tracey can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Shannon","Tracey"],"index":37144,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9838961363,"difficulty":0.0161038637}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret does not know whether or not everyone's forehead is muddy. It is publicly announced that Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Cristine can now know whether Kevin can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cristine","Lorine","Margaret","Kevin"],"index":31646,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994675517,"difficulty":0.0005324483}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chong knows whether or not everyone's forehead is muddy. It is publicly announced that Chong knows whether Chong's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Alex can now know whether Chong can know whether Alex's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alex","Chong"],"index":43876,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984677434,"difficulty":0.0015322566}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that Marina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Marina can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","James","Marina","Brian"],"index":18772,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989596605,"difficulty":0.0010403395}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin does not know whether David is thirsty. It is publicly announced that David does not know whether Mae is thirsty. It is publicly announced that Mae does not know whether Justin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Melinda can now know whether David can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melinda","Justin","Mae","David"],"index":53770,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994198084,"difficulty":0.0005801916}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether Gregg is thirsty. It is publicly announced that Stephanie knows whether someone is thirsty. It is publicly announced that Stephanie does not know whether Eric is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Gregg can now know that Michael can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Stephanie","Gregg","Michael"],"index":25462,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971575737,"difficulty":0.0028424263}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lynn can now know whether James can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronnie","Lynn","James"],"index":24647,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.979663074,"difficulty":0.020336926}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Anna can now know that William can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anna","Misty","William","Mathew"],"index":45428,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988582134,"difficulty":0.0011417866}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy. It is publicly announced that Doris knows whether or not everyone's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"James can now know whether David can know whether Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Nancy","Doris","James"],"index":45468,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990907907,"difficulty":0.0009092093}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Socorro's forehead is muddy. It is publicly announced that Bobby does not know whether Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know whether Socorro can know that Socorro's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bobby","James","Socorro"],"index":203,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9326236844,"difficulty":0.0673763156}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad knows whether someone's forehead is muddy. It is publicly announced that Erin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Joe can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joe","Jose","Erin","Chad"],"index":63778,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994353652,"difficulty":0.0005646348}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Agnes does not know whether Brenda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentd knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Agnes can now know that Antonio can know whether Agnes is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antonio","Brenda","Majorie","Agnes"],"index":13107,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9288896918,"difficulty":0.0711103082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Wendy can now know whether Jesse can know that Alfredo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesse","Alfredo","Nyla","Wendy"],"index":9855,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9743800163,"difficulty":0.0256199837}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Margie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Margie can now know whether Carl can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ricardo","Carl","Margie","Thomas"],"index":34846,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989283681,"difficulty":0.0010716319}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter knows whether or not everyone's forehead is muddy. It is publicly announced that Walter knows whether someone's forehead is muddy. It is publicly announced that Walter knows whether Walter's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Katherine can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Walter","Katherine"],"index":10968,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993373752,"difficulty":0.0006626248}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Brandon. Sharon's card is shown to Sharon. Joseph's card is shown to Sharon. Brandon's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Sharon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Brandon can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brandon","Sharon","Joseph"],"index":2952,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9401951432,"difficulty":0.0598048568}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether William is thirsty. It is publicly announced that George knows whether or not nobody is thirsty. It is publicly announced that William does not know whether George is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"William can now know whether George can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","George","Robert"],"index":1375,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993627667,"difficulty":0.0006372333}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Timothy can now know that Christopher can know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Timothy","Charles"],"index":37020,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999362886,"difficulty":0.000637114}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles is thirsty. It is publicly announced that Rose does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Rose can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rose","Charles","Michael","Vicky"],"index":49531,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979409575,"difficulty":0.0020590425}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hattie does not know whether Sara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Dorothy can now know that Sara can know whether Sara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Sara","Jennifer","Hattie"],"index":169,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9907504916,"difficulty":0.0092495084}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alison does not know whether Alison's forehead is muddy. It is publicly announced that Valorie does not know whether Valorie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Valorie can now know that Alison can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Valorie","Julie","Alison"],"index":32721,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994398952,"difficulty":0.0005601048}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Denise can now know that Mary can know that Dave's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ileana","Denise","Mary","Dave"],"index":14944,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997920692,"difficulty":0.002079308}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aldo does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Aldo can now know that Aldo's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Aldo","Mandie"],"index":46890,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.992873311,"difficulty":0.007126689}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kayla knows whether Virginia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Megan can now know that Kayla can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kayla","Megan","Virginia","Juan"],"index":45320,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989907146,"difficulty":0.0010092854}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lewis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Florence can now know that Hedy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lewis","Florence","Jose","Hedy"],"index":11902,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9885591865,"difficulty":0.0114408135}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jasmine does not know whether or not everyone's forehead is muddy. It is publicly announced that Denise's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Theresa can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Theresa","Byron","Denise","Jasmine"],"index":38221,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989655018,"difficulty":0.0010344982}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Kelley can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jesse","Albert","Kelley"],"index":57761,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994168282,"difficulty":0.0005831718}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"William can now know whether Steven can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Richard","William","Daryl"],"index":49982,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999333322,"difficulty":0.000666678}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sarah can now know whether Kenneth can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sarah","Kenneth","Ana","Jacqueline"],"index":15996,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992311001,"difficulty":0.0007688999}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ed does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Ed can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ed","Paul","James"],"index":25021,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9968444109,"difficulty":0.0031555891}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Cythia. Aaron's card is shown to Cythia. Joan's card is shown to Joan. Joan's card is shown to Cindy. Cindy's card is shown to Cindy. Aaron's card is shown to Cindy. Cythia's card is shown to Aaron. Joan's card is shown to Aaron. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2,3,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2,3,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Aaron can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cythia","Joan","Cindy","Aaron"],"index":11658,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993166924,"difficulty":0.0006833076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vanessa does not know whether Vanessa's forehead is muddy. It is publicly announced that Elizabeth knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Vanessa","James","Peggy"],"index":28522,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9896536469,"difficulty":0.0103463531}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alejandro's card is shown to Alejandro. Alejandro's card is shown to Stephanie. Stephanie's card is shown to Stephanie. It is publicly announced that someone picked a red card. It is publicly announced that Alejandro does not know whether or not everyone picked a red card. It is publicly announced that Stephanie picked a black card. It is publicly announced that Stephanie knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Alejandro can now know whether Stephanie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alejandro","Stephanie"],"index":31687,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994748235,"difficulty":0.0005251765}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Johnny. Jane's card is shown to Jane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Johnny can now know that Lacey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Linda","Jane","Lacey"],"index":53404,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980959296,"difficulty":0.0019040704}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Luis","James"],"index":56440,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9981915355,"difficulty":0.0018084645}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nilsa's card is shown to Jerry. Latoya's card is shown to Bobby. Jerry's card is shown to Latoya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know that Latoya picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Bobby","Latoya","Nilsa"],"index":30671,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971495271,"difficulty":0.0028504729}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ian is thirsty. It is publicly announced that Olivia does not know whether or not everyone is thirsty. It is publicly announced that Ian does not know whether Clarence is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ian can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Olivia","Ian","Clarence"],"index":39740,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9932229519,"difficulty":0.0067770481}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Marcus can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Heather","Marcus","William"],"index":60715,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986985922,"difficulty":0.0013014078}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dionne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Mae can now know whether Leona can know that Leona's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leona","Dionne","Elizabeth","Mae"],"index":18406,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9809519649,"difficulty":0.0190480351}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew does not know whether or not everyone's forehead is muddy. It is publicly announced that Tommy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Christopher can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tommy","Christopher","Lisa","Matthew"],"index":60253,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994841814,"difficulty":0.0005158186}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caroline's card is shown to Nathan. Shannon's card is shown to Shannon. Nathan's card is shown to Donald. Shannon's card is shown to Donald. Shannon's card is shown to Caroline. It is publicly announced that someone picked a red card. It is publicly announced that Shannon picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Caroline can now know that Nathan can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nathan","Shannon","Donald","Caroline"],"index":60513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984916449,"difficulty":0.0015083551}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joan does not know whether Ruth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Louis can now know that Louis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joan","Louis","Maria","Ruth"],"index":32832,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9922065139,"difficulty":0.0077934861}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene does not know whether or not everyone's forehead is muddy. It is publicly announced that Orville's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Eugene can now know whether Eugene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eugene","Orville"],"index":62823,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7891822457,"difficulty":0.2108177543}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Angela can now know that Noel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Lee","Noel","Christian"],"index":36226,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984248877,"difficulty":0.0015751123}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Candace knows whether Elbert's forehead is muddy. It is publicly announced that Amanda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Candace can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Candace","Michael","Elbert","Amanda"],"index":57125,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992130995,"difficulty":0.0007869005}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know whether Michael can know that Vernon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Michael","Vernon","Larry"],"index":19149,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9787371159,"difficulty":0.0212628841}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmie does not know whether Jimmie's forehead is muddy. It is publicly announced that Jimmie knows whether Pamela's forehead is muddy. It is publicly announced that Jimmie knows whether or not everyone's forehead is muddy. It is publicly announced that Pamela's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Jimmie can now know that Jimmie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jimmie","Henry","Pamela"],"index":1784,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9867896438,"difficulty":0.0132103562}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allison does not know whether Allison's forehead is muddy. It is publicly announced that Melanie does not know whether Melanie's forehead is muddy. It is publicly announced that Allison knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Melanie can now know whether Myron can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melanie","Myron","Allison","Gena"],"index":60821,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9546478391,"difficulty":0.0453521609}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Adam can now know whether William can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Diane","Adam","Vincent","William"],"index":18493,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9987738729,"difficulty":0.0012261271}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia does not know whether or not everyone's forehead is muddy. It is publicly announced that Cynthia knows whether Steven's forehead is muddy. It is publicly announced that Cynthia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Helen can now know whether Brad's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Helen","Cynthia","Brad"],"index":5429,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993659854,"difficulty":0.0006340146}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Vern can now know that Frances is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debra","Margaret","Vern","Frances"],"index":44755,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957815409,"difficulty":0.0042184591}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mikki does not know whether Mikki's forehead is muddy. It is publicly announced that Mikki does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mikki can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Evan","Mikki"],"index":18635,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975415468,"difficulty":0.0024584532}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herman knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether or not nobody's forehead is muddy. It is publicly announced that Wanda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] (Agenta knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] 0","hypothesis":"Wanda can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wanda","William","Herman"],"index":52700,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995036125,"difficulty":0.0004963875}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Tanya knows whether Tanya's forehead is muddy. It is publicly announced that Gregory knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Gregory can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tanya","Gregory"],"index":39244,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9830054641,"difficulty":0.0169945359}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy. It is publicly announced that Joseph knows whether someone's forehead is muddy. It is publicly announced that Harry's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Joseph can now know whether Harry can know whether Harry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Harry","Joseph"],"index":6761,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994600415,"difficulty":0.0005399585}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ola's card is shown to Ola. Angela's card is shown to Ola. Ola's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Ola can now know whether Angela can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ola","Angela"],"index":19113,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992770553,"difficulty":0.0007229447}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa's forehead is muddy. It is publicly announced that Season knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Rhonda can now know whether Lisa can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Season","Lisa","Rhonda","Rachel"],"index":4019,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9919224977,"difficulty":1.9919224977}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Shannon. Sherri's card is shown to Shannon. Sherri's card is shown to Paige. Sherri's card is shown to Kristen. Kristen's card is shown to Sherri. Sherri's card is shown to Sherri. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristen can now know that Shannon can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shannon","Paige","Kristen","Sherri"],"index":53826,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993643165,"difficulty":0.0006356835}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tammy's card is shown to Diane. Diane's card is shown to Tammy. Tammy's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Diane does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Samuel can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diane","Tammy","Samuel"],"index":36525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9720007777,"difficulty":0.0279992223}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Johnny does not know whether Michael is thirsty. It is publicly announced that Eugene does not know whether Johnny is thirsty. It is publicly announced that Michael is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Eugene can now know whether Johnny is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Johnny","Michael","Eugene"],"index":2456,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9747889638,"difficulty":0.0252110362}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Brenda's card is shown to James. Bryan's card is shown to James. Brenda's card is shown to Brenda. James's card is shown to Bryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Brenda","Bryan"],"index":45375,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9937791228,"difficulty":0.0062208772}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Rudolph can now know whether Ashley can know whether Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Rudolph","Ashley"],"index":59632,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7331250906,"difficulty":1.7331250906}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brett's card is shown to Jannie. Madeline's card is shown to Jannie. Brett's card is shown to Brett. It is publicly announced that someone picked a red card. It is publicly announced that Jannie does not know whether Jannie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jannie can now know whether Madeline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jannie","Brett","Madeline"],"index":2327,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9914193153,"difficulty":1.9914193153}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agentd knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Debra can now know whether Thomas can know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Jenifer","Thomas","Debra"],"index":56359,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.996368885,"difficulty":0.003631115}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gracie's card is shown to Shannon. Shannon's card is shown to Gracie. It is publicly announced that someone picked a red card. It is publicly announced that Gracie picked a red card. It is publicly announced that Shannon does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Shannon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shannon","Gracie"],"index":21931,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994561076,"difficulty":0.0005438924}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander knows whether Kevin's forehead is muddy. It is publicly announced that Alexander's forehead is not muddy. It is publicly announced that Susan knows whether Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kevin can now know that Alexander's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alexander","Kevin","Susan"],"index":9679,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9897253513,"difficulty":0.0102746487}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"George can now know whether George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Sally","Luisa"],"index":131,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936071634,"difficulty":0.0063928366}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deborah","Mary","Amber"],"index":35321,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9182446003,"difficulty":0.0817553997}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Elia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agentb knows whether (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Elia can now know whether William can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carol","Elia","William"],"index":53277,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9985578656,"difficulty":0.0014421344}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether Wanda's forehead is muddy. It is publicly announced that Kenneth knows whether Marguerite's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Charles can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marguerite","Charles","Wanda","Kenneth"],"index":48289,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991505146,"difficulty":0.0008494854}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lamar does not know whether Frieda is thirsty. It is publicly announced that Frieda knows whether Frieda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Frieda can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lamar","Robert","Frieda"],"index":51042,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989079237,"difficulty":0.0010920763}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dolores's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Harold can now know that Janet can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Jorge","Dolores","Harold"],"index":6380,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988766313,"difficulty":0.0011233687}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether someone's forehead is muddy. It is publicly announced that Debra does not know whether Debra's forehead is muddy. It is publicly announced that Curtis does not know whether or not everyone's forehead is muddy. It is publicly announced that Carol knows whether Carol's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Debra can now know that Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Debra","Carol","Joseph","Curtis"],"index":47163,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8544158936,"difficulty":0.1455841064}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Walter can now know whether Lee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Walter","Larry","Lee"],"index":11150,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994814992,"difficulty":0.0005185008}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wm does not know whether Helen is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Wm is thirsty. It is publicly announced that Wm does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Helen can now know whether Roderick can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roderick","Helen","Wm","Charles"],"index":26233,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994533658,"difficulty":0.0005466342}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice knows whether Luna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Luna can now know whether Clarissa can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clarissa","Beverly","Janice","Luna"],"index":62233,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989002943,"difficulty":0.0010997057}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Franklin knows whether Gloria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Gloria can now know that Patricia can know that Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Franklin","Patricia","Karen","Gloria"],"index":21421,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976400137,"difficulty":0.0023599863}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Georgiana's card is shown to Daphne. Georgiana's card is shown to Georgiana. Angela's card is shown to Georgiana. Georgiana's card is shown to Angela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Georgiana can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daphne","Georgiana","Angela"],"index":51557,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994383454,"difficulty":0.0005616546}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michelle does not know whether or not everyone is thirsty. It is publicly announced that Nicole knows whether someone is thirsty. It is publicly announced that Rufus does not know whether Nicole is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Rufus can now know that Michelle is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nicole","Rufus","Michelle"],"index":52242,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9645326734,"difficulty":1.9645326734}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Thomas can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Thomas","Lisa"],"index":53929,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9876846075,"difficulty":0.0123153925}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Jack. Jack's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Julie knows whether someone picked a red card. It is publicly announced that Julie does not know whether Julie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Julie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jack","Julie"],"index":14909,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994269609,"difficulty":0.0005730391}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gwendolyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Luis can now know that Jason can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Apolonia","Luis","Gwendolyn","Jason"],"index":55953,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987078905,"difficulty":0.0012921095}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Ronald. Ronald's card is shown to Lawrence. Guillermo's card is shown to Lawrence. Guillermo's card is shown to Guillermo. Guillermo's card is shown to Jessica. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lawrence can now know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Lawrence","Guillermo","Jessica"],"index":32872,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9927005172,"difficulty":0.0072994828}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Heather can now know whether Emily can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Emily","Heather"],"index":20613,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.981287539,"difficulty":0.018712461}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heriberto knows whether someone's forehead is muddy. It is publicly announced that Rachel knows whether Barbara's forehead is muddy. It is publicly announced that Barbara knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Heriberto can now know whether Barbara can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heriberto","Rachel","Linda","Barbara"],"index":19658,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993621707,"difficulty":0.0006378293}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher does not know whether Lea is thirsty. It is publicly announced that Christopher does not know whether Lea is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Lea can now know whether Christopher can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lea","Angel","Christopher","Kimberly"],"index":62261,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999456346,"difficulty":0.000543654}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen does not know whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Patricia can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Patricia","Pamela","Geraldine"],"index":50482,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988844991,"difficulty":0.0011155009}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Billie is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (~(1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (~(1&2)) ] 0","hypothesis":"Billie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Billie"],"index":47703,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990002513,"difficulty":0.0009997487}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgetta does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Georgetta can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Georgetta","Edward","Terry","Kathleen"],"index":23299,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989804626,"difficulty":0.0010195374}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Joanne can now know that Billy can know whether Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joanne","Billy","Carl","Steven"],"index":54374,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993807077,"difficulty":0.0006192923}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Grant can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Doris","Grant","Charles"],"index":25006,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990519881,"difficulty":0.0009480119}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Eleanor can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Dean","Daniel","Eleanor"],"index":3378,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9937361479,"difficulty":0.0062638521}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Albert. Billy's card is shown to Carmen. James's card is shown to Carmen. Albert's card is shown to Billy. James's card is shown to Billy. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Albert can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Carmen","Billy","James"],"index":19078,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983479977,"difficulty":0.0016520023}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eddie's card is shown to Eddie. Gladys's card is shown to Joseph. Joseph's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eddie can now know that Gladys can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gladys","Eddie","Joseph"],"index":8240,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992750287,"difficulty":0.0007249713}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty knows whether Betty is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Betty can now know whether Steven is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Steven","Betty"],"index":50127,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982921481,"difficulty":0.0017078519}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sean's card is shown to Lisa. Richard's card is shown to Richard. Richard's card is shown to Karrie. Sean's card is shown to Karrie. Lisa's card is shown to Sean. Richard's card is shown to Sean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karrie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Richard","Karrie","Sean"],"index":50673,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993077517,"difficulty":0.0006922483}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shari does not know whether Shari's forehead is muddy. It is publicly announced that Shari knows whether Trina's forehead is muddy. It is publicly announced that Shari knows whether or not everyone's forehead is muddy. It is publicly announced that Trina's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Trina can now know that Trina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shari","Shelley","Trina"],"index":49732,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.966760397,"difficulty":0.033239603}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Edwin. Gertrude's card is shown to Gertrude. Jonathan's card is shown to Gertrude. Lan's card is shown to Lan. Edwin's card is shown to Jonathan. Gertrude's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan does not know whether Lan picked a red card. It is publicly announced that Gertrude picked a black card. It is publicly announced that Gertrude knows whether Jonathan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Jonathan can now know that Lan can know that Gertrude picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edwin","Gertrude","Lan","Jonathan"],"index":51625,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9636382461,"difficulty":0.0363617539}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Ricky. Ricky's card is shown to Craig. Craig's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Ricky picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Earl picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Ricky can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wallace","Ricky","Craig","Earl"],"index":18961,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994072914,"difficulty":0.0005927086}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Paul can now know that Patricia can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Patricia","Paul","Robert"],"index":61538,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989564419,"difficulty":0.0010435581}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lloyd does not know whether Margaret is thirsty. It is publicly announced that Marian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Lloyd can now know that Margaret can know whether Marian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lloyd","Marian","Margaret","Robert"],"index":17767,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6660413146,"difficulty":1.6660413146}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alma knows whether or not nobody is thirsty. It is publicly announced that Alma does not know whether Mallory is thirsty. It is publicly announced that Lisa does not know whether or not everyone is thirsty. It is publicly announced that Alma does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Alma can now know whether Lisa can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mallory","Alma","Lisa"],"index":15948,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8442031741,"difficulty":1.8442031741}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie knows whether Howard's forehead is muddy. It is publicly announced that Howard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Melanie can now know that Howard can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Melanie","Howard"],"index":20483,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5738907456,"difficulty":1.5738907456}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amy can now know that Daniel can know that Adrian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Amy","Adrian","George"],"index":951,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976601601,"difficulty":0.0023398399}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andre can now know that James can know that Andre's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jason","Marlene","Andre","James"],"index":42242,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985278845,"difficulty":0.0014721155}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Genia does not know whether James is thirsty. It is publicly announced that James is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"James can now know whether Lena can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Lena","James","Genia"],"index":7057,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995028973,"difficulty":0.0004971027}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"James can now know that Jay can know whether Lonnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jay","James","Lonnie","Peter"],"index":58939,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981480837,"difficulty":0.0018519163}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether someone's forehead is muddy. It is publicly announced that Edward's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"Carlos can now know whether April's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carlos","Edward","Karen","April"],"index":3355,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999368012,"difficulty":0.000631988}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Scott. Scott's card is shown to Amanda. Christinia's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that Scott does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Christinia can now know that Scott can know whether Amanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Christinia","Amanda"],"index":19397,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5220459104,"difficulty":0.4779540896}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth is not thirsty. It is publicly announced that George knows whether or not everyone is thirsty. It is publicly announced that Kenneth knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Margaret can now know whether Kenneth can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Margaret","Kenneth","Jeffery"],"index":17205,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994986057,"difficulty":0.0005013943}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeannette knows whether Donald's forehead is muddy. It is publicly announced that Jeannette does not know whether Jeannette's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jeannette can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeannette","Donald","Melissa"],"index":25641,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994488358,"difficulty":0.0005511642}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwight's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Luis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Luis","Dwight","Adrian"],"index":44099,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988610744,"difficulty":0.0011389256}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"William can now know that Joan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dana","Joan","Matthew","William"],"index":61169,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982018471,"difficulty":0.0017981529}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Lisa. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know that Herman can know whether Lisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Herman","Lisa","William"],"index":65942,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9879435301,"difficulty":0.0120564699}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Angela can now know that Joanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Joanne","Angela"],"index":12847,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981358051,"difficulty":0.0018641949}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissia does not know whether or not everyone is thirsty. It is publicly announced that Melissia does not know whether Humberto is thirsty. It is publicly announced that Betty does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Betty can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Melissia","Jackie","Humberto"],"index":5392,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988755584,"difficulty":0.0011244416}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerald is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Patricia can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vernon","Gerald","Patricia"],"index":872,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984571934,"difficulty":0.0015428066}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rob does not know whether or not everyone's forehead is muddy. It is publicly announced that Rob knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Rob can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rob","Richard"],"index":32550,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983186722,"difficulty":0.0016813278}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Michael can now know that Mark can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mark","Michael"],"index":50608,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5058264136,"difficulty":0.4941735864}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether Miranda's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Amy can now know whether Miranda can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Miranda","Amy"],"index":22574,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993725419,"difficulty":0.0006274581}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether or not nobody's forehead is muddy. It is publicly announced that Jo does not know whether or not everyone's forehead is muddy. It is publicly announced that Jo's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Joan can now know whether Jo can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joan","Jo"],"index":57476,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994001389,"difficulty":0.0005998611}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gene's card is shown to Gene. John's card is shown to Gene. Roger's card is shown to Gene. John's card is shown to John. Gene's card is shown to Roger. John's card is shown to Roger. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gene can now know that Roger can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gene","John","Roger"],"index":18916,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9886335135,"difficulty":0.0113664865}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"John can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Irene","John"],"index":67475,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9420858026,"difficulty":0.0579141974}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Keith does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Marilynn is thirsty. It is publicly announced that Marilynn knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Keith can now know that Keith is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Keith","Marilynn"],"index":17180,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6788624525,"difficulty":0.3211375475}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Mildred. Mathew's card is shown to Darryl. Randy's card is shown to Darryl. Darryl's card is shown to Darryl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mathew can now know that Mildred can know whether Randy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Mathew","Randy","Darryl"],"index":48481,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9871129394,"difficulty":0.0128870606}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Lorenzo can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ella","Lorenzo","Linda"],"index":36597,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967522621,"difficulty":0.0032477379}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sabrina knows whether Cedric's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"George can now know that Sabrina can know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cedric","Sabrina","George","Alice"],"index":34238,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974092841,"difficulty":0.0025907159}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Walter does not know whether Christian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Christian can now know that Walter can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christian","Walter","Rose","William"],"index":46548,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9939554334,"difficulty":0.0060445666}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valencia's card is shown to Jon. Jon's card is shown to Valencia. Valencia's card is shown to Valencia. Cassandra's card is shown to Valencia. Valencia's card is shown to Cassandra. It is publicly announced that someone picked a red card. It is publicly announced that Cassandra knows whether someone picked a red card. It is publicly announced that Valencia picked a black card. It is publicly announced that Valencia picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] [ ! ~(2) ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Cassandra can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jon","Valencia","Cassandra"],"index":47595,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9813882113,"difficulty":0.0186117887}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamela's card is shown to Ruth. Ray's card is shown to Julie. Pamela's card is shown to Julie. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Julie can now know whether Pamela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ruth","Ray","Julie","Pamela"],"index":2975,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9739528298,"difficulty":0.0260471702}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Edward can now know whether Donna can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Donna","Tyler"],"index":45798,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994194508,"difficulty":0.0005805492}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelley's card is shown to Shelley. June's card is shown to June. Charles's card is shown to Jeremy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shelley can now know that Jeremy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shelley","June","Jeremy","Charles"],"index":22923,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993914366,"difficulty":0.0006085634}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Margaret can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Margaret","Mary"],"index":54923,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989639521,"difficulty":0.0010360479}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Iva knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Iva can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Iva","Domenica"],"index":15228,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9971988201,"difficulty":0.0028011799}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lee does not know whether Allen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agenta knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Veronica can now know that Lee can know that Veronica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Veronica","Allen","Andrew","Lee"],"index":9442,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974539876,"difficulty":0.0025460124}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alma's card is shown to Luisa. Alma's card is shown to Kathleen. It is publicly announced that someone picked a red card. It is publicly announced that Luisa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Alma can now know whether Luisa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Luisa","Alma","Kathleen"],"index":14847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994569421,"difficulty":0.0005430579}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Abbey can now know that Shannon can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shannon","Abbey","Ellen"],"index":59355,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964570403,"difficulty":0.0035429597}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is not muddy. It is publicly announced that Alisa does not know whether Alisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"William can now know whether Alisa can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Alisa","William"],"index":42989,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994732738,"difficulty":0.0005267262}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sherrie can now know that Victor can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Raymond","Victor","Sherrie"],"index":55601,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988922477,"difficulty":0.0011077523}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Donald can now know that Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Elsa","Michelle","Donald"],"index":52957,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978522062,"difficulty":0.0021477938}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jane does not know whether or not everyone is thirsty. It is publicly announced that Joyce does not know whether Rose is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jane can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joyce","Jane","Rose"],"index":29429,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988148212,"difficulty":0.0011851788}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice knows whether Janice is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jay can now know that Jay is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Jay","Michael","Robert"],"index":4272,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9424956441,"difficulty":0.0575043559}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy does not know whether Tammy's forehead is muddy. It is publicly announced that Carmen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Sarah can now know that Carmen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carmen","Sarah","Tammy"],"index":44401,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7443397045,"difficulty":0.2556602955}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Milton knows whether someone's forehead is muddy. It is publicly announced that Milton knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Gladys can now know whether Gladys's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Milton","Gladys","Martha"],"index":36483,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993860722,"difficulty":0.0006139278}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leta knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Leta can now know whether Karen can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leta","William","Karen"],"index":26850,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993051291,"difficulty":0.0006948709}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Noel does not know whether Michael is thirsty. It is publicly announced that Michael does not know whether Noel is thirsty. It is publicly announced that Noel is thirsty. It is publicly announced that Lewis does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] [ ! ~(Agentc knows whether 2) ] (Agentd knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Grace can now know whether Lewis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Noel","Michael","Lewis","Grace"],"index":39582,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9831941128,"difficulty":0.0168058872}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gayle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Lawrence can now know whether Matthew can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gayle","Lawrence","Matthew"],"index":16161,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9930045009,"difficulty":0.0069954991}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angie does not know whether Phillip is thirsty. It is publicly announced that Angie does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Angie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Phillip can now know whether Mary can know whether Phillip is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Phillip","Mary","Angie"],"index":60666,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9987077713,"difficulty":1.9987077713}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Donna's forehead is muddy. It is publicly announced that Donna knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Donna"],"index":44348,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8731210828,"difficulty":1.8731210828}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Sara can now know that Roy can know that Roy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Roy","Sara"],"index":60990,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949971437,"difficulty":0.0050028563}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Silvia is thirsty. It is publicly announced that Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 1 ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 1 ] 0","hypothesis":"Silvia can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Megan","Paul","Silvia"],"index":43326,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994903803,"difficulty":0.0005096197}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lisa can now know whether David can know whether Pearl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Jose","Pearl","David"],"index":4010,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999358952,"difficulty":0.000641048}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clinton's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Clinton can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gerard","Jeremy","Clinton"],"index":25765,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994904995,"difficulty":0.0005095005}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Jeremy's card is shown to Anthony. Anthony's card is shown to Jeremy. Maurice's card is shown to Jeremy. Stanley's card is shown to Jeremy. Maurice's card is shown to Maurice. Stanley's card is shown to Maurice. Anthony's card is shown to Stanley. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Maurice knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Anthony can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anthony","Jeremy","Maurice","Stanley"],"index":56456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994365573,"difficulty":0.0005634427}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Latoya's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Linda can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ellsworth","Linda","Joyce","Latoya"],"index":35927,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989203215,"difficulty":0.0010796785}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwardo's card is shown to Dorothy. Christina's card is shown to Dorothy. Edwardo's card is shown to Glenn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christina can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edwardo","Christina","Dorothy","Glenn"],"index":55016,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999296546,"difficulty":0.000703454}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether Tara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Bradly can now know that Debra can know that Debra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tara","Perry","Bradly","Debra"],"index":44119,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978183508,"difficulty":0.0021816492}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Michael can now know whether Michelle can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Michael","Arlene","Richard"],"index":19880,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994385839,"difficulty":0.0005614161}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adeline's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Lisa can now know that Adeline can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lisa","Adeline"],"index":54872,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986416698,"difficulty":0.0013583302}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether someone's forehead is muddy. It is publicly announced that Samuel knows whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Laura can now know whether Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roberto","Samuel","Laura"],"index":57635,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9465076923,"difficulty":0.0534923077}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kasey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"John can now know whether Clarence can know that Kasey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kasey","Bobby","Clarence","John"],"index":7126,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994376302,"difficulty":0.0005623698}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marie does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Marie can now know whether Florence can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Florence","Marie"],"index":23297,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994496703,"difficulty":0.0005503297}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Edward can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Edward","James"],"index":39204,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979510903,"difficulty":0.0020489097}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard's forehead is not muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Leonard can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Charles","Leonard"],"index":6823,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993494153,"difficulty":0.0006505847}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Vivian. Cynthia's card is shown to Vivian. Vivian's card is shown to Cynthia. Stefanie's card is shown to Cynthia. Leila's card is shown to Cynthia. Stefanie's card is shown to Stefanie. Leila's card is shown to Stefanie. Vivian's card is shown to Leila. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Stefanie knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Leila can now know whether Vivian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vivian","Cynthia","Stefanie","Leila"],"index":23720,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9968083501,"difficulty":0.0031916499}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Crystal can now know that Margaret can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Crystal","Shirley","Margaret","Robert"],"index":50033,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991883636,"difficulty":0.0008116364}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alton's forehead is muddy. It is publicly announced that Brittany's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] Agentd knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Margaret can now know whether Richard can know that Brittany's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Alton","Brittany","Margaret"],"index":46873,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9904093742,"difficulty":0.0095906258}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Lawrence's forehead is muddy. It is publicly announced that Cindy knows whether Cindy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ronnie can now know that Lawrence can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marsha","Cindy","Lawrence","Ronnie"],"index":28605,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989343286,"difficulty":0.0010656714}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Josie's card is shown to Mary. Michael's card is shown to Kyle. Mary's card is shown to Josie. Kyle's card is shown to Michael. Josie's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Josie can now know whether Mary can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Kyle","Josie","Michael"],"index":55686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986265898,"difficulty":0.0013734102}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Christopher can now know that Kenneth can know whether Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Donald","April","Kenneth"],"index":14357,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994499087,"difficulty":0.0005500913}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ana's forehead is muddy. It is publicly announced that Ada does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ada can now know whether Ana can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ada","Ana"],"index":50376,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9858996272,"difficulty":1.9858996272}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Stacy can now know that Ruth can know whether Anna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stacy","Marvin","Ruth","Anna"],"index":18359,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9915414453,"difficulty":0.0084585547}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Galen can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Galen","Toby","Robert","Stephen"],"index":13476,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9784539938,"difficulty":0.0215460062}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. John's card is shown to Maria. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether Maria picked a red card. It is publicly announced that Maria knows whether Maria picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know that Maria can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Maria"],"index":15673,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9404801726,"difficulty":0.0595198274}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula does not know whether Damion is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Stacey can now know whether Edward can know whether Damion is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Damion","Paula","Stacey","Edward"],"index":25489,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992434978,"difficulty":0.0007565022}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald knows whether someone is thirsty. It is publicly announced that Lula does not know whether Roger is thirsty. It is publicly announced that Hugo is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Ronald can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Hugo","Ronald","Lula","Roger"],"index":45140,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999423027,"difficulty":0.000576973}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helene's card is shown to Xavier. Shirley's card is shown to Xavier. Ana's card is shown to Xavier. Helene's card is shown to Helene. Helene's card is shown to Shirley. Shirley's card is shown to Shirley. Shirley's card is shown to Ana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helene can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Xavier","Helene","Shirley","Ana"],"index":30237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994071722,"difficulty":0.0005928278}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oliver's forehead is not muddy. It is publicly announced that Nancy knows whether Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Neda can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Oliver","Neda","Nancy","John"],"index":64424,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990365505,"difficulty":0.0009634495}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie knows whether Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Jose can now know whether Stephanie can know whether Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Jose","Stephanie","Jeffrey"],"index":26167,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6421141624,"difficulty":1.6421141624}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Candice does not know whether Concepcion is thirsty. It is publicly announced that Candice does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Mary can now know that Concepcion can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Candice","Concepcion","Mary","Richard"],"index":31686,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955134988,"difficulty":0.0044865012}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenda knows whether Jack's forehead is muddy. It is publicly announced that Jack knows whether Charles's forehead is muddy. It is publicly announced that Glenda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Jack can now know that Glenda can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Jack","Glenda"],"index":66238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985369444,"difficulty":0.0014630556}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley knows whether or not everyone is thirsty. It is publicly announced that Shirley knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Shirley can now know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patricia","Shirley"],"index":33296,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9976796508,"difficulty":1.9976796508}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra's forehead is not muddy. It is publicly announced that Juana does not know whether Juana's forehead is muddy. It is publicly announced that Juana knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Juana can now know that Adam can know that Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Adam","Debra","Juana"],"index":4902,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976420999,"difficulty":0.0023579001}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Kenneth. Kenneth's card is shown to Kimberly. Janice's card is shown to Kimberly. Kenneth's card is shown to Janice. Kimberly's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Lawrence picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lawrence can now know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Kimberly","Lawrence","Janice"],"index":32046,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9939243197,"difficulty":0.0060756803}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sandra can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sandra","James"],"index":39466,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994558692,"difficulty":0.0005441308}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jim can now know that Diane can know that Jim is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jim","Diane","Irene"],"index":50970,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9932103753,"difficulty":0.0067896247}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon knows whether Gordon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Asha can now know that Ellen can know that Gordon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gordon","Ellen","Asha"],"index":32491,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9925041199,"difficulty":1.9925041199}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ronald can now know that Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rosa","Candice","Ronald","Barbara"],"index":48369,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9698963165,"difficulty":0.0301036835}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Jamila is thirsty. It is publicly announced that Jamila does not know whether Joshua is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jamila can now know that Joshua can know that Joshua is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Ronald","Joshua","Jamila"],"index":6359,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9841995239,"difficulty":0.0158004761}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeff's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Ellen can now know whether Jeff can know whether Jeff's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeff","Wanda","Ellen"],"index":55140,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994345307,"difficulty":0.0005654693}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathaniel does not know whether Nathaniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Millie can now know that Craig can know whether Craig's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Craig","Millie","Joseph","Nathaniel"],"index":46331,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9942774177,"difficulty":0.0057225823}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emma knows whether Emma is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Tori can now know that Tori is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tori","Jim","Emma","Vicki"],"index":61060,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9422988296,"difficulty":0.0577011704}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Jane can now know whether Cheryl can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cheryl","Jane"],"index":31042,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999396801,"difficulty":0.000603199}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Reginald can now know that Martha can know that Reginald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Reginald","Martha","William"],"index":38007,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998319447,"difficulty":0.001680553}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chad does not know whether Ida is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Chad can now know that Ethel can know whether Ethel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ethel","Ida","Melissa","Chad"],"index":25445,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9112707376,"difficulty":1.9112707376}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Pamela can now know that Michael can know that Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lester","Michael","Chi","Pamela"],"index":609,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8460381031,"difficulty":0.1539618969}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. John's card is shown to Rosalind. Rosalind's card is shown to Rosalind. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"John can now know that Rosalind picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Rosalind"],"index":44988,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952558875,"difficulty":0.0047441125}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether or not nobody's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Shirley can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Aimee","Shirley","Mary"],"index":49811,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990087748,"difficulty":0.0009912252}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosario does not know whether Richard is thirsty. It is publicly announced that Rosario does not know whether or not everyone is thirsty. It is publicly announced that Rosario does not know whether or not everyone is thirsty. It is publicly announced that Richard is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Richard can now know whether Rosario can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Rosario"],"index":53823,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994817376,"difficulty":0.0005182624}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Gregory. Joyce's card is shown to Gregory. Gregory's card is shown to Kevin. Alan's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know whether Joyce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gregory","Kevin","Joyce","Alan"],"index":44077,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9133848548,"difficulty":1.9133848548}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Steven. Kyle's card is shown to Steven. Steven's card is shown to Kyle. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Kyle picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Kyle can now know whether Steven can know whether Kyle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Kyle"],"index":18415,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986482263,"difficulty":0.0013517737}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to John. Lois's card is shown to Lois. William's card is shown to Lois. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether John can know that Lois picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Lois","William"],"index":53840,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9772198796,"difficulty":0.0227801204}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Lisa can now know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Edna","Ronda","Barbara"],"index":5817,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9926229715,"difficulty":0.0073770285}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Annette. Robert's card is shown to Robert. Robert's card is shown to Stephen. Stephen's card is shown to Stephen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alice","Annette","Robert","Stephen"],"index":56574,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9865925908,"difficulty":0.0134074092}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"David can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeanine","Kelly","David","Teresa"],"index":11938,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9173101783,"difficulty":1.9173101783}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua does not know whether or not everyone's forehead is muddy. It is publicly announced that Margie knows whether Joshua's forehead is muddy. It is publicly announced that Margie knows whether Joshua's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Margie can now know that Theresa can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margie","Irene","Joshua","Theresa"],"index":6227,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994837046,"difficulty":0.0005162954}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy. It is publicly announced that William knows whether Kenneth's forehead is muddy. It is publicly announced that Violet knows whether Violet's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"William can now know that Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Violet","Kenneth","William"],"index":59976,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9772921801,"difficulty":0.0227078199}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Megan knows whether Carmon's forehead is muddy. It is publicly announced that Kathleen knows whether Kathleen's forehead is muddy. It is publicly announced that Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentd knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Carmon can now know that Corey can know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","Corey","Megan","Carmon"],"index":23759,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9182898402,"difficulty":1.9182898402}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Lester can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Glenn","Lakendra","Mabel","Lester"],"index":8365,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995254278,"difficulty":0.0004745722}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Heather can now know that Susan can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Vernon","David","Heather"],"index":61234,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.979167223,"difficulty":0.020832777}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Patricia's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Patricia can now know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Glenda","Julia","Melvin"],"index":23261,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9926416278,"difficulty":0.0073583722}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Greg's card is shown to Greg. Diane's card is shown to Greg. Greg's card is shown to Diane. Charlotte's card is shown to Travis. Diane's card is shown to Travis. Travis's card is shown to Travis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Diane can now know whether Greg can know that Travis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charlotte","Greg","Diane","Travis"],"index":56441,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9206478596,"difficulty":0.0793521404}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lauren can now know that David can know that Lauren's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Charles","David","Lauren"],"index":46751,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977253079,"difficulty":0.0022746921}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candace's card is shown to James. Lynn's card is shown to Nathaniel. Nathaniel's card is shown to Nathaniel. It is publicly announced that someone picked a red card. It is publicly announced that Candace does not know whether or not everyone picked a red card. It is publicly announced that James picked a red card. It is publicly announced that Lynn picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(2) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(2) ] 0","hypothesis":"Lynn can now know whether Candace picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Candace","Lynn","James","Nathaniel"],"index":24582,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.936091423,"difficulty":0.063908577}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela does not know whether Angela's forehead is muddy. It is publicly announced that Wesley knows whether Angela's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Angela can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Angela","Wesley"],"index":48627,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989709854,"difficulty":0.0010290146}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kristie can now know that Christopher can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stephanie","Richard","Christopher","Kristie"],"index":34444,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958946705,"difficulty":0.0041053295}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Andrea can now know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorraine","Jennifer","Andrea","Devin"],"index":8712,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9651067853,"difficulty":0.0348932147}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Robby's card is shown to John. Robby's card is shown to Valerie. Valerie's card is shown to Robby. Christopher's card is shown to Robby. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Valerie can now know that Christopher can know whether Valerie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Valerie","Christopher","Robby"],"index":60304,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6559253335,"difficulty":1.6559253335}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"William can now know that Anna can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anna","Thomas","William"],"index":62964,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9959994555,"difficulty":0.0040005445}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alexandria is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"James can now know whether Tina can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Tina","Alexandria"],"index":18083,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997636199,"difficulty":0.002363801}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carole's card is shown to Carole. Carole's card is shown to Joan. Carole's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Carole knows whether Carole picked a red card. It is publicly announced that Carole knows whether Carole picked a red card. It is publicly announced that Carole does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Patricia can now know whether Carole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carole","Joan","Patricia"],"index":55597,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.98981148,"difficulty":0.01018852}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pedro knows whether Courtney's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Pedro can now know that Sylvia can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvia","Clinton","Pedro","Courtney"],"index":42553,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994334579,"difficulty":0.0005665421}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bert knows whether or not everyone is thirsty. It is publicly announced that Bert knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Bert can now know that Bert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Aaron","Bert"],"index":29046,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6434874535,"difficulty":0.3565125465}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Garret knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Garret can now know that Gerald can know that Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gerald","Garret"],"index":57438,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972125888,"difficulty":0.0027874112}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Laura. Dorothea's card is shown to Dorothea. Jennifer's card is shown to Dorothea. It is publicly announced that someone picked a red card. It is publicly announced that Laura knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Laura can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","Dorothea","Jennifer"],"index":1913,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990654588,"difficulty":0.0009345412}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Agnes's card is shown to Chelsea. Clayton's card is shown to Chelsea. Chelsea's card is shown to Agnes. Clayton's card is shown to Agnes. Agnes's card is shown to James. Clayton's card is shown to James. Chelsea's card is shown to Clayton. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:2,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Agnes can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chelsea","Agnes","James","Clayton"],"index":12990,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984410405,"difficulty":0.0015589595}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bradley does not know whether Deann is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"John can now know that Deann can know whether Bradley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eddie","John","Deann","Bradley"],"index":43342,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.995402813,"difficulty":0.004597187}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darryl's forehead is not muddy. It is publicly announced that Ruben does not know whether Ruben's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ruben can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Darryl","Jose","Ruben"],"index":45122,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994464517,"difficulty":0.0005535483}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Terrell can know whether Bradley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Malcom","John","Bradley","Terrell"],"index":42679,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983195662,"difficulty":0.0016804338}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milagros knows whether or not everyone's forehead is muddy. It is publicly announced that David knows whether Milagros's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Milagros can now know that David can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Milagros","David"],"index":9481,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.999029398,"difficulty":0.000970602}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Patricia can now know that Michelle can know that Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Michelle"],"index":39435,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9733777046,"difficulty":1.9733777046}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Roxann can now know whether Margaret can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geoffrey","Margaret","Roxann","Michael"],"index":66121,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993696809,"difficulty":0.0006303191}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matt does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Andrew can now know whether Daniel can know that Adolph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matt","Daniel","Andrew","Adolph"],"index":17346,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.98810637,"difficulty":0.01189363}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Patricia can now know whether Edwin can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edwin","Peter","Patricia","Paul"],"index":46811,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993749261,"difficulty":0.0006250739}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Whitney knows whether Whitney is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Whitney can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Billy","Whitney"],"index":20531,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9403346777,"difficulty":0.0596653223}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not everyone's forehead is muddy. It is publicly announced that Christopher knows whether Benjamin's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Benjamin can now know whether Claude can know whether Claude's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Benjamin","Christopher","Claude"],"index":52533,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993925095,"difficulty":0.0006074905}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margarette does not know whether or not everyone's forehead is muddy. It is publicly announced that Anne knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Margarette can now know that Olivia can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margarette","Olivia","Charles","Anne"],"index":34999,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994774461,"difficulty":0.0005225539}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nick's card is shown to Helen. Helen's card is shown to Jason. Nick's card is shown to Jason. Jason's card is shown to Nick. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether Helen picked a red card. It is publicly announced that Helen knows whether Nick picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Helen can now know that Helen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Jason","Nick"],"index":41150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9606612325,"difficulty":0.0393387675}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor does not know whether Victor's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michele can now know whether Victor can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Victor","Michele","Alice"],"index":39692,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994243383,"difficulty":0.0005756617}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Ralph can now know whether Reuben can know whether Ralph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Reuben","Ralph","Richard"],"index":33704,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999363482,"difficulty":0.000636518}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julius's card is shown to Beverly. Mindy's card is shown to Beverly. Julius's card is shown to Mindy. Beverly's card is shown to Mindy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julius can now know that Beverly can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julius","Beverly","Mindy"],"index":28959,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987969398,"difficulty":0.0012030602}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dale does not know whether Jodi is thirsty. It is publicly announced that Dale does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Dale can now know that Michael can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dale","Jodi","Jason","Michael"],"index":5571,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994729161,"difficulty":0.0005270839}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard knows whether or not everyone's forehead is muddy. It is publicly announced that Brian's forehead is not muddy. It is publicly announced that Mary knows whether Jeffery's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jeffery can now know whether Jeffery's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Howard","Jeffery","Brian"],"index":57727,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9671719074,"difficulty":0.0328280926}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know that Hal can know that Hal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monique","Hal","Kyle","Michael"],"index":41917,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8574342132,"difficulty":0.1425657868}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Cecil can now know that Herman can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Herman","Cecil"],"index":57528,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999115169,"difficulty":0.000884831}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. John's card is shown to Kathleen. Allen's card is shown to Allen. John's card is shown to Allen. Kathleen's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know whether Allen can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Allen","John"],"index":56414,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984257221,"difficulty":0.0015742779}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know that Emily's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Margaret","Gerald","Emily"],"index":65956,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973368049,"difficulty":0.0026631951}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Reed. Tom's card is shown to Reed. Reed's card is shown to Tom. Tom's card is shown to Tom. Melissa's card is shown to Tom. Jeffrey's card is shown to Melissa. Melissa's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tom can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Reed","Tom","Melissa"],"index":4156,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989706278,"difficulty":0.0010293722}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annie knows whether someone is thirsty. It is publicly announced that Bill does not know whether Annie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Annie can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bill","Nicole","Annie","Reva"],"index":34582,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954051971,"difficulty":0.0045948029}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Larry can now know that Raymond can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Larry","Travis","Raymond"],"index":45203,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998857975,"difficulty":0.001142025}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether or not nobody's forehead is muddy. It is publicly announced that Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Helen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ashley","James","Evelyn","Helen"],"index":4561,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998316288,"difficulty":0.001683712}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roger does not know whether Roger's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Rosa can now know that Roger can know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rosa","Roger","Mark","Bryan"],"index":55131,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952760935,"difficulty":0.0047239065}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helena can now know that Derrick can know that Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Derrick","Roy","Helena","Ruth"],"index":66707,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976721406,"difficulty":0.0023278594}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cassandra knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Marie can now know whether Michaela can know whether Micheal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Michaela","Micheal","Cassandra"],"index":43127,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.874093473,"difficulty":0.125906527}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"James can now know that Nancy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nancy","James"],"index":49674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989461303,"difficulty":0.0010538697}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Melissa's card is shown to Martha. Martha's card is shown to Martha. Martha's card is shown to Glenn. Glenn's card is shown to Glenn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melissa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Martha","Moon","Glenn"],"index":17837,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989901185,"difficulty":0.0010098815}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Corey is thirsty. It is publicly announced that Patricia does not know whether William is thirsty. It is publicly announced that Patricia does not know whether Corey is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Patricia can now know whether Corey can know whether Corey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Corey","William","Patricia"],"index":45237,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9981887937,"difficulty":0.0018112063}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann does not know whether Dawn is thirsty. It is publicly announced that Ann is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Ann can now know that James can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dawn","James","Ann"],"index":64106,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999491334,"difficulty":0.000508666}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynne does not know whether Alice is thirsty. It is publicly announced that Brian does not know whether Ruben is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Brian can now know that Lynne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lynne","Ruben","Alice","Brian"],"index":46545,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966002107,"difficulty":0.0033997893}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marie knows whether someone is thirsty. It is publicly announced that Eric does not know whether Dawn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Dawn can now know that Eric can know whether Eric is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dawn","Marie","Eric"],"index":43546,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8113947511,"difficulty":0.1886052489}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Alejandro knows whether Alejandro's forehead is muddy. It is publicly announced that Bradley knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Alejandro can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alejandro","Bradley"],"index":3617,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993745685,"difficulty":0.0006254315}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Penny can now know whether Reginald can know that Reginald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Reginald","Ruth","Bertha","Penny"],"index":24485,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9818618894,"difficulty":0.0181381106}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juliette knows whether Ora's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Juliette can now know whether Ora can know that Ora's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Juliette","Ora"],"index":10500,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8201522231,"difficulty":1.8201522231}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Charles's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Charles can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lucille","Michael","Charles","Christopher"],"index":24589,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.995875299,"difficulty":0.004124701}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonnie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Barbara can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bonnie","Delma","Barbara"],"index":15631,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985635877,"difficulty":0.0014364123}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Danny does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Maude can now know that Glen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maude","Glen","Danny","Robert"],"index":60818,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9141180515,"difficulty":0.0858819485}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Troy can now know whether Shawn can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shawn","Larry","Troy"],"index":20716,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9846448302,"difficulty":0.0153551698}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerald is not thirsty. It is publicly announced that Ellen does not know whether Amy is thirsty. It is publicly announced that Amy does not know whether Ellen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Ellen can now know that Gerald can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerald","Ellen","Mark","Amy"],"index":24515,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994788766,"difficulty":0.0005211234}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Percy's card is shown to Wayne. Marie's card is shown to Wayne. Percy's card is shown to Percy. Wayne's card is shown to Marie. Edith's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Wayne picked a black card. It is publicly announced that Marie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! 3 ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! 3 ] 0","hypothesis":"Wayne can now know whether Percy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","Percy","Marie","Edith"],"index":59349,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9885643125,"difficulty":0.0114356875}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lissette can now know that Scott can know that Agnes's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lissette","Scott","Agnes","Carlos"],"index":27187,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976499677,"difficulty":0.0023500323}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"George can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harry","Susan","George","Steven"],"index":61886,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993237257,"difficulty":0.0006762743}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Robert can now know that Nina can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","William","Nina","Matthew"],"index":48536,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960768819,"difficulty":0.0039231181}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anita's card is shown to Andrew. Andrew's card is shown to Rick. Anita's card is shown to Rick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Connie can now know whether Connie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Connie","Anita","Rick"],"index":7742,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955685735,"difficulty":0.0044314265}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana knows whether or not nobody's forehead is muddy. It is publicly announced that Diana does not know whether Diana's forehead is muddy. It is publicly announced that Diana knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Kyle can now know whether Kyle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kyle","Diana","Jean"],"index":18990,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9399721026,"difficulty":1.9399721026}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roger knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether Kristen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elizabeth","Roger","Kristen"],"index":11473,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993811846,"difficulty":0.0006188154}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heidi's card is shown to Mary. Billy's card is shown to Heidi. Billy's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Billy knows whether or not nobody picked a red card. It is publicly announced that Heidi picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 2 ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Heidi","Billy","Denise"],"index":13543,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9141896367,"difficulty":0.0858103633}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicholas knows whether Nicholas is thirsty. It is publicly announced that Nicholas does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Fannie can now know that Marie can know that Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Fannie","Margaret","Nicholas","Marie"],"index":9864,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977805018,"difficulty":0.0022194982}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene knows whether someone's forehead is muddy. It is publicly announced that Patricia's forehead is muddy. It is publicly announced that Corrine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Corrine can now know whether Patricia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Irene","Corrine","Patricia"],"index":18933,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992944002,"difficulty":0.0007055998}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eduardo does not know whether Carl is thirsty. It is publicly announced that John knows whether someone is thirsty. It is publicly announced that Eduardo does not know whether or not everyone is thirsty. It is publicly announced that Linda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Linda can now know that Carl can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Eduardo","Carl","Linda"],"index":23949,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994401336,"difficulty":0.0005598664}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rick knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Rick can now know whether Jacquelyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jacquelyn","Robert","Rick"],"index":6996,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980099797,"difficulty":0.0019900203}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis does not know whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Earl can now know that Allison can know whether Earl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earl","Allison","Dennis","John"],"index":5258,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987078905,"difficulty":0.0012921095}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether Scott is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Scott can now know that Elizabeth can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Shirley","Jason","Elizabeth"],"index":42966,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990267754,"difficulty":0.0009732246}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy. It is publicly announced that Donna's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Donna can now know that Thomas can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Thomas","Donna"],"index":34621,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982398748,"difficulty":0.0017601252}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clinton does not know whether Marcus is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Marcus can now know whether Joyce can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clinton","Joyce","Marcus"],"index":54738,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9957369566,"difficulty":0.0042630434}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yvette knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Bruce can now know whether Tyler can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Yvette","Tyler","Barbara","Bruce"],"index":31596,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9960797429,"difficulty":0.0039202571}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqualine's card is shown to Jacqualine. Randall's card is shown to Jacqualine. Jacqualine's card is shown to Melody. Randall's card is shown to Melody. Melody's card is shown to Margarita. Margarita's card is shown to Margarita. Melody's card is shown to Randall. It is publicly announced that someone picked a red card. It is publicly announced that Melody knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Randall can now know whether Melody can know whether Margarita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jacqualine","Melody","Margarita","Randall"],"index":58002,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989259839,"difficulty":0.0010740161}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Daniel can now know that Wayne can know that Virginia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Virginia","Wayne"],"index":19471,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978029132,"difficulty":0.0021970868}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Carlos. Carlene's card is shown to Robert. Robert's card is shown to Carlene. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Carlos can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carlos","Robert","Carlene"],"index":54972,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9773311019,"difficulty":0.0226688981}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Mary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","John"],"index":53417,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994177818,"difficulty":0.0005822182}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Clarence does not know whether Doris is thirsty. It is publicly announced that William knows whether or not everyone is thirsty. It is publicly announced that William does not know whether Clarence is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"William can now know that Doris can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Clarence","William"],"index":33755,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999476254,"difficulty":0.000523746}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alicia does not know whether John is thirsty. It is publicly announced that John does not know whether Alicia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"John can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yolanda","John","Alicia"],"index":62085,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970017076,"difficulty":0.0029982924}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Lisa's card is shown to John. Dorothy's card is shown to John. Augusta's card is shown to Lisa. John's card is shown to Dorothy. John's card is shown to Augusta. Lisa's card is shown to Augusta. Dorothy's card is shown to Augusta. Augusta's card is shown to Augusta. It is publicly announced that someone picked a red card. It is publicly announced that Lisa does not know whether Dorothy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:1 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:1 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Augusta can now know whether Lisa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Lisa","Dorothy","Augusta"],"index":24959,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994075298,"difficulty":0.0005924702}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mitchell's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Dawn can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dawn","Lauren","Mitchell","Lionel"],"index":22831,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999420166,"difficulty":0.000579834}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vincent's card is shown to Beverly. Robert's card is shown to Vincent. Delmy's card is shown to Robert. Robert's card is shown to Delmy. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Beverly does not know whether Beverly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Delmy can now know whether Vincent can know whether Delmy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Vincent","Robert","Delmy"],"index":4631,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9976497293,"difficulty":0.0023502707}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clayton is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Clayton can now know whether Wayne can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Clayton","Wayne"],"index":49162,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9706532955,"difficulty":0.0293467045}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annette's card is shown to Gerald. Annette's card is shown to Linda. Annette's card is shown to Annette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Linda can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerald","Linda","Robert","Annette"],"index":67416,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9684076905,"difficulty":1.9684076905}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Barry. Barry's card is shown to Charles. Charles's card is shown to Charles. John's card is shown to Billie. Billie's card is shown to Billie. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Barry can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barry","Charles","John","Billie"],"index":65521,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9932923317,"difficulty":0.0067076683}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana knows whether Diana's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Darlene can now know that Diana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diana","Sonia","Annette","Darlene"],"index":13656,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966795444,"difficulty":0.0033204556}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Tracy's forehead is muddy. It is publicly announced that Steven does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Steven can now know that Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ashley","Tracy","Steven"],"index":26702,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9085294604,"difficulty":0.0914705396}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristine's card is shown to Cori. Howard's card is shown to Howard. Cori's card is shown to Michele. Howard's card is shown to Michele. Cristine's card is shown to Cristine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cristine can now know whether Howard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cori","Howard","Michele","Cristine"],"index":44777,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8150131106,"difficulty":0.1849868894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether Lupe's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Alberta can now know that Carrol can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anna","Alberta","Carrol","Lupe"],"index":31253,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993972778,"difficulty":0.0006027222}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon does not know whether or not everyone's forehead is muddy. It is publicly announced that Paula knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Gordon can now know whether Gordon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Gordon","Paula","Lawrence"],"index":18302,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.918841362,"difficulty":0.081158638}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Zella does not know whether Allan is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Zella can now know whether Allan can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Zella","Allan"],"index":39301,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994449019,"difficulty":0.0005550981}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Julie. Nancy's card is shown to Tonia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tonia can now know whether Julie can know whether Julie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julie","Tonia","Nancy","Jason"],"index":13384,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5044658184,"difficulty":1.5044658184}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chad's card is shown to Virginia. Virginia's card is shown to Virginia. Zelma's card is shown to Virginia. Chad's card is shown to Zelma. Sarah's card is shown to Zelma. Sarah's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Sarah picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Zelma can now know whether Chad can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chad","Virginia","Zelma","Sarah"],"index":59049,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.935518682,"difficulty":0.064481318}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeffrey can now know that Pamela can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frederick","Pamela","Jeffrey"],"index":14517,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9939540029,"difficulty":0.0060459971}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill does not know whether Bill's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Bill can now know whether Megan can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Joseph","Bill","Megan"],"index":60965,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994108677,"difficulty":0.0005891323}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Ryan. Roman's card is shown to Ryan. Mark's card is shown to Mark. Roman's card is shown to Mark. Roman's card is shown to Roman. Amanda's card is shown to Roman. Amanda's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Mark can now know that Amanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ryan","Mark","Roman","Amanda"],"index":57973,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9911245704,"difficulty":0.0088754296}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Duane. Stanley's card is shown to Duane. Sol's card is shown to Stanley. Rocky's card is shown to Sol. It is publicly announced that someone picked a red card. It is publicly announced that Duane does not know whether or not everyone picked a red card. It is publicly announced that Stanley knows whether Duane picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Duane can now know that Stanley can know whether Stanley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Duane","Stanley","Rocky","Sol"],"index":48399,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8113360405,"difficulty":0.1886639595}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth is thirsty. It is publicly announced that Mark knows whether Mark is thirsty. It is publicly announced that Kenneth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Mark can now know that Ronald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Kenneth","Ronald","Benjamin"],"index":19730,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9463716745,"difficulty":0.0536283255}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shantelle's card is shown to Derrick. Mary's card is shown to Derrick. Derrick's card is shown to Shantelle. Derrick's card is shown to Mickey. Shantelle's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Derrick does not know whether Derrick picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Shantelle can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Derrick","Shantelle","Mickey","Mary"],"index":40282,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990109205,"difficulty":0.0009890795}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Otis does not know whether Kent is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Katherine can now know that Otis can know whether Otis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Otis","Katherine","James","Kent"],"index":20032,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9900085926,"difficulty":0.0099914074}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"John can now know whether Norma can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Norma","Aaron","Shaun"],"index":11660,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999371469,"difficulty":0.000628531}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Mary can now know whether Patricia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Sybil","Eugene","Mary"],"index":39097,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.987244308,"difficulty":0.012755692}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Charles can now know that Miesha can know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Miesha","Cecil"],"index":22124,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988812804,"difficulty":0.0011187196}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether Wendy's forehead is muddy. It is publicly announced that Wendy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Thomas can now know that Wendy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Ruth","Wendy"],"index":59426,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993726611,"difficulty":0.0006273389}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Gladys can now know whether Robert can know that Gladys's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Gladys"],"index":38760,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994360805,"difficulty":0.0005639195}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Bonnie. Bonnie's card is shown to Brittany. Brittany's card is shown to Brittany. Brittany's card is shown to Christi. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Bonnie can now know whether Christi can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Brittany","Christi"],"index":2237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994223118,"difficulty":0.0005776882}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vanessa does not know whether Keith is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Keith can now know whether Keith is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Keith","Pedro","Vanessa","Elbert"],"index":59155,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9960100651,"difficulty":0.0039899349}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luis does not know whether or not everyone is thirsty. It is publicly announced that Luis knows whether or not nobody is thirsty. It is publicly announced that Tanya knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Tanya can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chrissy","Tanya","Patricia","Luis"],"index":45589,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985412359,"difficulty":0.0014587641}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Nancy. Marcene's card is shown to Marcene. Nancy's card is shown to Randy. Randy's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that Randy does not know whether Marcene picked a red card. It is publicly announced that Randy knows whether Nancy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Marcene can now know whether Nancy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Marcene","Randy"],"index":57856,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9751098752,"difficulty":1.9751098752}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janina knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Charlotte can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janina","Brian","Shannon","Charlotte"],"index":36049,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994882345,"difficulty":0.0005117655}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur's forehead is muddy. It is publicly announced that Darlene does not know whether Darlene's forehead is muddy. It is publicly announced that Darlene knows whether Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] Agentb knows that (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Nancy can now know that Arthur can know that Myra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arthur","Nancy","Myra","Darlene"],"index":8222,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937884212,"difficulty":0.0062115788}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Margarita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Teresa can now know that Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Margarita","Arturo","Mary","Teresa"],"index":38853,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974428415,"difficulty":0.0025571585}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason does not know whether Jason's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jason can now know whether Michael can know that Jason's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jason","Michael"],"index":19171,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6745359898,"difficulty":1.6745359898}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether someone's forehead is muddy. It is publicly announced that Laura knows whether Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentb knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Pamela can now know whether Jean can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jean","Pamela","James","Laura"],"index":42118,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994328618,"difficulty":0.0005671382}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nona does not know whether Rachel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Steven can now know whether Nona can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Candice","Steven","Rachel","Nona"],"index":42962,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992695451,"difficulty":0.0007304549}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentd knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Jennifer can now know whether James can know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wanda","James","Todd","Jennifer"],"index":57141,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9719991088,"difficulty":0.0280008912}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita does not know whether Rita's forehead is muddy. It is publicly announced that Nicholas knows whether Nicholas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Nicholas can now know whether Rita can know whether Rita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Nicholas","Rita"],"index":1959,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9206030965,"difficulty":0.0793969035}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Errol's card is shown to Errol. Jean's card is shown to Roger. Jean's card is shown to Lenora. Errol's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Lenora picked a red card. It is publicly announced that Lenora does not know whether Roger picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Roger can now know whether Jean can know that Errol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Errol","Roger","Lenora","Jean"],"index":37877,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9133840799,"difficulty":1.9133840799}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Carmen. Alice's card is shown to Carmen. David's card is shown to David. Alice's card is shown to David. Alice's card is shown to Joseph. David's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Joseph can now know whether Alice can know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carmen","David","Joseph","Alice"],"index":14906,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998723805,"difficulty":0.001276195}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether James's forehead is muddy. It is publicly announced that Dorothy knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mary can now know that Melody can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","James","Mary","Melody"],"index":19286,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972809553,"difficulty":0.0027190447}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathryn knows whether Mitchell is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Kathryn can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kathryn","Mitchell"],"index":6764,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995160103,"difficulty":0.0004839897}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jorge can now know whether Charles can know whether Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jorge","April","Charles"],"index":45560,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9970484376,"difficulty":0.0029515624}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa does not know whether Scott is thirsty. It is publicly announced that Scott does not know whether Allyson is thirsty. It is publicly announced that Allyson is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Allyson can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Josephine","Scott","Allyson","Teresa"],"index":42356,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8034144044,"difficulty":0.1965855956}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edwin knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Charles can now know whether Edwin can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edwin","Osvaldo","Charles"],"index":41832,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993752837,"difficulty":0.0006247163}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether Jared's forehead is muddy. It is publicly announced that Jared does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Debra can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jared","Debra"],"index":63137,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8075428605,"difficulty":0.1924571395}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Sammie can now know that Carroll can know that Sammie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sammie","Carroll"],"index":7660,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9895098209,"difficulty":0.0104901791}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Hannah can now know that Frances can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frances","Hannah"],"index":9745,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994804263,"difficulty":0.0005195737}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlotte's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Richard can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Charlotte","Sonja"],"index":25804,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988116026,"difficulty":0.0011883974}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether Anna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Helene can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Helene","Anna"],"index":22491,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986937642,"difficulty":0.0013062358}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Elizabeth. Douglas's card is shown to Douglas. Elizabeth's card is shown to Rosa. Rosa's card is shown to Rosa. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know that Rosa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Douglas","Rosa"],"index":32411,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9938515425,"difficulty":0.0061484575}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Robert is thirsty. It is publicly announced that Robert does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Troy can now know whether Richard can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Latonya","Richard","Robert","Troy"],"index":14984,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9937371016,"difficulty":0.0062628984}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Emily can now know that Maria can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Emily","Nora","Maria"],"index":9717,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989159107,"difficulty":0.0010840893}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Julius. Julius's card is shown to Kenneth. Julius's card is shown to Christy. It is publicly announced that someone picked a red card. It is publicly announced that Julius does not know whether or not everyone picked a red card. It is publicly announced that Julius does not know whether Julius picked a red card. It is publicly announced that Christy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Christy can now know whether Kenneth can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julius","Kenneth","Christy"],"index":23563,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994571805,"difficulty":0.0005428195}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Renee does not know whether Paige is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Renee can now know whether Joshua can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Renee","Joshua","Paige","Millicent"],"index":52837,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989769459,"difficulty":0.0010230541}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Becky's card is shown to Becky. Kevin's card is shown to Becky. Kevin's card is shown to Kevin. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Becky can now know whether Kevin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Becky","Kevin","Douglas"],"index":46989,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7713848352,"difficulty":1.7713848352}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Lisa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Lisa can now know whether Eunice can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Richard","John","Eunice"],"index":35933,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9956694841,"difficulty":0.0043305159}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lenora's card is shown to Kathryn. Kathryn's card is shown to Ruth. Ruth's card is shown to Ruth. Kathryn's card is shown to Scott. Ruth's card is shown to Scott. Kathryn's card is shown to Lenora. Lenora's card is shown to Lenora. It is publicly announced that someone picked a red card. It is publicly announced that Ruth picked a black card. It is publicly announced that Ruth does not know whether Lenora picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ruth can now know whether Kathryn can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Ruth","Scott","Lenora"],"index":35635,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9944850802,"difficulty":0.0055149198}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jeremy can now know that David can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Jeremy","David","James"],"index":28936,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928966165,"difficulty":0.0071033835}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hazel does not know whether Julie is thirsty. It is publicly announced that William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] Agentc knows that (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Julie can now know that Jack can know whether Julie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hazel","William","Julie","Jack"],"index":41152,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8440182805,"difficulty":1.8440182805}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Scott. Carolyn's card is shown to Carolyn. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Carolyn knows whether Scott picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Scott can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Scott","Carolyn"],"index":2934,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949132204,"difficulty":0.0050867796}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Pamela can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Geraldine","Pamela","Jordan","Virginia"],"index":38808,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990278482,"difficulty":0.0009721518}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sam knows whether Dennis's forehead is muddy. It is publicly announced that Dwayne does not know whether Dwayne's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dennis can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Dwayne","Sam"],"index":24924,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988802075,"difficulty":0.0011197925}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Warren knows whether Warren is thirsty. It is publicly announced that Sally does not know whether Warren is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Bryan does not know whether Jonathan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Warren can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Warren","Bryan","Jonathan","Sally"],"index":12572,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994675517,"difficulty":0.0005324483}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Carol can now know that Gina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Carol","Gina","Jamie"],"index":21025,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975247979,"difficulty":0.0024752021}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne knows whether Daphne's forehead is muddy. It is publicly announced that Joanne knows whether Daphne's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Daphne can now know whether Joanne can know that Joanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joanne","Daphne"],"index":52012,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992517829,"difficulty":0.0007482171}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Catherine can now know that Johnnie can know that Catherine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Johnnie","Catherine"],"index":34232,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9943038821,"difficulty":0.0056961179}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"John can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Eric","George"],"index":31831,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941138625,"difficulty":0.0058861375}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Christine knows whether Magali's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Corina can now know whether Christine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Magali","Christine","Corina"],"index":64432,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993952513,"difficulty":0.0006047487}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Betty can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thomas","Carol","Betty"],"index":30909,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990341663,"difficulty":0.0009658337}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Yvette can now know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Yvette","Crystal","Theodore"],"index":61325,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99923563,"difficulty":0.00076437}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jewell's card is shown to Charles. Christopher's card is shown to Christopher. Jewell's card is shown to Christopher. Charles's card is shown to Jewell. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Dennis","Christopher","Jewell"],"index":9732,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940683842,"difficulty":0.0059316158}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Peter's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Cynthia can now know that James can know that Cynthia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","James","Santana","Peter"],"index":8462,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998354435,"difficulty":0.001645565}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bertha knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Sarah can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bertha","Sarah"],"index":5209,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9952511787,"difficulty":0.0047488213}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chong's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"David can now know whether Chong can know whether Holly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronnie","Holly","David","Chong"],"index":9705,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993587136,"difficulty":0.0006412864}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Dena can now know that Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Dena","Rose","Michael"],"index":18282,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9910652041,"difficulty":0.0089347959}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bessie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bessie","Juan","Michael"],"index":60306,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984803796,"difficulty":0.0015196204}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Albert is not thirsty. It is publicly announced that Albert does not know whether Lovella is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Albert can now know that James can know whether Lovella is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lovella","James","Albert"],"index":38642,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9899431467,"difficulty":0.0100568533}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irving's card is shown to Irving. Laurence's card is shown to Laurence. Douglass's card is shown to Laurence. Douglass's card is shown to Douglass. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Irving can now know that Laurence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Irving","Laurence","Douglass"],"index":15666,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962294698,"difficulty":0.0037705302}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elmer's card is shown to Janelle. Elmer's card is shown to Elmer. It is publicly announced that someone picked a red card. It is publicly announced that Elmer does not know whether or not everyone picked a red card. It is publicly announced that Janelle knows whether Elmer picked a red card. It is publicly announced that Elmer does not know whether Janelle picked a red card. It is publicly announced that Elmer knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Janelle can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Janelle","Elmer"],"index":42465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994685054,"difficulty":0.0005314946}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Damon does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Lloyd can now know whether Brandon can know whether Damon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lloyd","Damon","Brandon","Helen"],"index":19980,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990311861,"difficulty":0.0009688139}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candice's card is shown to Candice. Paula's card is shown to Paula. It is publicly announced that someone picked a red card. It is publicly announced that Candice knows whether or not everyone picked a red card. It is publicly announced that Candice picked a black card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Candice can now know that Alison can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Candice","Alison","Paula"],"index":20951,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9427280426,"difficulty":0.0572719574}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard does not know whether Howard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Joshua can now know whether Howard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joshua","Patricia","Dorothy","Howard"],"index":13167,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991556406,"difficulty":0.0008443594}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delma knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Mildred can now know whether Easter can know whether Easter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Delma","Easter","Mildred"],"index":24661,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993158579,"difficulty":0.0006841421}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Belinda does not know whether Belinda's forehead is muddy. It is publicly announced that Belinda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Hubert can now know whether Antonette can know whether Hubert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Belinda","Hubert","Antonette","Lester"],"index":53015,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9981324077,"difficulty":0.0018675923}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy. It is publicly announced that Salvatore knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Royce can now know whether Elizabeth can know that Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Royce","Bryan","Elizabeth","Salvatore"],"index":67214,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994823933,"difficulty":0.0005176067}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"William can now know whether William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jennifer","Richard","Daniel","William"],"index":54995,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7751780748,"difficulty":0.2248219252}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Sonya. Brenda's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Sonya knows whether Brenda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sonya can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sonya","Brenda"],"index":65782,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999468863,"difficulty":0.000531137}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Jesus knows whether Lynette is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Lee can now know whether Lynette can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesus","Lynette","William","Lee"],"index":47934,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993315935,"difficulty":0.0006684065}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard does not know whether Leonard's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Leonard can now know whether Audie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Todd","Leonard","Audie"],"index":67674,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992126226,"difficulty":0.0007873774}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Tom. Susan's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Kim picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Susan can now know whether Kim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tom","Susan","Kim"],"index":66183,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.987711966,"difficulty":0.012288034}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doris does not know whether or not everyone is thirsty. It is publicly announced that Marvin does not know whether Israel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Freddie can now know whether Freddie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Freddie","Israel","Doris","Marvin"],"index":58394,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9418815374,"difficulty":0.0581184626}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kori knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Kori can now know that Ryan can know that Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ryan","Kori","Jeffrey"],"index":55609,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969800115,"difficulty":0.0030199885}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rick's card is shown to Rick. Thomas's card is shown to Rick. Rick's card is shown to Carmelina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carmelina can now know whether Rick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rick","Carmelina","Thomas"],"index":16355,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9621990323,"difficulty":0.0378009677}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricky's card is shown to Ricky. Caroline's card is shown to Darius. It is publicly announced that someone picked a red card. It is publicly announced that Caroline does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Caroline can now know whether Caroline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Caroline","Ricky","Darius"],"index":20802,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8234527111,"difficulty":1.8234527111}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Kristen can now know whether Kathleen can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kristen","Kathleen","James"],"index":54485,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993952513,"difficulty":0.0006047487}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Christopher. Christopher's card is shown to Ann. James's card is shown to Ann. Ann's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether or not everyone picked a red card. It is publicly announced that James picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Thomas can now know that Christopher can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Thomas","Ann","James"],"index":44972,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998899579,"difficulty":0.001100421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elsa's forehead is muddy. It is publicly announced that Joseph's forehead is not muddy. It is publicly announced that Elsa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Elsa can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elsa","Kathleen","Joseph"],"index":55751,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990314245,"difficulty":0.0009685755}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruby does not know whether Michael is thirsty. It is publicly announced that John does not know whether Michael is thirsty. It is publicly announced that John knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ruby","George","Michael","John"],"index":8785,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9981355667,"difficulty":0.0018644333}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roger's card is shown to Roger. George's card is shown to Roger. Roger's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know that Roger can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roger","Kevin","George","Timothy"],"index":53028,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993715882,"difficulty":0.0006284118}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pamela does not know whether or not everyone is thirsty. It is publicly announced that Pamela knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Pamela can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erna","Pamela"],"index":45730,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999071002,"difficulty":0.000928998}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathan's card is shown to Stephen. John's card is shown to Stephen. Stephen's card is shown to Irvin. Nathan's card is shown to John. Stephen's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nathan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nathan","Stephen","Irvin","John"],"index":47069,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951692224,"difficulty":0.0048307776}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jonathan can now know whether Maria can know that Jonathan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jonathan","Maria","Juanita"],"index":23262,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999352634,"difficulty":0.000647366}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheri's card is shown to Sheri. Denise's card is shown to Victor. Sheri's card is shown to Janelle. Janelle's card is shown to Janelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sheri can now know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sheri","Victor","Janelle","Denise"],"index":42973,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917068481,"difficulty":0.0082931519}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Connie's card is shown to Sheri. Connie's card is shown to Curt. Curt's card is shown to Curt. Charlie's card is shown to Curt. Sheri's card is shown to Charlie. Charlie's card is shown to Charlie. It is publicly announced that someone picked a red card. It is publicly announced that Curt picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Sheri can now know whether Connie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Connie","Sheri","Curt","Charlie"],"index":54755,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994339347,"difficulty":0.0005660653}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Regina's card is shown to Linda. Linda's card is shown to Regina. Jacquelyn's card is shown to Regina. Regina's card is shown to Jacquelyn. It is publicly announced that someone picked a red card. It is publicly announced that Regina knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Linda can now know whether Jacquelyn can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Regina","Jacquelyn"],"index":31799,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9824403524,"difficulty":1.9824403524}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maida does not know whether Maida's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Julieta can now know that Casey can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Casey","Maida","Julieta"],"index":1426,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989321828,"difficulty":0.0010678172}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michelle's card is shown to Michelle. Rita's card is shown to Michelle. Olga's card is shown to Olga. Leif's card is shown to Olga. Rita's card is shown to Olga. Michelle's card is shown to Leif. Leif's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Rita knows whether or not nobody picked a red card. It is publicly announced that Rita picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Olga can now know whether Michelle can know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Olga","Leif","Rita"],"index":12225,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9709165096,"difficulty":1.9709165096}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allen knows whether Sylvia's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvia does not know whether Sylvia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Betty can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Allen","Betty","Sylvia"],"index":46409,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994795918,"difficulty":0.0005204082}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Linda knows whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Faye can now know whether Linda can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Faye","Frances"],"index":19787,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993639588,"difficulty":0.0006360412}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carla knows whether Carla's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jessie can now know that Carla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessie","Carla","Katrina"],"index":63482,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9950813055,"difficulty":0.0049186945}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharilyn does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"William can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","Sharilyn","William","Amy"],"index":20505,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.937464416,"difficulty":0.062535584}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patrick does not know whether Mark is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Crystal can now know that Keith can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Crystal","Mark","Patrick"],"index":8665,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993632436,"difficulty":0.0006367564}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glen's card is shown to Glen. Holly's card is shown to Glen. Glen's card is shown to Joseph. Holly's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Glen knows whether or not nobody picked a red card. It is publicly announced that Holly knows whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 3) ] (Agenta knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Glen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Glen","Holly","Joseph"],"index":20401,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994571805,"difficulty":0.0005428195}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judy does not know whether or not everyone is thirsty. It is publicly announced that Judy knows whether or not nobody is thirsty. It is publicly announced that Catherine does not know whether Marcia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Judy can now know that Marcia can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Judy","Marcia","Catherine"],"index":17463,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9940342307,"difficulty":0.0059657693}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Alice. Marsha's card is shown to Marsha. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Alice can now know that Marsha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alice","Marsha"],"index":9803,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959290624,"difficulty":0.0040709376}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Carol can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Cecil","Carol"],"index":24638,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994026423,"difficulty":0.0005973577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Polly does not know whether or not everyone is thirsty. It is publicly announced that Polly does not know whether David is thirsty. It is publicly announced that Antoinette does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Polly can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Antoinette","Polly","Robert","David"],"index":52738,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9759776592,"difficulty":0.0240223408}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to James. Larry's card is shown to Gail. James's card is shown to Alexandra. Alexandra's card is shown to Alexandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Gail","Alexandra","Larry"],"index":2777,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988683462,"difficulty":0.0011316538}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Carlos can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willie","Richard","Kenneth","Carlos"],"index":64691,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99672544,"difficulty":0.00327456}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Sherry. Michael's card is shown to Sherry. Wayne's card is shown to Wayne. Sherry's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Wayne does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sherry can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherry","Wayne","Michael"],"index":8177,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9247772098,"difficulty":0.0752227902}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Jack. Beth's card is shown to Martin. Beth's card is shown to Cathy. Cathy's card is shown to Cathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beth can now know that Martin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","Beth","Martin","Cathy"],"index":56179,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984677434,"difficulty":0.0015322566}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ryan does not know whether Nestor is thirsty. It is publicly announced that Bryan does not know whether Ryan is thirsty. It is publicly announced that Bryan does not know whether Ryan is thirsty. It is publicly announced that Maria knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ryan can now know whether Nestor can know whether Ryan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nestor","Maria","Bryan","Ryan"],"index":8561,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988307357,"difficulty":0.0011692643}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Judith can now know that John can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Judith","John","Karin"],"index":50542,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994879961,"difficulty":0.0005120039}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Donna does not know whether Michael is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Michael does not know whether Nola is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Michael can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nola","Michael","Donna"],"index":38767,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993941784,"difficulty":0.0006058216}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sean's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Donna can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sean","Donna"],"index":14247,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988626242,"difficulty":0.0011373758}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dario's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Cynthia can now know whether John can know that Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Dario","Cynthia"],"index":15424,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9764716029,"difficulty":0.0235283971}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Roy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roy","David","Stanley","Donn"],"index":42441,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989808202,"difficulty":0.0010191798}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lee's card is shown to Lee. Nicholas's card is shown to Lee. Tara's card is shown to Lee. Lee's card is shown to Nicholas. Nicholas's card is shown to Nicholas. Lee's card is shown to Tara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nicholas can now know whether Lee can know whether Nicholas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lee","Nicholas","Tara"],"index":61958,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982224107,"difficulty":0.0017775893}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether Carolyn's forehead is muddy. It is publicly announced that Georgia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] Agentd knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Maria can now know whether Georgia can know whether Georgia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Clifford","Georgia","Maria"],"index":14303,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994469285,"difficulty":0.0005530715}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marilee knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Maureen can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maureen","Marilee","Gary"],"index":45016,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.990060091,"difficulty":0.009939909}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria does not know whether Maria's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Andrea can now know whether Maria can know whether Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maria","Andrea"],"index":51288,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9268399477,"difficulty":0.0731600523}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martine's card is shown to Dorthy. Christopher's card is shown to Martine. Martine's card is shown to Jimmy. Jimmy's card is shown to Jimmy. Martine's card is shown to Christopher. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dorthy","Martine","Jimmy","Christopher"],"index":22155,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994029999,"difficulty":0.0005970001}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Eileen can now know that Patricia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jay","Ryan","Eileen","Patricia"],"index":8904,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989601374,"difficulty":0.0010398626}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pam does not know whether Pam's forehead is muddy. It is publicly announced that Pam does not know whether Pam's forehead is muddy. It is publicly announced that Pam's forehead is not muddy. It is publicly announced that Amy does not know whether Amy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jodi can now know that Amy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jodi","Pam","Amy"],"index":53701,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998832047,"difficulty":0.001167953}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Brenda can now know that Daniel can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Daniel","John","Wayne"],"index":25780,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995115995,"difficulty":0.0004884005}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Leo is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Jacqueline knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"David can now know whether Jacqueline can know that Leo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leo","David","Jacqueline"],"index":3916,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9678009152,"difficulty":0.0321990848}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Toni does not know whether Willie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Riley can now know that Willie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Toni","Riley","Willie"],"index":36520,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963294864,"difficulty":0.0036705136}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ana can now know whether Jean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerald","Ana","Jean","James"],"index":51321,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994244576,"difficulty":0.0005755424}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha is thirsty. It is publicly announced that Miriam does not know whether Gerald is thirsty. It is publicly announced that James knows whether or not nobody is thirsty. It is publicly announced that James is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Gerald can now know whether James can know whether Miriam is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerald","Miriam","James","Martha"],"index":48418,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992413521,"difficulty":0.0007586479}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Elizabeth can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alan","Elizabeth","Linda"],"index":42909,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993988276,"difficulty":0.0006011724}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Allen can now know that Allen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diana","Allen","Michelle"],"index":45619,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983648658,"difficulty":0.0016351342}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Trisha's card is shown to John. Josephine's card is shown to Josephine. Josephine's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Trisha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Trisha","John","Josephine","Maria"],"index":11172,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993811965,"difficulty":0.006188035}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Casey's card is shown to Casey. Seth's card is shown to Casey. Casey's card is shown to Seth. It is publicly announced that someone picked a red card. It is publicly announced that Seth does not know whether or not everyone picked a red card. It is publicly announced that Seth picked a black card. It is publicly announced that Seth knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Seth can now know that Casey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Casey","Seth"],"index":5626,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7801541686,"difficulty":1.7801541686}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Danielle. Anna's card is shown to Mark. Anna's card is shown to Claudia. Claudia's card is shown to Claudia. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Claudia picked a red card. It is publicly announced that Danielle does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Anna can now know that Danielle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danielle","Mark","Anna","Claudia"],"index":7699,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9708945751,"difficulty":0.0291054249}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Micah can now know that Heather can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Heather","Rachel","Micah"],"index":2817,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993911982,"difficulty":0.0006088018}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Charles knows whether Charles is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Charles can now know that Marlon can know that Marlon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marlon","Charles"],"index":29154,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954289198,"difficulty":0.0045710802}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Edward. Crystal's card is shown to Edward. Jimmy's card is shown to Mary. Mary's card is shown to Jimmy. Crystal's card is shown to Crystal. It is publicly announced that someone picked a red card. It is publicly announced that Edward does not know whether Jimmy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mary can now know that Crystal can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Mary","Jimmy","Crystal"],"index":57456,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993490577,"difficulty":0.0006509423}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ariana's card is shown to Thelma. Alix's card is shown to Thelma. Thelma's card is shown to Alix. Alix's card is shown to Alix. Thelma's card is shown to Jeffrey. Ariana's card is shown to Jeffrey. Alix's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thelma can now know whether Alix picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thelma","Ariana","Alix","Jeffrey"],"index":57801,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6050261855,"difficulty":0.3949738145}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Missy. Robert's card is shown to Robert. Jean's card is shown to Robert. Jean's card is shown to Jean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Jean picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Missy","Robert","Jean"],"index":9566,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9900553226,"difficulty":0.0099446774}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Teresa can now know whether Teresa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Phyllis","Teresa","Elisabeth","Janita"],"index":65251,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9954156876,"difficulty":0.0045843124}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Edward can now know that Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Jose","Edward"],"index":64891,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9739596248,"difficulty":0.0260403752}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian is not thirsty. It is publicly announced that Brian does not know whether Alan is thirsty. It is publicly announced that Lon knows whether Lon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Alan can now know whether Donald can know that Lon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Alan","Lon","Donald"],"index":17236,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9885968566,"difficulty":0.0114031434}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to Ryan. Myra's card is shown to Diane. Richard's card is shown to Myra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Myra can now know that Myra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","Diane","Myra","Richard"],"index":40342,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953559637,"difficulty":0.0046440363}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sherry does not know whether Wilfred is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Wilfred can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sherry","Matthew","Wilfred"],"index":39419,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994428754,"difficulty":0.0005571246}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen does not know whether or not everyone's forehead is muddy. It is publicly announced that Marsha knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Monique can now know whether Marsha can know whether Walter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marsha","Monique","Walter","Stephen"],"index":60772,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992544055,"difficulty":0.0007455945}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joline's card is shown to Joline. David's card is shown to Joline. David's card is shown to Carrie. Carrie's card is shown to Carrie. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Joline can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joline","David","Carrie"],"index":1860,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Elva knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Elva can now know whether Mamie can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mamie","Elva"],"index":28755,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992396832,"difficulty":0.0007603168}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leah is thirsty. It is publicly announced that Stewart is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(1) ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(1) ] 0","hypothesis":"Stewart can now know that Joanne can know that Joanne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stewart","Leah","Joanne","Ruth"],"index":2642,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9947811961,"difficulty":0.0052188039}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Jose. Reginia's card is shown to Reginia. Christopher's card is shown to Reginia. Tomasa's card is shown to Tomasa. Jose's card is shown to Christopher. Reginia's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Tomasa picked a red card. It is publicly announced that Reginia picked a black card. It is publicly announced that Reginia knows whether Christopher picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Jose can now know that Christopher can know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Reginia","Tomasa","Christopher"],"index":22999,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.982363224,"difficulty":1.982363224}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Charles. Lonnie's card is shown to Lonnie. Kenneth's card is shown to Lonnie. Lonnie's card is shown to Kenneth. Linda's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether Kenneth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Lonnie","Kenneth","Linda"],"index":61684,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994130135,"difficulty":0.0005869865}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bessie's card is shown to Jessica. Barbara's card is shown to Bessie. It is publicly announced that someone picked a red card. It is publicly announced that Jessica does not know whether Jessica picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Barbara can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Barbara","Carlotta","Bessie"],"index":65907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999432385,"difficulty":0.000567615}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether Bill can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Bill"],"index":14745,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994199276,"difficulty":0.0005800724}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Megan's card is shown to Christopher. Shirley's card is shown to Shirley. Megan's card is shown to Shirley. Edna's card is shown to Shirley. Edna's card is shown to Edna. It is publicly announced that someone picked a red card. It is publicly announced that Shirley knows whether Megan picked a red card. It is publicly announced that Megan does not know whether Shirley picked a red card. It is publicly announced that Megan does not know whether Shirley picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Megan can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Shirley","Megan","Edna"],"index":56088,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8005000353,"difficulty":0.1994999647}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that May knows whether Juanita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kyle can now know that Juanita can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kyle","Juanita","May"],"index":39528,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9759844542,"difficulty":0.0240155458}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Lawrence. Lawrence's card is shown to Nicole. Rebecca's card is shown to Nicole. Nicole's card is shown to Nicole. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rebecca can now know that Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Rebecca","Nicole","Maria"],"index":577,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982162118,"difficulty":0.0017837882}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Michele. Michele's card is shown to Ronald. Kathryn's card is shown to Kathryn. It is publicly announced that someone picked a red card. It is publicly announced that Kathryn picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Michele can now know that Kathryn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michele","Ronald","Kathryn"],"index":31380,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8741513491,"difficulty":0.1258486509}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosie's card is shown to Samuel. Samuel's card is shown to Ralph. Patricia's card is shown to Ralph. Rosie's card is shown to Ralph. Samuel's card is shown to Patricia. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Samuel can now know whether Ralph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Samuel","Ralph","Patricia","Rosie"],"index":51759,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975126982,"difficulty":0.0024873018}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pinkie does not know whether Pinkie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Pinkie can now know that James can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Pinkie","Chris","Erica"],"index":34711,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9767286777,"difficulty":0.0232713223}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Helen's card is shown to Jonathan. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Jonathan can now know that Helen can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Helen","Jonathan"],"index":17280,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8938529491,"difficulty":0.1061470509}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Max can now know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Richard","Max","Oscar"],"index":1607,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9903070927,"difficulty":0.0096929073}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raven knows whether or not nobody's forehead is muddy. It is publicly announced that Pearl does not know whether or not everyone's forehead is muddy. It is publicly announced that Pearl's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Raven can now know that Pearl can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Raven","Pearl"],"index":31675,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988372922,"difficulty":0.0011627078}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. Curtis's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Curtis does not know whether Arthur picked a red card. It is publicly announced that Curtis does not know whether Arthur picked a red card. It is publicly announced that Arthur does not know whether or not everyone picked a red card. It is publicly announced that Curtis does not know whether Arthur picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Arthur can now know that Curtis can know whether Curtis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Curtis","Arthur"],"index":1475,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7771441936,"difficulty":0.2228558064}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether George is thirsty. It is publicly announced that George does not know whether Karen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"George can now know whether George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","David","Karen","George"],"index":56133,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9972752929,"difficulty":0.0027247071}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esther's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Stephanie can now know that Esther can know whether Esther's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Lula","Stephanie","Esther"],"index":31485,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8889213204,"difficulty":0.1110786796}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Carissa can now know that Carissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristy","Carissa","Charlotte"],"index":48632,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983172417,"difficulty":0.0016827583}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick knows whether or not nobody's forehead is muddy. It is publicly announced that Doris knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Patrick can now know whether Doris can know whether Doris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Doris","Patrick"],"index":33657,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994105101,"difficulty":0.0005894899}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Blanche knows whether Cory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Cory can now know whether Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bryan","Robert","Blanche","Cory"],"index":46192,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952483773,"difficulty":0.0047516227}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rufus does not know whether Rufus's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Rufus can now know whether Ray can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aurora","Ray","Blanche","Rufus"],"index":37400,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993866682,"difficulty":0.0006133318}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juan is thirsty. It is publicly announced that Cheryl knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Cheryl can now know whether Kenneth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cheryl","Kenneth","Juan"],"index":12833,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998034656,"difficulty":0.001965344}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether or not everyone is thirsty. It is publicly announced that Andre knows whether someone is thirsty. It is publicly announced that Amy does not know whether Andre is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Andre can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andre","Amy","Linda"],"index":26593,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990912676,"difficulty":0.0009087324}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wm knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Wm can now know that Leslie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sophia","Leslie","Wm"],"index":33445,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998267293,"difficulty":0.001732707}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lilia knows whether or not nobody's forehead is muddy. It is publicly announced that Victoria's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Victoria can now know whether Victoria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Victoria","Lilia"],"index":67304,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994649291,"difficulty":0.0005350709}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gloria knows whether someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Rubin can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rubin","Gloria"],"index":21146,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994676709,"difficulty":0.0005323291}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharron knows whether Roger's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Roger can now know that Sharron can know that Roger's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Roger","Sharron"],"index":16600,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9954124093,"difficulty":0.0045875907}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marilyn knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Eddie can now know that Marilyn can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eddie","Marilyn"],"index":55407,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993717074,"difficulty":0.0006282926}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Michael knows whether Mathew's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Mathew can now know that Mathew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","John","Mathew","Kay"],"index":26787,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9919828773,"difficulty":0.0080171227}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa knows whether Conrad's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Conrad can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Conrad","Theresa","Shawanda"],"index":23218,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994353652,"difficulty":0.0005646348}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Amanda. Jessica's card is shown to Amanda. Amanda's card is shown to Jessica. Jessica's card is shown to Jessica. Johnny's card is shown to Jessica. Jessica's card is shown to Johnny. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amanda can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amanda","Jessica","Johnny"],"index":45963,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994087219,"difficulty":0.0005912781}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Harvey can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kim","Mark","John","Harvey"],"index":22562,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7900214195,"difficulty":0.2099785805}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Tara can now know that Ben can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Ben","Tara","Harry"],"index":23081,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9910048246,"difficulty":0.0089951754}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie knows whether Ralph's forehead is muddy. It is publicly announced that Ralph knows whether Jamie's forehead is muddy. It is publicly announced that Jamie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Richard can now know whether Jamie can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ralph","Jamie","Richard"],"index":57098,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994719625,"difficulty":0.0005280375}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dora does not know whether Grace is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Grace can now know whether Charlie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Camilla","Dora","Charlie","Grace"],"index":64638,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994002581,"difficulty":0.0005997419}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Doris knows whether Leon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Doris can now know that Jane can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Brittany","Jane","Leon"],"index":26967,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989768267,"difficulty":0.0010231733}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Justine. Justine's card is shown to Lois. Lois's card is shown to Lois. Leslie's card is shown to Victor. Victor's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Justine can now know that Victor picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Justine","Lois","Leslie","Victor"],"index":26469,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9835267663,"difficulty":0.0164732337}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Meg can now know that Carmen can know that Samuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Carmen","Samuel","Meg"],"index":21548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973370433,"difficulty":0.0026629567}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Neal can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Neal","Kirsten","Sharon"],"index":29585,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989282489,"difficulty":0.0010717511}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Abraham can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Abraham","Jennifer","Robert"],"index":12851,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989025593,"difficulty":0.0010974407}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Jeannine can now know that Willie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Willie","Luis","Clara","Jeannine"],"index":63898,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988226295,"difficulty":0.0011773705}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenna's card is shown to Guy. Hector's card is shown to Guy. Fatima's card is shown to Guy. Fatima's card is shown to Fatima. It is publicly announced that someone picked a red card. It is publicly announced that Brenna does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Brenna can now know that Brenna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Guy","Brenna","Hector","Fatima"],"index":52866,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.813513875,"difficulty":0.186486125}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joy knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Joy can now know that William can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joy","William"],"index":12736,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9828720093,"difficulty":1.9828720093}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cliff knows whether Merle's forehead is muddy. It is publicly announced that Cliff does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Cliff can now know that Merle can know that Cliff's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cliff","Merle"],"index":62184,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8103317618,"difficulty":1.8103317618}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie does not know whether Marie's forehead is muddy. It is publicly announced that Harriet knows whether Harriet's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Harriet can now know that Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marie","Harriet"],"index":13230,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9807443023,"difficulty":0.0192556977}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sophia's card is shown to Megan. Angel's card is shown to Megan. Annette's card is shown to Megan. Angel's card is shown to Sophia. Angel's card is shown to Annette. Annette's card is shown to Annette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Megan can now know that Sophia can know whether Annette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Megan","Sophia","Angel","Annette"],"index":60273,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6280258894,"difficulty":1.6280258894}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Michelle can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mitzi","Robert","Michelle"],"index":60449,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994524121,"difficulty":0.0005475879}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Betty is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nancy can now know that James can know whether Betty is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","James","Nancy","Doris"],"index":5703,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974820018,"difficulty":0.0025179982}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Derek knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Christina can now know whether Don can know that Derek's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Christina","Don","Derek"],"index":54916,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999427557,"difficulty":0.000572443}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Gregory. Eunice's card is shown to Gregory. Gregory's card is shown to Mildred. Mildred's card is shown to Mildred. Eunice's card is shown to Mildred. Gregory's card is shown to Eunice. It is publicly announced that someone picked a red card. It is publicly announced that Gregory does not know whether Gregory picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Eunice can now know whether Eunice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregory","Mildred","Eunice"],"index":61223,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5052964091,"difficulty":0.4947035909}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie knows whether or not nobody's forehead is muddy. It is publicly announced that Cora knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Melanie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Melanie","Cora"],"index":3026,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.984382689,"difficulty":0.015617311}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Winnifred knows whether or not nobody's forehead is muddy. It is publicly announced that Michelle knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Winnifred can now know that Ruben's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ruben","Michelle","Winnifred"],"index":20837,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983002543,"difficulty":0.0016997457}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Christina can now know that Christina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christina","Cesar","Shirley"],"index":42929,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8770233989,"difficulty":0.1229766011}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fred's card is shown to Mary. Mary's card is shown to Fred. Lori's card is shown to Fred. Mary's card is shown to Lori. Lori's card is shown to Lori. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lori can now know that Mary can know that Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Fred","Lori"],"index":13894,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982669353,"difficulty":0.0017330647}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dolores's card is shown to Deborah. Deborah's card is shown to Dolores. Felipe's card is shown to Dolores. Deborah's card is shown to Felipe. Felipe's card is shown to Felipe. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Deborah can now know that Felipe can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deborah","Dolores","Felipe"],"index":58966,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993863106,"difficulty":0.0006136894}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that Mary knows whether Patricia's forehead is muddy. It is publicly announced that Rita knows whether Rita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know that Rita can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Rita","Mary"],"index":39035,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993618131,"difficulty":0.0006381869}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cody knows whether or not everyone's forehead is muddy. It is publicly announced that Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Lisa can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cody","Lisa"],"index":33118,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989283681,"difficulty":0.0010716319}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leland knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Gina can now know that Roy can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Roy","Leland","Gina"],"index":25379,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991131425,"difficulty":0.0008868575}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Sally can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sally","Jon","Ernest"],"index":67144,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9942418933,"difficulty":0.0057581067}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Barbara. Cleo's card is shown to Cleo. It is publicly announced that someone picked a red card. It is publicly announced that Annie does not know whether Barbara picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Barbara can now know whether Annie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annie","Barbara","Cleo"],"index":1542,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7403714061,"difficulty":0.2596285939}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry does not know whether Terry's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy. It is publicly announced that Terry does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Terry can now know whether Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Terry"],"index":38194,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5782866478,"difficulty":1.5782866478}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester knows whether Richard's forehead is muddy. It is publicly announced that Lester knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Modesta","Richard","Lester"],"index":38943,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990502,"difficulty":0.0009498}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edna's card is shown to Edna. Patricia's card is shown to Edna. Seth's card is shown to Edna. Edna's card is shown to Patricia. Seth's card is shown to Patricia. Edna's card is shown to Seth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"June can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edna","June","Patricia","Seth"],"index":28886,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989903569,"difficulty":0.0010096431}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Steven can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Steven","John","Pamela"],"index":12730,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994235039,"difficulty":0.0005764961}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Susan can now know that Michael can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","Anne","Sean","Michael"],"index":46627,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8235818744,"difficulty":0.1764181256}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Iris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Keisha","Michael","Iris"],"index":23776,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955323935,"difficulty":0.0044676065}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rhonda can now know whether Andrew can know whether Rhonda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Rhonda","Andrew"],"index":16553,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993757606,"difficulty":0.0006242394}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is muddy. It is publicly announced that Mary knows whether Kelly's forehead is muddy. It is publicly announced that Kelly does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Mary can now know that Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Kelly","Richard","Mary"],"index":3089,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9227501154,"difficulty":0.0772498846}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis's forehead is muddy. It is publicly announced that Audrey knows whether Darryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Darryl can now know that Audrey can know that Darryl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darryl","Dennis","Audrey"],"index":44615,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9799383283,"difficulty":0.0200616717}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Cornell. Myron's card is shown to Anthony. John's card is shown to Anthony. Cornell's card is shown to Myron. Cornell's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Myron knows whether or not everyone picked a red card. It is publicly announced that Anthony knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Cornell can now know whether John can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cornell","Anthony","Myron","John"],"index":19405,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994270802,"difficulty":0.0005729198}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennie","Richard","David"],"index":49518,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967922568,"difficulty":0.0032077432}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emily's card is shown to Emily. Mike's card is shown to Emily. Emily's card is shown to Mike. Felix's card is shown to Mike. Felix's card is shown to Felix. It is publicly announced that someone picked a red card. It is publicly announced that Mike knows whether someone picked a red card. It is publicly announced that Felix picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Emily can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emily","Mike","Felix"],"index":41309,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994747043,"difficulty":0.0005252957}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Susan. Patsy's card is shown to Joe. Joe's card is shown to Patsy. Patsy's card is shown to Patsy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patsy can now know that Joe can know whether Joe picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Joe","Patsy"],"index":40872,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8966659904,"difficulty":0.1033340096}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clifton's forehead is not muddy. It is publicly announced that Andrea's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Christopher can now know that Andrea can know whether Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Andrea","Clifton","Amanda"],"index":58815,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994643331,"difficulty":0.0005356669}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Angela's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! 1 ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! 1 ] 0","hypothesis":"Angela can now know that Darren's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Angela","Darren"],"index":38810,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9882429242,"difficulty":0.0117570758}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Brianne does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"James can now know whether William can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","William","Brianne"],"index":1291,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993866682,"difficulty":0.0006133318}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis knows whether Albert's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Albert can now know whether Louis can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Albert","Louis"],"index":35098,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994202852,"difficulty":0.0005797148}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Williams knows whether someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Blake","Williams","Arnold"],"index":29188,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9916881919,"difficulty":0.0083118081}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leann does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Leann can now know whether Larry can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Larry","Leann"],"index":59640,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7758993506,"difficulty":1.7758993506}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy. It is publicly announced that Ruth knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ruth can now know that Timmy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Timmy","Ruth","Michael"],"index":31510,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997877121,"difficulty":0.002122879}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Charlotte can now know whether Joseph can know whether Charlotte is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charlotte","Alexander","Joseph","Todd"],"index":27933,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989925027,"difficulty":0.0010074973}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Janet is thirsty. It is publicly announced that Janet does not know whether Stephanie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Janet can now know that Daniel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janet","Stephanie","Daniel"],"index":12910,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977487922,"difficulty":0.0022512078}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that Kayla knows whether Thomas's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Thomas","Kayla"],"index":12636,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990268946,"difficulty":0.0009731054}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kenneth can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Matthew","William","Kenneth","Margie"],"index":66765,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993678927,"difficulty":0.0006321073}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Velma knows whether Jackson's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Marcos can now know that James can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marcos","Velma","Jackson","James"],"index":11333,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989232421,"difficulty":0.0010767579}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence does not know whether Clarence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Karl can now know that Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sarah","Shawn","Clarence","Karl"],"index":39180,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997520268,"difficulty":0.002479732}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eleanor knows whether Eleanor is thirsty. It is publicly announced that Adam is thirsty. It is publicly announced that Adam knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Adam can now know that Eleanor can know whether Eleanor is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eleanor","Adam"],"index":45745,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9893711805,"difficulty":0.0106288195}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason does not know whether Walter is thirsty. It is publicly announced that Walter knows whether or not everyone is thirsty. It is publicly announced that Charles knows whether or not everyone is thirsty. It is publicly announced that Charles does not know whether Jason is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Walter can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Jason","Walter"],"index":33282,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990823269,"difficulty":0.0009176731}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vicki's forehead is muddy. It is publicly announced that Loretta knows whether Vicki's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Loretta can now know that Kelly can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Ernestine","Vicki","Loretta"],"index":1363,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990065694,"difficulty":0.0009934306}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether Gloria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jessie can now know whether Gloria can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Julian","Jessie","Gina"],"index":5546,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993410707,"difficulty":0.0006589293}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Gregory can now know whether Frances can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jim","Gregory","Frances"],"index":52623,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994538426,"difficulty":0.0005461574}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Cassandra knows whether Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Norma can now know that Susie can know that Pamela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cassandra","Susie","Norma","Pamela"],"index":9644,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9905029535,"difficulty":0.0094970465}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cory's card is shown to Joanne. Terrance's card is shown to Joanne. Cory's card is shown to Terrance. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joanne can now know that Terrance picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joanne","Cory","Terrance"],"index":28818,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997001946,"difficulty":0.002998054}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Verna does not know whether Verna's forehead is muddy. It is publicly announced that Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Dinah can now know whether Verna can know whether Verna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Verna","Dinah","Donald"],"index":31463,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5345401764,"difficulty":0.4654598236}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marylin knows whether or not everyone's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Thomas can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","John","Thomas","Marylin"],"index":49757,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983023405,"difficulty":0.0016976595}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Patricia. Janice's card is shown to Patricia. Patricia's card is shown to Pamela. Steven's card is shown to Janice. Patricia's card is shown to Janice. Janice's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Patricia","Pamela","Janice"],"index":32026,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5637430549,"difficulty":1.5637430549}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Bonnie. Bonnie's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether Robert picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bonnie can now know whether Robert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bonnie","Robert"],"index":26795,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994465709,"difficulty":0.0005534291}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Sara can now know whether David can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Charles","Sara","Seth"],"index":12655,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6002067327,"difficulty":0.3997932673}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy is thirsty. It is publicly announced that Chris does not know whether Lisandra is thirsty. It is publicly announced that Dorothy knows whether Dorothy is thirsty. It is publicly announced that Chris does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Chris can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Chris","Lisandra","Dorothy"],"index":55316,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999509573,"difficulty":0.000490427}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tania knows whether Paul's forehead is muddy. It is publicly announced that Tania knows whether Tania's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Paul can now know that James can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Tania","Paul"],"index":51372,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979320765,"difficulty":0.0020679235}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Hattie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"James can now know that Lizzie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lizzie","Hattie","James"],"index":55571,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987291694,"difficulty":0.0012708306}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carolyn's card is shown to Richard. Eugene's card is shown to Richard. Richard's card is shown to Carolyn. Richard's card is shown to Eugene. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Richard can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Carolyn","Eugene"],"index":25549,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999404192,"difficulty":0.000595808}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Guillermo can now know that Guillermo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Guillermo","Jason","Ruby"],"index":55814,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982562661,"difficulty":0.0017437339}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jay's card is shown to Jose. Jose's card is shown to Jay. Jay's card is shown to Jay. Sam's card is shown to Jay. Kristin's card is shown to Jay. Jose's card is shown to Kristin. Kristin's card is shown to Kristin. It is publicly announced that someone picked a red card. It is publicly announced that Sam does not know whether or not everyone picked a red card. It is publicly announced that Sam does not know whether Sam picked a red card. It is publicly announced that Jay knows whether Jay picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sam can now know that Jay can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Jay","Sam","Kristin"],"index":65217,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977711439,"difficulty":0.0022288561}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Dean can now know that Dean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amanda","Dean","Jennifer"],"index":48057,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9926543236,"difficulty":0.0073456764}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Wayne. Marvin's card is shown to Wayne. Wayne's card is shown to Robert. Marvin's card is shown to Robert. Robert's card is shown to Christine. It is publicly announced that someone picked a red card. It is publicly announced that Marvin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Marvin can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wayne","Marvin","Robert","Christine"],"index":58723,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994367957,"difficulty":0.0005632043}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julia's card is shown to Adrienne. Allison's card is shown to Julia. Adrienne's card is shown to Allison. Annie's card is shown to Allison. Adrienne's card is shown to Annie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Allison can now know whether Julia can know that Allison picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Adrienne","Julia","Allison","Annie"],"index":628,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7802016735,"difficulty":1.7802016735}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Reginald. Bonita's card is shown to Kyle. Mary's card is shown to Mary. Reginald's card is shown to Bonita. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kyle can now know that Reginald can know whether Kyle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Reginald","Kyle","Mary","Bonita"],"index":56465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9951493144,"difficulty":0.0048506856}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Helene. Gregory's card is shown to John. Helene's card is shown to Gregory. Ben's card is shown to Ben. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Helene can know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helene","John","Gregory","Ben"],"index":25299,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988874793,"difficulty":0.0011125207}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Michael can now know whether Whitney can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Whitney","Bridget","Charles"],"index":2106,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992668033,"difficulty":0.0007331967}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonnie's card is shown to Candice. Jayme's card is shown to Cecila. Cecila's card is shown to Bonnie. Candice's card is shown to Jayme. It is publicly announced that someone picked a red card. It is publicly announced that Jayme does not know whether or not everyone picked a red card. It is publicly announced that Cecila picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Cecila can now know whether Candice can know whether Bonnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Candice","Cecila","Bonnie","Jayme"],"index":67077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981014132,"difficulty":0.0018985868}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcus is thirsty. It is publicly announced that Janet knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Marcus can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clark","Michael","Janet","Marcus"],"index":17957,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.782404542,"difficulty":0.217595458}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"William can now know that Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","William"],"index":58761,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9813435674,"difficulty":1.9813435674}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Darron does not know whether Darron's forehead is muddy. It is publicly announced that Maurice knows whether Darron's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mary can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darron","Maurice","Mary","Ursula"],"index":39702,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966388941,"difficulty":0.0033611059}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ralph can now know that Joseph can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Betty","Cheryl","Ralph"],"index":50738,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990611672,"difficulty":0.0009388328}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Robert can now know that Brenda can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Robert","Richard","Brenda"],"index":41093,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992967844,"difficulty":0.0007032156}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Johnnie can now know that Justin can know whether Justin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Johnnie","Justin"],"index":8044,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985623956,"difficulty":0.0014376044}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Bernard. Lina's card is shown to Lina. Bernard's card is shown to Warren. Lina's card is shown to Warren. Jeremy's card is shown to Jeremy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lina can now know whether Lina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bernard","Lina","Warren","Jeremy"],"index":56300,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6733216643,"difficulty":0.3266783357}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jason can now know that Virgina can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Jason","Virgina"],"index":32548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989501834,"difficulty":0.0010498166}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Eric. Natalie's card is shown to Eric. Natalie's card is shown to Marie. Eric's card is shown to Natalie. Natalie's card is shown to Natalie. It is publicly announced that someone picked a red card. It is publicly announced that Eric does not know whether Eric picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card. It is publicly announced that Natalie picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Natalie can now know that Marie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eric","Marie","Natalie"],"index":62979,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6705040336,"difficulty":1.6705040336}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole does not know whether Nicole's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Nicole can now know that Sandra can know whether Kathleen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","Sandra","Florence","Nicole"],"index":15293,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992550015,"difficulty":0.0007449985}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Harriet's card is shown to Leland. It is publicly announced that someone picked a red card. It is publicly announced that Harriet knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know that Harriet picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harriet","Kenneth","Leland"],"index":9699,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9310543537,"difficulty":0.0689456463}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Domingo can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Domingo","Larry","Gerald"],"index":32112,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993488193,"difficulty":0.0006511807}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruben does not know whether or not everyone is thirsty. It is publicly announced that Ruben knows whether Ruben is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Rose can now know that Richard can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rose","Ruben","Richard"],"index":17562,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.960409224,"difficulty":0.039590776}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Kay. Christine's card is shown to Christine. Bertha's card is shown to Christine. Christine's card is shown to Bertha. It is publicly announced that someone picked a red card. It is publicly announced that Kay picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Christine can now know that Christine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Freeman","Kay","Christine","Bertha"],"index":24680,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7456364632,"difficulty":0.2543635368}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. Kristen's card is shown to Kristen. Kristen's card is shown to Charlotte. It is publicly announced that someone picked a red card. It is publicly announced that Daniel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Daniel can now know that Patricia can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Kristen","Patricia","Charlotte"],"index":59012,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994702935,"difficulty":0.0005297065}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Dale. Leah's card is shown to Dale. Dale's card is shown to Leah. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Leah picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Leah can now know whether Dale can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dale","Leah"],"index":23466,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9962764382,"difficulty":0.0037235618}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlie knows whether Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Shirley can now know whether Charlie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charlie","Shirley"],"index":38678,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9037311673,"difficulty":0.0962688327}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sylvia's card is shown to Jason. Kevin's card is shown to Jason. Sylvia's card is shown to Sylvia. Jason's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sylvia can now know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Sylvia","Kevin"],"index":6101,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9564365745,"difficulty":0.0435634255}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rodney's card is shown to Matthew. Matthew's card is shown to Terry. Terry's card is shown to Terry. Rodney's card is shown to Terry. Matthew's card is shown to Rodney. Terry's card is shown to Rodney. Rodney's card is shown to Rodney. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rodney can now know whether Matthew can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Terry","Rodney"],"index":45752,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994125366,"difficulty":0.0005874634}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Florentino can now know that Candida's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Florentino","Candida"],"index":22951,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975675344,"difficulty":0.0024324656}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Russell does not know whether Michelle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Keith can now know that Michelle can know that Keith is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Russell","Janet","Keith"],"index":22438,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978037477,"difficulty":0.0021962523}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josephine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Chris can now know that Chris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Josephine","Chris","Roy"],"index":12201,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980580211,"difficulty":0.0019419789}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Marion. Albert's card is shown to Wayne. Marion's card is shown to Albert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marion can now know whether Albert can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marion","Wayne","Albert"],"index":1947,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9928969741,"difficulty":0.0071030259}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittney's card is shown to Brittney. John's card is shown to Brittney. Brittney's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"John can now know whether Brittney picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brittney","John"],"index":23807,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9909385443,"difficulty":0.0090614557}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ronald can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Ronald","Lance","Mack"],"index":55053,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949656129,"difficulty":0.0050343871}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pamela's card is shown to Pamela. Crystal's card is shown to Barbara. Crystal's card is shown to Crystal. Mark's card is shown to Crystal. Barbara's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Barbara knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Mark can now know that Barbara can know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Barbara","Crystal","Mark"],"index":34620,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6197276115,"difficulty":1.6197276115}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Linda. Bryan's card is shown to Jeremiah. Linda's card is shown to Grant. Grant's card is shown to Grant. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether Bryan can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Jeremiah","Bryan","Grant"],"index":1709,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8583707809,"difficulty":1.8583707809}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Flossie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Anthony can now know whether Flossie can know that Anthony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jacqueline","Jerry","Anthony","Flossie"],"index":43252,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994249344,"difficulty":0.0005750656}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"William can now know whether Veronica can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Veronica","Richard","William","Darnell"],"index":52722,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993445277,"difficulty":0.0006554723}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole knows whether or not nobody's forehead is muddy. It is publicly announced that Nicole's forehead is muddy. It is publicly announced that Lillie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Barbara can now know whether Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Nicole","Lillie","Jake"],"index":52857,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9546917081,"difficulty":0.0453082919}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether Robert's forehead is muddy. It is publicly announced that Phillip does not know whether Phillip's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether Phillip's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Phillip","Doris"],"index":31065,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998550117,"difficulty":0.001449883}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Victor knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Shannon can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Victor","Shannon","Emanuel"],"index":42278,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993982315,"difficulty":0.0006017685}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Hazel can now know that Mary can know that Hazel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Hazel","Mary"],"index":64831,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981883168,"difficulty":0.0018116832}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Billy does not know whether Dorothy is thirsty. It is publicly announced that Mary does not know whether Dorothy is thirsty. It is publicly announced that Dorothy does not know whether Billy is thirsty. It is publicly announced that Billy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Billy can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Dorothy","Billy"],"index":40509,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8155630827,"difficulty":0.1844369173}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin knows whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Erin can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ann","Erin","Christopher"],"index":2556,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999252975,"difficulty":0.000747025}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Edwin's card is shown to Mary. Edwin's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Pamela","Edwin"],"index":59212,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6039940119,"difficulty":1.6039940119}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nancy can now know that Richard can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Heather","Nancy"],"index":352,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9901352525,"difficulty":0.0098647475}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Alene's card is shown to Brenda. Jose's card is shown to Gregory. Alene's card is shown to Alene. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Alene picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Gregory does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Brenda can now know whether Gregory can know that Brenda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Jose","Gregory","Alene"],"index":28326,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8857743144,"difficulty":0.1142256856}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jordan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Jordan can now know that Tony can know that Jordan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tammy","Tony","Jordan"],"index":65464,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.8545316458,"difficulty":1.8545316458}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Albert can now know whether Jonathan can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Albert","Jonathan","Sadye"],"index":22537,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993036985,"difficulty":0.0006963015}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leanna's card is shown to Leanna. David's card is shown to Leanna. Leanna's card is shown to Vicki. Vicki's card is shown to Vicki. David's card is shown to Vicki. Leanna's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Vicki knows whether or not nobody picked a red card. It is publicly announced that Leanna does not know whether Vicki picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Vicki can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leanna","Vicki","David"],"index":29595,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6752631068,"difficulty":1.6752631068}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bess knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Bess can now know whether Steve can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Maria","Bess","Steve"],"index":57627,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9776297808,"difficulty":0.0223702192}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony knows whether or not nobody is thirsty. It is publicly announced that Georgia does not know whether Anthony is thirsty. It is publicly announced that Hong does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Hong can now know whether Georgia can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Georgia","Anthony","Hong"],"index":43899,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994462132,"difficulty":0.0005537868}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martin is thirsty. It is publicly announced that Martin does not know whether or not everyone is thirsty. It is publicly announced that Martin does not know whether or not everyone is thirsty. It is publicly announced that Rosemary does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Elizabeth can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Martin","Rosemary"],"index":25585,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990596175,"difficulty":0.0009403825}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Guadalupe can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Guadalupe","Carol","Philip","Robert"],"index":62044,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988569021,"difficulty":0.0011430979}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Henry can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carolyn","Henry","Carol"],"index":43775,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993121624,"difficulty":0.0006878376}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glen's card is shown to Glen. Glen's card is shown to Octavio. Glen's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Ron picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Octavio can now know that Ron picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ron","Glen","Octavio","Alice"],"index":64702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9822973013,"difficulty":0.0177026987}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Calvin knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Calvin can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Denise","Jay","Calvin"],"index":44552,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9943585992,"difficulty":0.0056414008}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leslie does not know whether or not everyone is thirsty. It is publicly announced that Leslie does not know whether Frances is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] Agentd knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Leslie can now know that James can know that Susie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susie","Frances","James","Leslie"],"index":64360,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.960486114,"difficulty":0.039513886}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lauren's forehead is muddy. It is publicly announced that Lauren knows whether or not nobody's forehead is muddy. It is publicly announced that Jerry does not know whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Anita can now know whether Jerry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jerry","Anita","Lauren"],"index":59724,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994082451,"difficulty":0.0005917549}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Ocie's forehead is muddy. It is publicly announced that Robin knows whether or not nobody's forehead is muddy. It is publicly announced that Ocie knows whether Robin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Helen can now know that Robin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Helen","Robin","Ocie"],"index":57500,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9984770417,"difficulty":0.0015229583}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shane does not know whether Evelyn is thirsty. It is publicly announced that Pablo does not know whether Evelyn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Shane can now know that Pablo is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Howard","Shane","Pablo"],"index":65345,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970213771,"difficulty":0.0029786229}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl knows whether Jesusita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Julia can now know that Cheryl can know whether Jesusita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesusita","Julia","Cheryl"],"index":51812,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993890524,"difficulty":0.0006109476}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether Summer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Summer can now know that Nelson can know that Joan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Summer","Nelson","Joan"],"index":50028,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998231709,"difficulty":0.001768291}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl does not know whether Audry is thirsty. It is publicly announced that Audry does not know whether Isaac is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Isaac can now know whether Audry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carl","Joseph","Isaac","Audry"],"index":58669,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9809633493,"difficulty":0.0190366507}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Dorothy is not thirsty. It is publicly announced that Dorothy is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] [ ! ~(4) ] (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] [ ! ~(4) ] 0","hypothesis":"Joe can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Willie","Bobby","Joe","Dorothy"],"index":29086,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9959171414,"difficulty":0.0040828586}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brianna knows whether someone is thirsty. It is publicly announced that Maria does not know whether Brianna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Adriane can now know whether Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Adriane","Brianna","Dawn"],"index":26219,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9935261011,"difficulty":0.0064738989}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Virginia. Nathan's card is shown to Virginia. Virginia's card is shown to Lucille. Nathan's card is shown to Lucille. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nathan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virginia","Nathan","Lucille"],"index":25729,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955708385,"difficulty":0.0044291615}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessie's card is shown to Nicole. Chantal's card is shown to Nicole. Nicole's card is shown to Joseph. Joseph's card is shown to Chantal. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Jessie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jessie can now know that Nicole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessie","Nicole","Joseph","Chantal"],"index":15555,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965769649,"difficulty":0.0034230351}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Andrew can now know that James can know that Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Andrew","Michael","James"],"index":40890,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969496131,"difficulty":0.0030503869}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Maria can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maria","Michael","Catherine"],"index":21337,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993954897,"difficulty":0.0006045103}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"John can now know that Alberta's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alberta","John","Kenneth"],"index":11222,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9956186414,"difficulty":0.0043813586}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Quinn knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know that Quinn can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Quinn","David","Edward","Linda"],"index":3127,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99928087,"difficulty":0.00071913}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether someone is thirsty. It is publicly announced that Martha does not know whether or not everyone is thirsty. It is publicly announced that Martha does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Ronald can know that Martha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martha","Ronald","James"],"index":67603,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9851390719,"difficulty":1.9851390719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Micheal does not know whether Micheal's forehead is muddy. It is publicly announced that Micheal's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Brandon can now know whether Rafael can know whether Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Micheal","Matthew","Brandon","Rafael"],"index":62529,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993152618,"difficulty":0.0006847382}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Rachael. Joyce's card is shown to Sarah. Lavern's card is shown to Sarah. Rachael's card is shown to Lavern. Sarah's card is shown to Lavern. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know whether Rachael can know that Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachael","Joyce","Sarah","Lavern"],"index":51267,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8981223106,"difficulty":1.8981223106}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Nicole. Nicole's card is shown to Carl. Sara's card is shown to Carl. Nicole's card is shown to Sara. Carl's card is shown to Sara. Sara's card is shown to Petra. It is publicly announced that someone picked a red card. It is publicly announced that Petra knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Nicole can now know whether Sara can know that Sara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicole","Carl","Sara","Petra"],"index":28114,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9112590551,"difficulty":0.0887409449}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larae knows whether Tommy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Tommy can now know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brooke","Peter","Larae","Tommy"],"index":20521,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982995391,"difficulty":0.0017004609}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erica's card is shown to Matthew. Tanya's card is shown to Matthew. Erica's card is shown to Erica. Tanya's card is shown to Erica. Matthew's card is shown to Tanya. Erica's card is shown to Tanya. Tanya's card is shown to Tanya. It is publicly announced that someone picked a red card. It is publicly announced that Tanya picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Erica can now know that Erica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Erica","Tanya"],"index":3379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5912272334,"difficulty":0.4087727666}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Garry does not know whether Noah is thirsty. It is publicly announced that Sheryl does not know whether Jason is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Noah can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sheryl","Noah","Jason","Garry"],"index":50683,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963704348,"difficulty":0.0036295652}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell does not know whether Darrell's forehead is muddy. It is publicly announced that Dana does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Darrell can now know whether Darrell's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dana","Felton","Annie","Darrell"],"index":14546,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8525319099,"difficulty":0.1474680901}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to David. David's card is shown to Ann. Pauline's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Ann picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Pauline can now know whether Pauline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","David","Ann","William"],"index":51538,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7065901756,"difficulty":1.7065901756}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether Billie's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billie does not know whether Billie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gary can now know whether Gary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jacqueline","Gary","Billie"],"index":2706,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9911757708,"difficulty":0.0088242292}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shelby does not know whether Harold is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"James can now know that Shelby can know that Harold is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shelby","James","Harold","Tommy"],"index":17545,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982434511,"difficulty":0.0017565489}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Frankie. Harry's card is shown to Harry. Forrest's card is shown to Forrest. Forrest's card is shown to Danielle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Forrest can now know whether Frankie can know that Danielle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frankie","Harry","Forrest","Danielle"],"index":34966,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.953746736,"difficulty":1.953746736}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Sean. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sean can now know whether Aaron picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aaron","Sean","Helen","Timothy"],"index":29852,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980541468,"difficulty":0.0019458532}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether Jeffrey's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Howard can now know that Deborah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Florence","Deborah","Howard"],"index":50164,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9914315939,"difficulty":0.0085684061}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Anna can now know that Richard can know that Anna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frances","Anna","Richard","Clara"],"index":1494,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9920045733,"difficulty":0.0079954267}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"James can now know whether Timothy can know that Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Denise","Timothy","James","Charles"],"index":47331,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939445853,"difficulty":0.0060554147}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy. It is publicly announced that Patricia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Craig can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Craig","Mary","David","Patricia"],"index":49377,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9835839868,"difficulty":0.0164160132}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shari's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Ernesto can now know whether Brianne can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shari","Ernesto","Brianne"],"index":64064,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993867874,"difficulty":0.0006132126}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Debra knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Isabel can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mildred","Isabel","Debra","Stephen"],"index":3809,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994962215,"difficulty":0.0005037785}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda knows whether Amanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jacqueline can now know that Amanda can know that Tommy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tommy","Jacqueline","Amanda","Douglas"],"index":50046,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971030354,"difficulty":0.0028969646}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Brandie can now know whether David can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Brandie","Jim"],"index":40686,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999340713,"difficulty":0.000659287}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Florentina's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Florentina","James"],"index":2392,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990093708,"difficulty":0.0009906292}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Esther is thirsty. It is publicly announced that Rosa does not know whether Nellie is thirsty. It is publicly announced that Nellie does not know whether Brian is thirsty. It is publicly announced that Brian knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Rosa can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rosa","Esther","Brian","Nellie"],"index":37669,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969005585,"difficulty":0.0030994415}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Gail's card is shown to Elizabeth. Gail's card is shown to Gail. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that Elizabeth can know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Elizabeth","Gail"],"index":34545,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7802782655,"difficulty":1.7802782655}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ashley can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Solomon","Georgia","Ashley"],"index":7869,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989282489,"difficulty":0.0010717511}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nichole knows whether or not everyone's forehead is muddy. It is publicly announced that Nichole's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Charles can now know that Angela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nichole","Charles","Angela"],"index":3500,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948653579,"difficulty":0.0051346421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tabitha does not know whether Edna is thirsty. It is publicly announced that Patricia does not know whether Edna is thirsty. It is publicly announced that Tabitha knows whether Tabitha is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Patricia can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Edna","Tabitha"],"index":35435,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999476254,"difficulty":0.000523746}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ben knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Ben can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ben","April","James"],"index":16267,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991856217,"difficulty":0.0008143783}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Tamara. Darren's card is shown to Tamara. Tamara's card is shown to Cheryl. Tamara's card is shown to Darren. It is publicly announced that someone picked a red card. It is publicly announced that Cheryl does not know whether Cheryl picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Darren can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tamara","Cheryl","Darren"],"index":66107,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990068078,"difficulty":0.0009931922}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether Chet can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Virgil","Chet"],"index":14670,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9765728116,"difficulty":0.0234271884}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Vicki","Kenneth","Mary"],"index":41043,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5883270502,"difficulty":0.4116729498}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Raymond can now know that Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","James","Tony"],"index":62408,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998054266,"difficulty":0.001945734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy. It is publicly announced that Shannon knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Richard can now know whether Shannon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shannon","Daniel","Merrill","Richard"],"index":44653,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9951123595,"difficulty":0.0048876405}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to Ryan. Ryan's card is shown to Crystal. Evan's card is shown to Crystal. Crystal's card is shown to Evan. Dustin's card is shown to Evan. It is publicly announced that someone picked a red card. It is publicly announced that Ryan does not know whether Dustin picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ryan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ryan","Crystal","Evan","Dustin"],"index":65820,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994445443,"difficulty":0.0005554557}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Wilson can now know that Charles can know whether Wilson's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Eddie","Thomas","Wilson"],"index":43887,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999055922,"difficulty":0.000944078}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether Cecilia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Allen can now know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Teresa","Cecilia","Allen","Jacqueline"],"index":7338,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994044304,"difficulty":0.0005955696}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melinda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Vernice can now know that Melinda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leticia","Melinda","Robert","Vernice"],"index":55065,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7140552402,"difficulty":1.7140552402}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sally's card is shown to Angela. Sally's card is shown to Sally. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether Angela picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Angela can now know that Sally can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Angela","Sally"],"index":22166,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988779426,"difficulty":0.0011220574}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debbie's card is shown to Scott. Delpha's card is shown to Delpha. Debbie's card is shown to Delpha. Debbie's card is shown to Debbie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Scott can now know whether Delpha can know that Debbie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Delpha","David","Debbie"],"index":7777,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9161696434,"difficulty":0.0838303566}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond does not know whether Barbara is thirsty. It is publicly announced that Raymond does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Raymond can now know whether William can know that Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raymond","Barbara","William"],"index":19808,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.988470912,"difficulty":0.011529088}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley knows whether or not nobody is thirsty. It is publicly announced that Dan does not know whether Shirley is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dan can now know whether Brian can know that Shirley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dan","Shirley","Brian"],"index":59202,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9902272224,"difficulty":0.0097727776}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carlos's card is shown to Carlos. Patricia's card is shown to Carlos. Carlos's card is shown to George. George's card is shown to George. Carlos's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Carlos knows whether or not nobody picked a red card. It is publicly announced that Patricia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Carlos can now know whether George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carlos","George","Patricia"],"index":33431,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5869328976,"difficulty":0.4130671024}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory's forehead is muddy. It is publicly announced that George knows whether Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Andrew can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Gregory","Andrew","George"],"index":26294,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988675117,"difficulty":0.0011324883}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Florence can now know that Mary can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Florence","Mary","Joseph"],"index":21564,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992050529,"difficulty":0.0007949471}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Douglas can now know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jody","Marie","Douglas"],"index":26448,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947056174,"difficulty":0.0052943826}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Jack is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jack can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brian","Jack","David","Frances"],"index":7032,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994350076,"difficulty":0.0005649924}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lia's card is shown to Lia. Sara's card is shown to Lia. Lia's card is shown to Matthew. Matthew's card is shown to Matthew. Matthew's card is shown to Adolfo. Matthew's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Matthew can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lia","Matthew","Adolfo","Sara"],"index":3828,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988926053,"difficulty":0.0011073947}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"James can now know whether Maria can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Maria","James"],"index":41820,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994502664,"difficulty":0.0005497336}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Victor is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Emily can now know that Victor can know that Emily is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Emma","Emily","Victor"],"index":6326,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969447255,"difficulty":0.0030552745}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Charlotte can now know that Richard can know that Melvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlotte","Richard","Melvin","Michael"],"index":64714,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997622788,"difficulty":0.002377212}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether or not everyone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy. It is publicly announced that Bryan's forehead is muddy. It is publicly announced that Bryan knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Bryan can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Linda","Bryan"],"index":39272,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6007193327,"difficulty":1.6007193327}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dana's card is shown to Dana. Dana's card is shown to Amy. Don's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Amy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Dana can now know that Don picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dana","Amy","Don"],"index":41838,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9576960206,"difficulty":0.0423039794}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Russell can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Janet","Jane","Russell"],"index":49231,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982604384,"difficulty":0.0017395616}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Patricia's card is shown to Eric. Eric's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether Patricia picked a red card. It is publicly announced that Patricia does not know whether Eric picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Eric can now know that Patricia can know that Eric picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Patricia","Eric"],"index":25239,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9665847421,"difficulty":0.0334152579}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joyce can now know that Lucius can know that Lucius's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lucius","Hilda","Joyce","Anna"],"index":64603,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960200191,"difficulty":0.0039799809}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred knows whether Mary's forehead is muddy. It is publicly announced that Gary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agenta knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Gary can now know that Raymond can know that Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Fred","Mary","Raymond"],"index":51724,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980579019,"difficulty":0.0019420981}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Gary's card is shown to Joan. Gary's card is shown to Gary. Barbara's card is shown to Gary. Clifton's card is shown to Barbara. Barbara's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joan","Gary","Clifton","Barbara"],"index":7406,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999409318,"difficulty":0.000590682}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"James can now know that Wayne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peter","Wayne","Kerry","James"],"index":65500,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959928989,"difficulty":0.0040071011}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Delbert's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne knows whether Delbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Daniel can now know whether Wayne can know that Wayne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Delbert","Robert","Wayne","Daniel"],"index":22809,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.998800993,"difficulty":0.001199007}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Manuel. Vernon's card is shown to Dwayne. Dwayne's card is shown to Vernon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dwayne can now know that Manuel can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Manuel","Dwayne","Vernon"],"index":10580,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990290403,"difficulty":0.0009709597}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew does not know whether Andrew's forehead is muddy. It is publicly announced that Arlene knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Andrew can now know whether Arlene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andrew","Michael","Arlene","Christopher"],"index":381,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986044765,"difficulty":0.0013955235}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marquita does not know whether Violet is thirsty. It is publicly announced that Michael does not know whether Marquita is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Marquita can now know that Daniel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Daniel","Marquita","Violet"],"index":31220,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960539341,"difficulty":0.0039460659}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Collin's card is shown to Collin. Bill's card is shown to Collin. Don's card is shown to Wilma. Collin's card is shown to Bill. Wilma's card is shown to Don. Bill's card is shown to Don. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Don can now know whether Collin can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Collin","Wilma","Bill","Don"],"index":43948,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9818018079,"difficulty":0.0181981921}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Justin can now know that Dewey can know whether Justin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Justin","Dewey","Javier"],"index":33065,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9977076054,"difficulty":0.0022923946}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Felicitas does not know whether Eddie is thirsty. It is publicly announced that Brandon knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Brandi can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eddie","Brandon","Brandi","Felicitas"],"index":12097,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993547797,"difficulty":0.0006452203}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kayla's card is shown to William. Michael's card is shown to Michael. Kayla's card is shown to Michael. Kayla's card is shown to Mary. Mary's card is shown to Kayla. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Kayla can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Michael","Mary","Kayla"],"index":2995,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9810732603,"difficulty":0.0189267397}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter knows whether Brian's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy. It is publicly announced that Walter knows whether Lowell's forehead is muddy. It is publicly announced that Walter knows whether Armando's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Lowell can now know that Armando's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Walter","Lowell","Armando","Brian"],"index":9058,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7093945742,"difficulty":0.2906054258}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raquel's card is shown to Hope. David's card is shown to Hope. Hope's card is shown to Raquel. Hope's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Hope can now know whether Raquel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hope","Raquel","David"],"index":14848,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9818243384,"difficulty":1.9818243384}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Frank can now know that Frank's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beverly","Eric","Frank","Maggie"],"index":58328,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977037311,"difficulty":0.0022962689}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josephine's card is shown to Josephine. Maurice's card is shown to Josephine. Josephine's card is shown to Chris. Chris's card is shown to Maurice. Maurice's card is shown to Maurice. Maurice's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Josephine can now know whether Maurice can know whether Chris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josephine","Chris","Maurice","Heather"],"index":1070,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998573184,"difficulty":0.001426816}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether Shannon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Juanita can now know whether Shannon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shannon","Ernest","Juanita"],"index":33889,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991630316,"difficulty":0.0008369684}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Rebecca's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Victor can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rebecca","Victor","Mark"],"index":45949,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990025163,"difficulty":0.0009974837}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether George is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"Arlene can now know that George can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","David","Rex","Arlene"],"index":15696,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993776679,"difficulty":0.0006223321}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet knows whether Leonardo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Janet can now know that Leonardo can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janet","Leonardo","Bruce"],"index":40499,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999362886,"difficulty":0.000637114}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Kim can now know that David can know that Kim's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Kim"],"index":1351,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9970735312,"difficulty":1.9970735312}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachel's card is shown to Carolyn. Mary's card is shown to Carolyn. Rachel's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rachel can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carolyn","Rachel","Mary"],"index":2321,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999368608,"difficulty":0.000631392}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gilda does not know whether Timothy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Virginia can now know that Virginia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Todd","Gilda","Timothy"],"index":41366,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958580136,"difficulty":0.0041419864}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynn does not know whether or not everyone is thirsty. It is publicly announced that Cynthia knows whether Lynn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Lynn can now know whether Charles can know that Vicente is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vicente","Charles","Lynn","Cynthia"],"index":5369,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9959426522,"difficulty":0.0040573478}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Karla. Helen's card is shown to Helen. Helen's card is shown to Charles. Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Karla does not know whether Charles picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Karla can now know that Charles can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karla","Helen","Charles"],"index":38038,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9853724837,"difficulty":0.0146275163}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joanne does not know whether Irma is thirsty. It is publicly announced that Irma does not know whether Carl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Carl can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joanne","Nancy","Carl","Irma"],"index":3629,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963371754,"difficulty":0.0036628246}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley's forehead is muddy. It is publicly announced that Stanley's forehead is muddy. It is publicly announced that Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Albert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dianne","Albert","Stanley"],"index":1185,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989744425,"difficulty":0.0010255575}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna does not know whether Donna's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Beatrice can now know that Donna can know that Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Beatrice","Donna"],"index":38744,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9951076508,"difficulty":0.0048923492}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Rosa's card is shown to John. Robert's card is shown to John. John's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rosa can now know that John can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Rosa","Robert"],"index":51647,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5781203508,"difficulty":1.5781203508}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kerry's card is shown to Michael. Mary's card is shown to Michael. Jean's card is shown to Kerry. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Jean picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Michael can now know whether Kerry can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Kerry","Mary","Jean"],"index":43548,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7240920067,"difficulty":0.2759079933}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Berta. Troy's card is shown to Berta. Davis's card is shown to Davis. Berta's card is shown to Troy. Thomas's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that Davis picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Davis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Berta","Davis","Thomas","Troy"],"index":36034,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985456467,"difficulty":0.0014543533}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jose can now know that Gary can know that Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gary","Jose"],"index":14723,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978712797,"difficulty":0.0021287203}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon knows whether Mary's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Lawrence does not know whether Lawrence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lawrence can now know whether Gordon can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Wayne","Gordon","Mary"],"index":51775,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994520545,"difficulty":0.0005479455}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Donna. Donna's card is shown to Becky. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donna can now know whether Fred can know whether Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fred","Donna","Becky","Virginia"],"index":6358,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.834556222,"difficulty":1.834556222}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Louise can now know that Janet can know that Tamara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tamara","Louise","Janet"],"index":11538,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979445338,"difficulty":0.0020554662}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Charlotte can now know that Ronald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Virginia","Charlotte","Ronald"],"index":47557,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986745119,"difficulty":0.0013254881}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann does not know whether Waylon is thirsty. It is publicly announced that Edna knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Waylon can now know that Ann can know that Alec is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ann","Alec","Waylon","Edna"],"index":2362,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998321712,"difficulty":0.001678288}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know whether Josephine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Josephine","Pauline","Timothy"],"index":23714,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962853193,"difficulty":0.0037146807}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Kevin is thirsty. It is publicly announced that Krystyna knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that Krystyna can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Krystyna","Kevin","David"],"index":65938,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6184371114,"difficulty":0.3815628886}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jose can now know whether Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dalila","Michaela","Jose"],"index":37955,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994052649,"difficulty":0.0005947351}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence knows whether or not everyone's forehead is muddy. It is publicly announced that Florence knows whether or not nobody's forehead is muddy. It is publicly announced that Jenna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jenna can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Florence","Jenna"],"index":9098,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993531108,"difficulty":0.0006468892}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kerry's card is shown to Robert. Robert's card is shown to Kerry. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Bradley can now know whether Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Bradley","Kerry"],"index":18503,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999440372,"difficulty":0.000559628}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether or not everyone's forehead is muddy. It is publicly announced that Gerald does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Gerald can now know that Kari can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kari","Gerald"],"index":47164,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994601607,"difficulty":0.0005398393}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patty's card is shown to Patty. William's card is shown to Patty. Patty's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Patty can now know that Patty picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patty","William"],"index":24899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9931070209,"difficulty":0.0068929791}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Troy's card is shown to Jonathan. Diana's card is shown to Diana. Jonathan's card is shown to Troy. Dorothy's card is shown to Troy. Diana's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan does not know whether Diana picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jonathan can now know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jonathan","Dorothy","Diana","Troy"],"index":50743,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9766765833,"difficulty":0.0233234167}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paula does not know whether Paula's forehead is muddy. It is publicly announced that Paula's forehead is muddy. It is publicly announced that Richard's forehead is muddy. It is publicly announced that Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Joshua can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paula","Mark","Richard","Joshua"],"index":4133,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990081191,"difficulty":0.0009918809}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Travis does not know whether Barbara is thirsty. It is publicly announced that Travis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Barbara can now know that Elsie can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elsie","Travis","Carrie","Barbara"],"index":41331,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990200996,"difficulty":0.0009799004}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angela does not know whether Robert is thirsty. It is publicly announced that Robert does not know whether Angela is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Angela can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laurie","Robert","Angela"],"index":61454,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9874786139,"difficulty":0.0125213861}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Carolyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Kenneth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carolyn","Kenneth","Robert","Jeanne"],"index":31250,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998883903,"difficulty":0.001116097}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Julia can now know whether Alfreda can know that Julia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Julia","Alfreda","Edward"],"index":62051,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9771520495,"difficulty":0.0228479505}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Larraine. Larraine's card is shown to Larraine. Bridget's card is shown to Norman. Kevin's card is shown to Bridget. Larraine's card is shown to Bridget. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larraine can now know that Kevin can know whether Larraine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Larraine","Norman","Bridget"],"index":34732,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8654347658,"difficulty":0.1345652342}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rozella is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Joanne can now know that Wilma can know that Rozella is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wilma","Joanne","Rozella","Donna"],"index":3567,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8663119078,"difficulty":1.8663119078}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah does not know whether Phillip is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jennifer can now know that Deborah can know that Deborah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Phillip","Deborah","Jennifer"],"index":43627,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6345560551,"difficulty":0.3654439449}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dale can now know that Brian can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Lincoln","David","Dale"],"index":63173,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988761544,"difficulty":0.0011238456}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Solomon can now know that Marjorie can know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Solomon","Marjorie","Matthew","Patrick"],"index":62447,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993120432,"difficulty":0.0006879568}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rufus does not know whether or not everyone is thirsty. It is publicly announced that Deborah is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (~(1&2)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (~(1&2)) ] 0","hypothesis":"Deborah can now know that Deborah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rufus","Deborah"],"index":7150,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6348714828,"difficulty":1.6348714828}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether Susie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentd knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Emily can now know whether Susie can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susie","Dennis","Charles","Emily"],"index":23162,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9799495339,"difficulty":0.0200504661}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Susan. Susan's card is shown to Kati. Kati's card is shown to Kati. Michael's card is shown to Kati. Susan's card is shown to Michael. Michael's card is shown to Michael. Susan's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know that Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","Kati","Michael","Mark"],"index":42959,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957661629,"difficulty":0.0042338371}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tyler knows whether Albert's forehead is muddy. It is publicly announced that Elba knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Albert can now know that Tyler can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elba","Albert","Tyler"],"index":22988,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993390441,"difficulty":0.0006609559}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Floyd is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"James can now know that Floyd can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roberto","Tara","Floyd","James"],"index":40006,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989939332,"difficulty":0.0010060668}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Andreas can now know whether Charles can know that Michele is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michele","Martha","Andreas","Charles"],"index":7867,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9965202808,"difficulty":0.0034797192}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Joseph. Alexander's card is shown to Kelly. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Kelly knows whether Clarence picked a red card. It is publicly announced that Alexander does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alexander can now know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Alexander","Kelly","Clarence"],"index":42159,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962127209,"difficulty":0.0037872791}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Timothy's card is shown to Christopher. Christopher's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Christopher picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Christopher can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christopher","Timothy"],"index":60252,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994663596,"difficulty":0.0005336404}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn knows whether someone is thirsty. It is publicly announced that Carol does not know whether or not everyone is thirsty. It is publicly announced that Carol does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Victor can now know that Carol can know whether Victor is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carol","Victor","Evelyn"],"index":13074,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9781939387,"difficulty":0.0218060613}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janene knows whether or not nobody's forehead is muddy. It is publicly announced that Janet knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Janet can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cedric","Janet","Janene"],"index":65806,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987773299,"difficulty":0.0012226701}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Mark can now know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Thomas","Wayne"],"index":25784,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9950038791,"difficulty":0.0049961209}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michele knows whether Linda's forehead is muddy. It is publicly announced that Clara does not know whether Clara's forehead is muddy. It is publicly announced that Freddie knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Linda can now know that Clara can know that Michele's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Freddie","Michele","Clara"],"index":37397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973305464,"difficulty":0.0026694536}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Julia. Julia's card is shown to Eddie. It is publicly announced that someone picked a red card. It is publicly announced that Margaret picked a black card. It is publicly announced that Julia knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Margaret can now know that Julia can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Julia","Eddie"],"index":37318,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989185333,"difficulty":0.0010814667}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Monica can now know whether Faye can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frederick","Monica","Faye"],"index":35630,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992483258,"difficulty":0.0007516742}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Calvin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Reyna can now know whether Reyna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Reyna","Linda","Calvin"],"index":12863,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9972156286,"difficulty":0.0027843714}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cesar does not know whether Ferne is thirsty. It is publicly announced that Cesar does not know whether Julian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Julian can now know whether Cesar can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ferne","Robert","Julian","Cesar"],"index":2354,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990895987,"difficulty":0.0009104013}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Mary can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Mary","Fredrick"],"index":23633,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989179373,"difficulty":0.0010820627}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louie does not know whether or not everyone is thirsty. It is publicly announced that Patricia knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Gregory can now know that Patricia can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louie","Gregory","Barbara","Patricia"],"index":22260,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994544387,"difficulty":0.0005455613}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Otis knows whether or not nobody is thirsty. It is publicly announced that Otis does not know whether May is thirsty. It is publicly announced that Ramon knows whether or not everyone is thirsty. It is publicly announced that May knows whether May is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ramon can now know that Otis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Otis","Ramon","May"],"index":64556,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9519461989,"difficulty":0.0480538011}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Calvin. Margaret's card is shown to Margaret. Tina's card is shown to Margaret. Calvin's card is shown to Tina. Tina's card is shown to Tina. It is publicly announced that someone picked a red card. It is publicly announced that Tina knows whether Calvin picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Margaret can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Calvin","Margaret","Tina"],"index":62839,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999052465,"difficulty":0.000947535}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Cary can now know that Dale's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Cary","Matthew","Dale"],"index":56616,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.993947506,"difficulty":0.006052494}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ellie's card is shown to Ellie. Kenny's card is shown to Ellie. Sylvia's card is shown to Sylvia. Sylvia's card is shown to Kenny. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sylvia can now know that Sylvia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ellie","Sylvia","Kenny"],"index":53942,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9895811081,"difficulty":0.0104188919}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mack's card is shown to Mack. Mack's card is shown to Cameron. Mack's card is shown to Joshua. Joshua's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Mack does not know whether Joshua picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Cameron can now know that Mack can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mack","Cameron","Joshua"],"index":57380,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994186163,"difficulty":0.0005813837}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher does not know whether Sean is thirsty. It is publicly announced that Samantha does not know whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Samantha can now know whether Christopher can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Samantha","Christopher","Sean"],"index":60138,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994077682,"difficulty":0.0005922318}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candace's forehead is muddy. It is publicly announced that Candace's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"John can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sara","John","Candace"],"index":4168,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994606376,"difficulty":0.0005393624}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janie's card is shown to Larry. Sarah's card is shown to Larry. Sarah's card is shown to Wesley. Larry's card is shown to Janie. Wesley's card is shown to Sarah. Janie's card is shown to Sarah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know whether Wesley can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Wesley","Janie","Sarah"],"index":13502,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999363482,"difficulty":0.000636518}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edwina knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Steve can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Steve","Edwina"],"index":61136,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989849925,"difficulty":0.0010150075}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca does not know whether Rebecca's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Rebecca can now know whether Olga's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Leonard","Olga","Rebecca"],"index":45753,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992353916,"difficulty":0.0007646084}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mitchell knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Raymond can now know that Susan can know that Mitchell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mitchell","Susan","Raymond"],"index":28058,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998413682,"difficulty":0.001586318}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phillis is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Geoffrey can now know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Phillis","Geoffrey","Jennifer","Thomas"],"index":44517,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977152348,"difficulty":0.0022847652}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Corey's card is shown to Cynthia. Cynthia's card is shown to Daniel. Daniel's card is shown to Daniel. Corey's card is shown to Daniel. Daniel's card is shown to Corey. Corey's card is shown to Corey. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know that Cynthia can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cynthia","Daniel","Corey"],"index":6006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989302754,"difficulty":0.0010697246}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sara does not know whether or not everyone's forehead is muddy. It is publicly announced that Sara does not know whether Sara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sara can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sara","Adam","Willie"],"index":63138,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990677238,"difficulty":0.0009322762}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty. It is publicly announced that Mary does not know whether Ted is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Oralia can now know whether Mary can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Ted","Oralia","Mary"],"index":6391,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993433356,"difficulty":0.0006566644}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wilma's card is shown to Marie. Janice's card is shown to Marie. Wilma's card is shown to Wilma. Marie's card is shown to Janice. Wilma's card is shown to Janice. Janice's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janice can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marie","Wilma","Janice"],"index":6316,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993884563,"difficulty":0.0006115437}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Robin can now know whether Leonard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leonard","Vanessa","Robin"],"index":15952,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994792342,"difficulty":0.0005207658}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Caitlin is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Susan can now know whether Sean is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Caitlin","Susan","Sean","Diane"],"index":23124,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997907877,"difficulty":0.002092123}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Bryan can now know that Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bryan","Sandy","Peter"],"index":17103,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9951063395,"difficulty":0.0048936605}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Donna can now know that Lavonne can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donna","Michael","Lavonne","Joyce"],"index":26019,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989269376,"difficulty":0.0010730624}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"James can now know that Harold can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Harold","James"],"index":45841,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8797428012,"difficulty":0.1202571988}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether David's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that Timothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know that Alice can know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Alice","Timothy"],"index":49615,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9876258969,"difficulty":0.0123741031}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Israel can now know that Martha can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Ellen","Israel","Martha"],"index":17942,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998847723,"difficulty":0.001152277}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jermaine knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Melvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Mario can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jermaine","Hulda","Melvin","Mario"],"index":14387,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989564419,"difficulty":0.0010435581}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Nicole. Michael's card is shown to Michael. Katherine's card is shown to Michael. Michael's card is shown to Katherine. Katherine's card is shown to Katherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Nicole can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicole","Michael","Katherine"],"index":11919,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9280747771,"difficulty":0.0719252229}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Susan can now know whether James can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Priscila","James"],"index":37371,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994081259,"difficulty":0.0005918741}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Sergio can now know whether John can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Sergio","Anthony"],"index":2082,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9043238163,"difficulty":1.9043238163}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emerson's card is shown to Emerson. Glenn's card is shown to Emerson. Emerson's card is shown to Shirley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emerson can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emerson","Shirley","Glenn","Grace"],"index":55077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999347508,"difficulty":0.000652492}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Michael. Mary's card is shown to Michael. Mary's card is shown to Jeremy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Jeremy","Mary"],"index":52903,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993944168,"difficulty":0.0006055832}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Dominique can now know whether Adam can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rita","James","Dominique","Adam"],"index":64900,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999309659,"difficulty":0.000690341}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffrey's card is shown to Letha. Letha's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Jeffrey can now know that Letha picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Letha","Jeffrey"],"index":6989,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9246172905,"difficulty":1.9246172905}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Matthew can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kristina","Matthew","James","Arla"],"index":57593,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9624257684,"difficulty":0.0375742316}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Della knows whether someone is thirsty. It is publicly announced that Kurt does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kurt can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andre","Della","Kurt","Lindsay"],"index":5195,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994914532,"difficulty":0.0005085468}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Gena's card is shown to Joanne. Eugene's card is shown to Harold. Gena's card is shown to Harold. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joanne can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eugene","Gena","Joanne","Harold"],"index":30508,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993145466,"difficulty":0.0006854534}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether or not everyone is thirsty. It is publicly announced that Melissa knows whether or not nobody is thirsty. It is publicly announced that Sandra does not know whether Raul is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sandra can now know that Melissa can know that Melissa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melissa","Raul","Sandra"],"index":48036,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8210033178,"difficulty":1.8210033178}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol does not know whether Chantal is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Carol can now know that Chantal can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carol","Chantal","John"],"index":53837,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992842078,"difficulty":0.0007157922}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Giselle knows whether Giselle's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Giselle can now know that Rosemarie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Giselle","Rosemarie"],"index":53048,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996348083,"difficulty":0.003651917}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"John can now know that Donald can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elia","Joshua","Donald","John"],"index":31436,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992966652,"difficulty":0.0007033348}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Diane. Diane's card is shown to Linda. Diane's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Diane can now know that Diane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diane","Linda","Angela"],"index":49382,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9961398244,"difficulty":0.0038601756}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremy's card is shown to Jeremy. Jeremy's card is shown to Wesley. Wesley's card is shown to Wesley. It is publicly announced that someone picked a red card. It is publicly announced that Wesley knows whether Wesley picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Wesley can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeremy","Wesley"],"index":39039,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994408488,"difficulty":0.0005591512}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tony knows whether or not nobody is thirsty. It is publicly announced that Glenna does not know whether Tony is thirsty. It is publicly announced that Zelda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Tony can now know whether Glenna can know whether Glenna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Glenna","Tony","Zelda"],"index":49561,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977499843,"difficulty":0.0022500157}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kent does not know whether Jeannette is thirsty. It is publicly announced that Vera does not know whether Kent is thirsty. It is publicly announced that Jeannette does not know whether Cassandra is thirsty. It is publicly announced that Cassandra does not know whether Vera is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Vera can now know whether Cassandra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vera","Kent","Cassandra","Jeannette"],"index":13049,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9904318452,"difficulty":0.0095681548}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Walter can now know that Velma can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Velma","Walter","Maria"],"index":19490,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9915465713,"difficulty":0.0084534287}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy. It is publicly announced that Ina knows whether or not nobody's forehead is muddy. It is publicly announced that Ina does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ina can now know that John can know that Ina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ina","John"],"index":59350,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8487588763,"difficulty":1.8487588763}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Lauren. Antonio's card is shown to Timothy. Antonio's card is shown to Antonio. Lauren's card is shown to Maria. Timothy's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Antonio does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Antonio can now know whether Maria can know that Timothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lauren","Timothy","Antonio","Maria"],"index":18848,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9015852809,"difficulty":1.9015852809}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nellie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Thomas can now know that Virginia can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nellie","Virginia","Thomas"],"index":46853,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986761212,"difficulty":0.0013238788}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marion knows whether Irma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Willie can now know that Marion can know that Irma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irma","Mary","Willie","Marion"],"index":15776,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979603291,"difficulty":0.0020396709}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gina's card is shown to Gina. Heather's card is shown to Gina. Gina's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that Gina knows whether or not nobody picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Gina can now know whether Heather can know whether Gina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gina","Heather"],"index":49667,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977554679,"difficulty":0.0022445321}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Evette's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Dan can now know that Joseph can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dan","Evette","Joseph"],"index":46797,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969900846,"difficulty":0.0030099154}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hellen does not know whether Loretta is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2) ] 0","hypothesis":"Hellen can now know that Loretta can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hellen","Loretta"],"index":63015,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9971640706,"difficulty":1.9971640706}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marilyn","Gary","Christopher","John"],"index":62768,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988812804,"difficulty":0.0011187196}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Timothy knows whether Timothy's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Timothy can now know that Jenny can know that Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jenny","Timothy","Terry"],"index":21720,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949455857,"difficulty":0.0050544143}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"William can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dana","William","Dennis","Elaine"],"index":22086,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993281364,"difficulty":0.0006718636}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila knows whether Jose's forehead is muddy. It is publicly announced that Sheila does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Sheila can now know whether Sheila's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Jose","Sheila"],"index":23273,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5876930356,"difficulty":0.4123069644}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Wanda. Teresa's card is shown to Teresa. Wanda's card is shown to Jose. Teresa's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Jose picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Melissa can now know that Wanda can know that Jose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wanda","Teresa","Jose","Melissa"],"index":23823,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9946764708,"difficulty":0.0053235292}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Paul's forehead is muddy. It is publicly announced that Greg knows whether Donovan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentd knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Paul can now know that Gladys can know whether Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donovan","Greg","Gladys","Paul"],"index":31870,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999206841,"difficulty":0.000793159}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Derek does not know whether Shelby is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Rolando can now know whether Derek is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Derek","Shelby","Rolando"],"index":62994,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9842735529,"difficulty":0.0157264471}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy. It is publicly announced that Patricia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agentb knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"William can now know that Mildred can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Billie","William","Patricia","Mildred"],"index":24264,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954615235,"difficulty":0.0045384765}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Ernest can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Ernest","Olive","Donald"],"index":24877,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986872077,"difficulty":0.0013127923}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether Kelly's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Kelly can now know that George can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kelly","George"],"index":28925,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989913106,"difficulty":0.0010086894}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy. It is publicly announced that Damaris knows whether Craig's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Elizabeth can now know that Craig can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Craig","Elizabeth","Damaris"],"index":44431,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992048144,"difficulty":0.0007951856}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Etta can now know whether Jody can know that Jody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Jody","Andrew","Etta"],"index":54737,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9932750463,"difficulty":0.0067249537}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Lisa can now know whether Anthony can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Quincy","Lisa","Thomas","Anthony"],"index":54994,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999452889,"difficulty":0.000547111}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorri knows whether Mary's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Lorri can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","Lorri"],"index":13541,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978690147,"difficulty":0.0021309853}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill knows whether or not nobody's forehead is muddy. It is publicly announced that Douglas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Douglas can now know whether Bill can know whether Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Douglas","Bill"],"index":57562,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993886948,"difficulty":0.0006113052}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack's forehead is muddy. It is publicly announced that Joel knows whether Jack's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Hazel can now know that Hazel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hazel","Jack","Robert","Joel"],"index":19352,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.971811533,"difficulty":0.028188467}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether or not nobody's forehead is muddy. It is publicly announced that Jaqueline's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Jaqueline can now know that Donna can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jaqueline","Donna"],"index":50514,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993402362,"difficulty":0.0006597638}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chelsea's card is shown to Chelsea. Thomas's card is shown to Chelsea. Chelsea's card is shown to Dorothy. Dorothy's card is shown to Dorothy. Chelsea's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Chelsea","Dorothy","Thomas"],"index":59113,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989051819,"difficulty":0.0010948181}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Troy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Alan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Mike","Troy","Alan"],"index":20872,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987478256,"difficulty":0.0012521744}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joy's card is shown to Lillian. Sergio's card is shown to Lillian. Lillian's card is shown to Joy. Lillian's card is shown to Sergio. It is publicly announced that someone picked a red card. It is publicly announced that Lillian picked a red card. It is publicly announced that Joy knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Lillian knows whether Sergio picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Lillian can now know that Sergio can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lillian","Joy","Sergio"],"index":28138,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986172915,"difficulty":0.0013827085}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos knows whether or not nobody's forehead is muddy. It is publicly announced that Carlos knows whether Carlos's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carlos can now know that Frank can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carlos","Frank"],"index":52804,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998975873,"difficulty":0.001024127}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leona knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Linda can now know that Argelia can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Argelia","Linda","Leona"],"index":41285,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9945582151,"difficulty":0.0054417849}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Kaye can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kaye","Darlene","Chris"],"index":15307,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9894920588,"difficulty":0.0105079412}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neil's forehead is muddy. It is publicly announced that Jeanene does not know whether Jeanene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Steven can now know that Jeanene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Neil","Beth","Steven","Jeanene"],"index":49594,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9128294587,"difficulty":0.0871705413}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessie knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Vaughn can now know that Jessie can know that Vaughn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vaughn","Jessie","Jason","Travis"],"index":19079,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981577992,"difficulty":0.0018422008}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Paul can now know that Elizabeth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Paul","Robert","Elizabeth"],"index":30790,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998875916,"difficulty":0.001124084}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Jennifer can now know that Marie can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Marie","Jennifer","Florence"],"index":23791,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993721843,"difficulty":0.0006278157}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Morgan. Vicki's card is shown to Morgan. Morgan's card is shown to Vicki. Vicki's card is shown to Vicki. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Morgan","Charles","Vicki"],"index":47658,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994057417,"difficulty":0.0005942583}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Troy can now know that Carol can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Troy","Carol","Bettye"],"index":45578,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998952508,"difficulty":0.001047492}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie knows whether Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"James can now know whether Courtney can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Carmen","Courtney","James"],"index":6202,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993876219,"difficulty":0.0006123781}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Steven can now know that Mickey can know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Steven","Mickey"],"index":5346,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951624274,"difficulty":0.0048375726}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether someone's forehead is muddy. It is publicly announced that Carolyn's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kyle can now know that Peter's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peter","Kyle","Robin","Carolyn"],"index":53159,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965522289,"difficulty":0.0034477711}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Chris does not know whether Miles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Joseph can now know that Chris can know whether Chris is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Chris","Miles","John"],"index":15676,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975800514,"difficulty":0.0024199486}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Jennifer can now know whether Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Matthew","Gladys","Jennifer"],"index":18582,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994396567,"difficulty":0.0005603433}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Grant does not know whether Lena is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Maria can now know that Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brandie","Maria","Lena","Grant"],"index":34110,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9913074374,"difficulty":0.0086925626}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Dawn. Ruth's card is shown to Ruth. Cheryl's card is shown to Ruth. Charles's card is shown to Ruth. Charles's card is shown to Cheryl. Cheryl's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Cheryl does not know whether Cheryl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Dawn can now know that Cheryl can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dawn","Ruth","Cheryl","Charles"],"index":66446,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994142056,"difficulty":0.0005857944}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan knows whether Deborah's forehead is muddy. It is publicly announced that Jonathan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Jonathan can now know whether Deborah can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Deborah","Jonathan"],"index":52009,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994714856,"difficulty":0.0005285144}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether Suzette's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that Suzette can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Suzette"],"index":8524,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977701902,"difficulty":0.0022298098}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alonzo's card is shown to Alonzo. Hattie's card is shown to Alonzo. Alonzo's card is shown to Hazel. Hazel's card is shown to Hazel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alonzo can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alonzo","Hattie","Hazel"],"index":8026,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945905209,"difficulty":0.0054094791}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph's forehead is not muddy. It is publicly announced that Marie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Deborah can now know that Deborah's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deborah","Marie","Ralph"],"index":32058,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9897893071,"difficulty":0.0102106929}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Henry can now know whether Carol is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Henry","Preston","Judith"],"index":50407,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969353676,"difficulty":0.0030646324}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Minnie does not know whether Angel is thirsty. It is publicly announced that Alan does not know whether Angel is thirsty. It is publicly announced that Alan knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Minnie can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Minnie","Misty","Angel","Alan"],"index":18830,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995026588,"difficulty":0.0004973412}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paula's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Harley can now know whether Peggy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paula","Harley","Peggy"],"index":33749,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994449019,"difficulty":0.0005550981}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Kelly. Kelly's card is shown to James. Meta's card is shown to James. James's card is shown to Meta. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether James picked a red card. It is publicly announced that Meta does not know whether Kelly picked a red card. It is publicly announced that Kelly does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kelly can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kelly","James","Meta"],"index":36150,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994344115,"difficulty":0.0005655885}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Tiffany. Tiffany's card is shown to Jackie. Jackie's card is shown to Jackie. Roland's card is shown to Roland. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tiffany can now know whether Tiffany picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tiffany","Jackie","Roland"],"index":49681,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5143606067,"difficulty":0.4856393933}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephanie does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Stephanie can now know whether Annie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","William","Stephanie","Annie"],"index":30034,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9946492314,"difficulty":0.0053507686}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Patricia. Marc's card is shown to Patricia. Debra's card is shown to Debra. Debra's card is shown to Marc. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Debra can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Frances","Debra","Marc"],"index":34676,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993621707,"difficulty":0.0006378293}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dan does not know whether Dan's forehead is muddy. It is publicly announced that Norman knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Norman can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dan","Norman"],"index":42052,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989885688,"difficulty":0.0010114312}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Amy can now know that Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nan","Aaron","Amy"],"index":51911,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9946914315,"difficulty":0.0053085685}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jayna knows whether someone is thirsty. It is publicly announced that Tamela does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Tamela can now know that Jayna can know that Jayna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jayna","Tamela"],"index":46769,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9956331849,"difficulty":0.0043668151}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Miriam. David's card is shown to Rebecca. Miriam's card is shown to David. Rebecca's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Miriam","Rebecca","David"],"index":12993,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5240505934,"difficulty":0.4759494066}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Brandy knows whether Brandy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Hannah can now know that Brandy can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hannah","Gary","Brandy"],"index":24919,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994645715,"difficulty":0.0005354285}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Martin. Martin's card is shown to Richard. Richard's card is shown to Richard. Kevin's card is shown to Richard. Martin's card is shown to Kevin. Richard's card is shown to Kevin. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Martin can now know that Kevin can know that Martin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martin","Richard","Kevin"],"index":51854,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944492579,"difficulty":0.0055507421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether Tanya is thirsty. It is publicly announced that Brenda knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Maria can now know that Brenda can know whether Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tanya","Brenda","Maria"],"index":4639,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7386524081,"difficulty":0.2613475919}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Terry is thirsty. It is publicly announced that Kathy is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] [ ! (1|2|3) ] 0","hypothesis":"Kathy can now know whether Terry can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Kathy","Terry"],"index":37630,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994933605,"difficulty":0.0005066395}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"James can now know that Robert can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Robert","Eddie","Alma"],"index":748,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992004037,"difficulty":0.0007995963}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to David. Evelyn's card is shown to Evelyn. Evelyn's card is shown to Elaine. It is publicly announced that someone picked a red card. It is publicly announced that Elaine picked a red card. It is publicly announced that Bobby knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Bobby can now know that David can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Evelyn","Bobby","Elaine"],"index":5157,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982281327,"difficulty":0.0017718673}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Judith. Laura's card is shown to Laura. Laura's card is shown to Geri. It is publicly announced that someone picked a red card. It is publicly announced that Laura does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Laura can now know whether Judith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judith","Laura","Geri"],"index":19614,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8267656565,"difficulty":0.1732343435}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothea can now know whether Bobbi can know that Bobbi's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lewis","Dorothea","Bobbi"],"index":32470,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963249564,"difficulty":0.0036750436}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Desiree's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know whether Desiree can know that Desiree's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Desiree"],"index":66250,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994428754,"difficulty":0.0005571246}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacie does not know whether Stacie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Stacie can now know whether Veronica can know whether Veronica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stacie","Kim","Veronica"],"index":2652,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9897738099,"difficulty":1.9897738099}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Victor. Victor's card is shown to Kim. Kim's card is shown to Kim. Victor's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Kim knows whether Kim picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Evelyn can now know whether Victor can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Victor","Kim","Evelyn"],"index":25628,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9747728705,"difficulty":0.0252271295}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicholas can now know that June can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patsy","Nicholas","June","Calvin"],"index":26714,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991422892,"difficulty":0.0008577108}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cherlyn's card is shown to Nick. Nick's card is shown to Cherlyn. Shirley's card is shown to Cherlyn. Nick's card is shown to Shirley. Cherlyn's card is shown to Shirley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cherlyn can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nick","Cherlyn","Shirley"],"index":43888,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994021654,"difficulty":0.0005978346}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Edwin. William's card is shown to William. Annette's card is shown to Annette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Edwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edwin","William","Annette"],"index":8389,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975341558,"difficulty":0.0024658442}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley does not know whether Paul is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Shirley can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","John","Shirley"],"index":46070,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961858392,"difficulty":0.0038141608}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Graham. Christopher's card is shown to Richard. Graham's card is shown to Christopher. Christopher's card is shown to Christopher. Christopher's card is shown to Rhonda. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Graham can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Graham","Richard","Christopher","Rhonda"],"index":38084,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994283319,"difficulty":0.0005716681}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josephine does not know whether or not everyone is thirsty. It is publicly announced that Josephine does not know whether Brady is thirsty. It is publicly announced that Brady knows whether Brady is thirsty. It is publicly announced that Brady knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Brady can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brady","Josephine"],"index":39750,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9619384408,"difficulty":1.9619384408}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua does not know whether Sergio is thirsty. It is publicly announced that Morton does not know whether Sergio is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Johnnie can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Morton","Sergio","Johnnie"],"index":5852,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964964986,"difficulty":0.0035035014}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Willie can now know whether Fred can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fred","Rocco","Dorothy","Willie"],"index":25080,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994226694,"difficulty":0.0005773306}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelvin's card is shown to Thomas. Kelvin's card is shown to Kelvin. It is publicly announced that someone picked a red card. It is publicly announced that Kelvin knows whether or not nobody picked a red card. It is publicly announced that Kelvin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Kelvin can now know that Kelvin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thomas","Kelvin"],"index":65714,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6216364503,"difficulty":1.6216364503}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Wanda can now know whether Daphne can know that Daphne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wanda","Pearl","Daphne"],"index":52918,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991512299,"difficulty":0.0008487701}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Frank can now know that Frank's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Leslie","Harold","Frank"],"index":21792,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9904181361,"difficulty":0.0095818639}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lana's card is shown to Elizabeth. Elizabeth's card is shown to Lana. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Elizabeth picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","Lana"],"index":12394,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994314313,"difficulty":0.0005685687}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jocelyn knows whether Shannon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Shannon can now know that Anita can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Shannon","Jocelyn","Anita"],"index":12815,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993126392,"difficulty":0.0006873608}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine does not know whether Catherine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Catherine can now know that Kenneth can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kenneth","Catherine"],"index":24810,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989349246,"difficulty":0.0010650754}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Glenn. Ruby's card is shown to Glenn. Glenn's card is shown to Juan. Juan's card is shown to Juan. Gordon's card is shown to Ruby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruby can now know that Glenn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Glenn","Juan","Ruby","Gordon"],"index":52148,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977983832,"difficulty":0.0022016168}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy. It is publicly announced that Phuong knows whether Phuong's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Annie can now know whether Robert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phuong","Annie","Robert"],"index":13303,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993900061,"difficulty":0.0006099939}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramona's forehead is not muddy. It is publicly announced that Diana's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ramona can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christine","Diana","Ramona"],"index":24132,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993684888,"difficulty":0.0006315112}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerrold knows whether Jerrold's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Angel can now know whether Jesse can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesse","Angel","Jerrold","Glenn"],"index":14510,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994499087,"difficulty":0.0005500913}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Victor's forehead is muddy. It is publicly announced that Victor does not know whether Victor's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Olga can now know that Victor can know that Victor's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Olga","Jennifer","Victor"],"index":49400,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9665210247,"difficulty":0.0334789753}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Bobby is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Tami can now know whether Bobby can know whether Bobby is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hoa","Bobby","Robert","Tami"],"index":37097,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998636663,"difficulty":0.001363337}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William is thirsty. It is publicly announced that William does not know whether Ronda is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ronda can now know whether William can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronda","William"],"index":20538,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9794567227,"difficulty":0.0205432773}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Michael can now know that Robert can know that Samuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Samuel","Robert","Michael"],"index":12227,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981250167,"difficulty":0.0018749833}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Blanche's forehead is not muddy. It is publicly announced that Beatriz knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Blanche can now know that Ima's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Blanche","Beatriz","Ima"],"index":28906,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982017279,"difficulty":0.0017982721}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Verna's card is shown to Verna. Douglas's card is shown to Verna. Brenda's card is shown to Douglas. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Douglas knows whether Brenda picked a red card. It is publicly announced that Douglas knows whether Verna picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Douglas can now know that Brenda can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brenda","Verna","Douglas"],"index":59844,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994177818,"difficulty":0.0005822182}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Kevin. Kevin's card is shown to Joyce. Joyce's card is shown to Joyce. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Joyce knows whether Joyce picked a red card. It is publicly announced that Kevin knows whether Kevin picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kevin can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kevin","Joyce"],"index":34128,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9933755994,"difficulty":0.0066244006}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Tracey is thirsty. It is publicly announced that Tracey does not know whether Thomas is thirsty. It is publicly announced that Paige does not know whether or not everyone is thirsty. It is publicly announced that Paige is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Paige can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracey","Paige","Thomas"],"index":7669,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8894941807,"difficulty":0.1105058193}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl does not know whether Doris is thirsty. It is publicly announced that Elizabeth does not know whether Carl is thirsty. It is publicly announced that Doris is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] (Agentd knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Elizabeth can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Frank","Carl","Doris","Elizabeth"],"index":6948,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9667649865,"difficulty":1.9667649865}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Eduardo can now know whether Alice can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alice","Eduardo","Dominick"],"index":60035,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983804226,"difficulty":0.0016195774}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Meaghan does not know whether Meaghan's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Meaghan can now know that Scott can know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Meaghan","Scott"],"index":46775,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948861003,"difficulty":0.0051138997}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cody does not know whether Andre is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Chad can now know whether Andre can know that Andre is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Andre","Cody","Chad"],"index":54036,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9653752446,"difficulty":1.9653752446}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francisco does not know whether or not everyone is thirsty. It is publicly announced that Clifford knows whether Clifford is thirsty. It is publicly announced that Francisco does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Francisco can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clifford","Francisco","Mary"],"index":7682,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99858284,"difficulty":0.00141716}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Brian. Ralph's card is shown to Brian. Miguel's card is shown to Miguel. Miguel's card is shown to Lori. Ralph's card is shown to Lori. Ralph's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Brian does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lori can now know that Ralph can know that Lori picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Miguel","Lori","Ralph"],"index":46237,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7255437374,"difficulty":0.2744562626}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Eileen can now know that Monica can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Monica","Eileen"],"index":40190,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993314743,"difficulty":0.0006685257}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Shea knows whether Alice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Timothy can now know that Alice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janette","Alice","Shea","Timothy"],"index":13687,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9982553124,"difficulty":0.0017446876}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. Serena's card is shown to David. David's card is shown to Serena. Serena's card is shown to Serena. Adam's card is shown to Serena. David's card is shown to Adam. Serena's card is shown to Adam. Adam's card is shown to Adam. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Adam can now know whether Adam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Serena","Adam"],"index":45306,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8920806646,"difficulty":0.1079193354}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cecil does not know whether Elizabeth is thirsty. It is publicly announced that Brenda is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Cecil can now know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Brenda","Cecil"],"index":27506,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996542871,"difficulty":0.003457129}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chester's card is shown to Chester. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Tommy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tommy","Chester"],"index":3289,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989578724,"difficulty":0.0010421276}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Robert. David's card is shown to Robert. Anna's card is shown to Octavia. David's card is shown to Octavia. David's card is shown to Anna. Robert's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Octavia knows whether Anna picked a red card. It is publicly announced that Octavia knows whether someone picked a red card. It is publicly announced that Octavia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] Agentc knows that (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Anna can now know that David can know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Octavia","Anna","David"],"index":22989,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9880644679,"difficulty":1.9880644679}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred's forehead is muddy. It is publicly announced that Fred's forehead is muddy. It is publicly announced that Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Mark can now know whether Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Krystyna","Mark","Fred"],"index":33476,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994418025,"difficulty":0.0005581975}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nellie's card is shown to Virgil. Louis's card is shown to Virgil. Nellie's card is shown to Nellie. Nellie's card is shown to Louis. Louis's card is shown to Louis. It is publicly announced that someone picked a red card. It is publicly announced that Virgil does not know whether Virgil picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Nellie can now know whether Virgil can know that Louis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Virgil","Nellie","Louis"],"index":31547,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9494909048,"difficulty":1.9494909048}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Michael can now know that James can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Ernest","James"],"index":62452,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9935981035,"difficulty":0.0064018965}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helena is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Enrique can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helena","Robbie","Enrique"],"index":17760,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9255895615,"difficulty":1.9255895615}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know that Patricia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roberta","John","Patricia"],"index":35009,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994404912,"difficulty":0.0005595088}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Loria does not know whether Lera is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lera can now know whether Evelyn can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Loria","Lera","Evelyn"],"index":50205,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990270138,"difficulty":0.0009729862}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Faye does not know whether Faye's forehead is muddy. It is publicly announced that Faye knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Faye can now know that Charles can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Faye","Olivia","Charles","Ronald"],"index":1161,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990111589,"difficulty":0.0009888411}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Chris. Thomas's card is shown to Chris. Jerry's card is shown to Jessica. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know whether Jessica can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chris","Jessica","Thomas","Jerry"],"index":64006,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848337173,"difficulty":0.0151662827}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether Michele's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Alberto can now know whether Michele's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janine","Shirley","Michele","Alberto"],"index":31630,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993483424,"difficulty":0.0006516576}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Miguel knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Stephen can now know that Justin can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Miguel","Justin","Stephen"],"index":67315,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990292788,"difficulty":0.0009707212}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clara's card is shown to Lashanda. Linda's card is shown to Lashanda. Clara's card is shown to Linda. Michael's card is shown to Linda. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clara can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clara","Lashanda","Linda","Michael"],"index":15540,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942030311,"difficulty":0.0057969689}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Sheila is thirsty. It is publicly announced that Sheila does not know whether Brian is thirsty. It is publicly announced that Brian does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Marie can now know whether Brian can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Patricia","Brian","Sheila"],"index":55966,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994176626,"difficulty":0.0005823374}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy. It is publicly announced that Michael knows whether Jessie's forehead is muddy. It is publicly announced that Jessie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] Agentc knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"Michael can now know that Harvey can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jessie","Harvey","Michael"],"index":30126,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9774936438,"difficulty":0.0225063562}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dennis can now know whether Connie can know whether Dennis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dennis","Belva","Mary","Connie"],"index":48897,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988592863,"difficulty":0.0011407137}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oscar's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Holly can now know whether Oscar can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janine","Oscar","Caroline","Holly"],"index":26286,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993294477,"difficulty":0.0006705523}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Chadwick can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chadwick","John","Julie","Stacey"],"index":36680,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993740916,"difficulty":0.0006259084}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Johnny does not know whether Margaret is thirsty. It is publicly announced that Cornelius does not know whether Margaret is thirsty. It is publicly announced that Margaret does not know whether Johnny is thirsty. It is publicly announced that Johnny is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Johnny can now know whether Cornelius is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cornelius","Margaret","Johnny"],"index":35253,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954740405,"difficulty":0.0045259595}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julio's card is shown to Michael. Michael's card is shown to Michael. Michael's card is shown to Beverly. Beverly's card is shown to Denis. Denis's card is shown to Denis. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Julio can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julio","Michael","Beverly","Denis"],"index":42543,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.986196816,"difficulty":0.013803184}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ryan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deborah","Richard","Ryan"],"index":27813,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990205765,"difficulty":0.0009794235}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Deanna. Brandon's card is shown to Brandon. Tanya's card is shown to John. Deanna's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandon can now know whether Deanna can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tanya","Deanna","Brandon","John"],"index":5325,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993935823,"difficulty":0.0006064177}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Lawrence. Anna's card is shown to Phillip. Phillip's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Anna can now know that Phillip can know whether Phillip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lawrence","Phillip","Anna"],"index":52351,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6848420501,"difficulty":1.6848420501}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas's forehead is muddy. It is publicly announced that Steven knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marilyn can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Miriam","Thomas","Marilyn"],"index":1353,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994933605,"difficulty":0.0005066395}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia is thirsty. It is publicly announced that Marshall does not know whether Eric is thirsty. It is publicly announced that Marshall does not know whether Marty is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Marty can now know that Eric can know that Eric is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marshall","Marty","Eric","Patricia"],"index":62723,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9841633439,"difficulty":0.0158366561}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wendy's card is shown to Wendy. Wendy's card is shown to Martin. Amanda's card is shown to Martin. Amanda's card is shown to Amanda. Dale's card is shown to Amanda. Martin's card is shown to Dale. It is publicly announced that someone picked a red card. It is publicly announced that Dale does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Dale can now know that Amanda can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wendy","Martin","Amanda","Dale"],"index":28351,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9292667508,"difficulty":0.0707332492}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott is not thirsty. It is publicly announced that Scott knows whether Scott is thirsty. It is publicly announced that Scott does not know whether Harold is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Harold can now know that James can know whether Scott is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Harold","James"],"index":19181,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9064661264,"difficulty":0.0935338736}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Daniel can now know that Fidela is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Otis","Daniel","Marion","Fidela"],"index":10362,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949656129,"difficulty":0.0050343871}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy. It is publicly announced that Dorothy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Dorothy can now know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Dorothy"],"index":39468,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994589686,"difficulty":0.0005410314}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Jennifer. Sandra's card is shown to Sandra. Andrea's card is shown to Andrea. Andrea's card is shown to Therese. Therese's card is shown to Therese. It is publicly announced that someone picked a red card. It is publicly announced that Therese does not know whether Jennifer picked a red card. It is publicly announced that Jennifer does not know whether Jennifer picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Therese can now know whether Jennifer can know whether Sandra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Sandra","Andrea","Therese"],"index":20553,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988740087,"difficulty":0.0011259913}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth knows whether Kenneth is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Kenneth can now know whether Raleigh can know that Raleigh is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raleigh","Kenneth"],"index":30852,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.532453835,"difficulty":1.532453835}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"David can now know that Linda can know that Jessica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Adrian","Linda","David","Jessica"],"index":48478,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.8995704651,"difficulty":1.8995704651}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurie knows whether Laurie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Patricia can now know whether Charles can know that Laurie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Charles","Laurie"],"index":17592,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994561076,"difficulty":0.0005438924}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ethel knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Ethel can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ethel","Scott","Richard"],"index":16050,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986813664,"difficulty":0.0013186336}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Taisha can now know that Kimberly can know that Hilda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","Hilda","Cora","Taisha"],"index":56913,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9449490905,"difficulty":0.0550509095}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Jon can now know whether Raymond can know that Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Jon"],"index":53515,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993596673,"difficulty":0.0006403327}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. James's card is shown to Charles. Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card. It is publicly announced that Charles picked a black card. It is publicly announced that Charles knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Charles can now know whether James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Charles"],"index":34922,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9870485663,"difficulty":0.0129514337}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Donald can now know whether Ryan can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eugene","Clyde","Ryan","Donald"],"index":44395,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999473393,"difficulty":0.000526607}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clarence knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Franklin can now know whether Clarence can know whether Clarence is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Franklin","Clarence","Eugene"],"index":64861,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982511401,"difficulty":0.0017488599}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eve's card is shown to Joseph. Cami's card is shown to Joseph. Eve's card is shown to Cami. Kenneth's card is shown to Cami. Cami's card is shown to Kenneth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eve can now know whether Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Eve","Cami","Kenneth"],"index":66749,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9662625194,"difficulty":1.9662625194}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cory knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Laura can now know whether Morgan can know that Laura is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cory","Dominica","Laura","Morgan"],"index":49556,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9783665538,"difficulty":0.0216334462}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jodie is thirsty. It is publicly announced that Karen does not know whether Patricia is thirsty. It is publicly announced that Karen does not know whether Walter is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Walter can now know whether Patricia can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Walter","Patricia","Jodie"],"index":1954,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994744658,"difficulty":0.0005255342}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether or not everyone is thirsty. It is publicly announced that Tammy knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Elizabeth can now know whether Julie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Francisco","Tammy","Julie"],"index":50795,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954152107,"difficulty":0.0045847893}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Ann can now know that Tamara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ann","Joan","Tamara"],"index":9779,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985443354,"difficulty":0.0014556646}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether Rodney's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ronald can now know that Rodney can know that Rodney's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Rodney","Ronald"],"index":15986,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975836277,"difficulty":0.0024163723}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annie knows whether Annie is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Mary can now know that Annie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Annie"],"index":50042,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9724294543,"difficulty":1.9724294543}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Patrick can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","John","David","Alice"],"index":46525,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9794075489,"difficulty":0.0205924511}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Larry. Charles's card is shown to Charles. Karen's card is shown to Charles. Karen's card is shown to Amy. Amy's card is shown to Karen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know whether Charles can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Charles","Amy","Karen"],"index":3341,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993934631,"difficulty":0.0006065369}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Calvin can now know that Joann can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Calvin","Eileen","Rosemary","Joann"],"index":54141,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991933703,"difficulty":0.0008066297}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Nettie knows whether Nettie's forehead is muddy. It is publicly announced that Yvette knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Nettie can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nettie","Yvette"],"index":64761,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9975814819,"difficulty":0.0024185181}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Roy is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sidney","Michael","Billy","Roy"],"index":38450,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994443059,"difficulty":0.0005556941}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Doris. Janet's card is shown to Janet. Kathleen's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Doris can now know that Janet can know whether Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Janet","Kathleen"],"index":10867,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9890294075,"difficulty":1.9890294075}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Douglas can now know that William can know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Douglas","William","Gerald"],"index":57792,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968480468,"difficulty":0.0031519532}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carlos's card is shown to Leland. Leland's card is shown to Julius. Carlos's card is shown to Julius. Leland's card is shown to Carlos. It is publicly announced that someone picked a red card. It is publicly announced that Carlos does not know whether Kevin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Carlos can now know whether Julius can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leland","Julius","Carlos","Kevin"],"index":35756,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989824891,"difficulty":0.0010175109}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrea knows whether Gary's forehead is muddy. It is publicly announced that Victor's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Gary can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lucy","Victor","Andrea","Gary"],"index":35579,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994072914,"difficulty":0.0005927086}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Pamela can now know that Billy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Billy","Brittany","Richard","Pamela"],"index":6737,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998914361,"difficulty":0.001085639}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lawrence does not know whether James is thirsty. It is publicly announced that Lawrence does not know whether Robin is thirsty. It is publicly announced that James knows whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"James can now know that Lawrence can know that Lawrence is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robin","Lawrence","James"],"index":7927,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9759976268,"difficulty":0.0240023732}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Enrique can now know whether Norman can know that Enrique's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hugo","Norman","Enrique","Julia"],"index":29846,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999460876,"difficulty":0.000539124}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Erika. Erika's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer knows whether or not nobody picked a red card. It is publicly announced that Jennifer does not know whether Jennifer picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Erika can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Erika","Jennifer"],"index":25668,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994383454,"difficulty":0.0005616546}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica does not know whether Jessica's forehead is muddy. It is publicly announced that Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Jessica can now know whether Donald can know that Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Sandra","Donald"],"index":15559,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9569176435,"difficulty":0.0430823565}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Deandre can now know whether Melanie can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Melanie","Deandre"],"index":22759,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993314743,"difficulty":0.0006685257}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bessie does not know whether Bessie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Chris can now know that Bessie can know whether Bessie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bessie","Chris","Juan"],"index":32000,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9867266417,"difficulty":0.0132733583}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty. It is publicly announced that Michael does not know whether or not everyone is thirsty. It is publicly announced that Michael does not know whether Clair is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Michael can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Clair","Michael"],"index":11564,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994989634,"difficulty":0.0005010366}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. William's card is shown to Curtis. William's card is shown to Dean. William's card is shown to Mary. Mary's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dean can now know whether Curtis can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Curtis","Dean","Mary","William"],"index":9009,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9405843616,"difficulty":0.0594156384}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Juan knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"April can now know that Melissa can know that April is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juan","April","Melissa"],"index":1146,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949547648,"difficulty":0.0050452352}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chelsea's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Chelsea can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Philomena","Chelsea"],"index":61621,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985651374,"difficulty":0.0014348626}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Daniella can now know that Harold's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sam","Daniella","Harold"],"index":54862,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997418046,"difficulty":0.002581954}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy. It is publicly announced that Lorraine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Lorraine can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lorraine","Ruth"],"index":18318,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989952445,"difficulty":0.0010047555}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delbert knows whether Maria's forehead is muddy. It is publicly announced that Maria does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Maria can now know whether Delbert can know whether Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Delbert","Maria"],"index":30389,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988699555,"difficulty":0.0011300445}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kelly can now know whether Ella can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Theresa","Ella","Kelly","Curtis"],"index":52529,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993519187,"difficulty":0.0006480813}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Sherman. Sherman's card is shown to William. William's card is shown to Patrice. Patrice's card is shown to Patrice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sherman can now know that William can know whether Sherman picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sherman","William","Patrice"],"index":12314,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7775333524,"difficulty":1.7775333524}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Devon's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Chadwick can now know whether John can know that Devon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Chadwick","Devon"],"index":48667,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994648099,"difficulty":0.0005351901}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maynard knows whether Becky's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Becky can now know that Maynard can know that Maynard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maynard","Becky","Lisa"],"index":65460,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956080317,"difficulty":0.0043919683}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christine knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Craig can now know whether Christine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christine","Donna","Craig"],"index":33388,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6881994009,"difficulty":0.3118005991}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecelia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Leslie can now know whether Randy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leslie","Arthur","Randy","Cecelia"],"index":21399,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9959671497,"difficulty":0.0040328503}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Pedro is thirsty. It is publicly announced that Eva does not know whether Pedro is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Eva can now know that Anthony is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Anthony","Eva","Pedro"],"index":19922,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982209802,"difficulty":0.0017790198}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherman's card is shown to Lynn. Joanna's card is shown to Joanna. Sherman's card is shown to Joanna. Lynn's card is shown to Sherman. Joanna's card is shown to Sherman. Sherman's card is shown to Sherman. It is publicly announced that someone picked a red card. It is publicly announced that Joanna does not know whether or not everyone picked a red card. It is publicly announced that Sherman knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Sherman can now know that Lynn can know whether Lynn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lynn","Joanna","Sherman"],"index":4444,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5873601437,"difficulty":0.4126398563}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Sharon. Steven's card is shown to Sharon. Lillie's card is shown to Lillie. Steven's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know whether Sharon can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Lillie","Steven"],"index":52217,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8330318332,"difficulty":0.1669681668}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacey knows whether or not everyone's forehead is muddy. It is publicly announced that Catherine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Charles can now know whether Stacey can know whether Stacey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stacey","Catherine","Charles"],"index":53744,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9249714613,"difficulty":1.9249714613}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esperanza knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Pauline can now know that Kristen can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pauline","Esperanza","Kristen"],"index":33003,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987595081,"difficulty":0.0012404919}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clayton's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Clayton can now know whether Richard can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Clayton","Richard"],"index":16236,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993138313,"difficulty":0.0006861687}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Santiago knows whether Santiago's forehead is muddy. It is publicly announced that Nicole knows whether Jeanette's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mary can now know that Jeanette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeanette","Santiago","Nicole","Mary"],"index":17267,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971252084,"difficulty":0.0028747916}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Janie does not know whether Brandon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Brandon can now know whether Brandon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brandon","Janie","Asia","Keith"],"index":48073,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9945794344,"difficulty":0.0054205656}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Willard can now know that Willard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Willard","James","David"],"index":45496,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979652166,"difficulty":0.0020347834}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanette knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Jeanette can now know that William can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeanette","William"],"index":24044,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989477992,"difficulty":0.0010522008}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cesar does not know whether Tiffany is thirsty. It is publicly announced that Robert knows whether someone is thirsty. It is publicly announced that Cesar does not know whether or not everyone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that James can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Cesar","Tiffany","James"],"index":40230,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9728374481,"difficulty":0.0271625519}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Thomas can now know whether Albert can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Albert","Jeanette"],"index":66269,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994615912,"difficulty":0.0005384088}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Bryan. Harold's card is shown to Bryan. Clifford's card is shown to Bryan. Clifford's card is shown to Paul. Bryan's card is shown to Harold. Paul's card is shown to Clifford. Harold's card is shown to Clifford. It is publicly announced that someone picked a red card. It is publicly announced that Harold picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Harold can now know whether Clifford can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bryan","Paul","Harold","Clifford"],"index":13556,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.990911305,"difficulty":0.009088695}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Constance knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Shelia can now know that Constance can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Constance","Shelia"],"index":47905,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989978671,"difficulty":0.0010021329}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald's forehead is not muddy. It is publicly announced that Harold does not know whether Harold's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Gerald can now know that Virgil can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Virgil","Harold","Gerald"],"index":48766,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999458015,"difficulty":0.000541985}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Alonzo can now know that Marcia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alonzo","Marcia","Brandie","Cynthia"],"index":37979,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969435334,"difficulty":0.0030564666}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Lisa. Grace's card is shown to Grace. Mary's card is shown to Grace. Lisa's card is shown to Mary. Lisa's card is shown to Bret. Grace's card is shown to Bret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Grace","Mary","Bret"],"index":42110,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.928185761,"difficulty":0.071814239}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Alice. Alice's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Alice knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Kelly can now know that Alice can know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alice","Kelly"],"index":61090,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9370346665,"difficulty":1.9370346665}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Retta does not know whether Retta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Retta","Robert"],"index":6154,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989836812,"difficulty":0.0010163188}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margarete does not know whether Margarete's forehead is muddy. It is publicly announced that Margarete knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ignacio can now know whether Michael can know that Ignacio's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margarete","Brenda","Michael","Ignacio"],"index":61064,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9892410636,"difficulty":0.0107589364}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Agustin. Jamel's card is shown to Larry. Fanny's card is shown to Fanny. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Agustin can now know whether Larry can know that Jamel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Agustin","Larry","Jamel","Fanny"],"index":66665,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9030269384,"difficulty":1.9030269384}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alyssa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Dale can now know that William can know that Alyssa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dale","William","Alyssa"],"index":1471,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997448504,"difficulty":0.002551496}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know that Adam can know that Adam is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Adam","William","Douglas","Linda"],"index":6728,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942272902,"difficulty":0.0057727098}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jonathan knows whether Jonathan's forehead is muddy. It is publicly announced that Greg knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Jonathan can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jonathan","Greg"],"index":16573,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990952015,"difficulty":0.0009047985}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn does not know whether Evelyn's forehead is muddy. It is publicly announced that Elizabeth knows whether or not everyone's forehead is muddy. It is publicly announced that Evelyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Evelyn can now know that Stephen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Stephen","Michael","Evelyn"],"index":17485,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8251338005,"difficulty":0.1748661995}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Susana can now know that Sylvia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sylvia","Tamela","Susana"],"index":56196,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963676929,"difficulty":0.0036323071}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joann's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Nicholas can now know that Anita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joann","Anita","Nicholas","Doyle"],"index":30114,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981853366,"difficulty":0.0018146634}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Opal's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Charles can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Van","Annie","Charles","Opal"],"index":62941,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989722967,"difficulty":0.0010277033}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stanley's card is shown to Stanley. Daniel's card is shown to Stanley. Alicia's card is shown to Alicia. Stanley's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Alicia does not know whether Stanley picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Daniel can now know that Alicia can know that Daniel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stanley","Alicia","Daniel"],"index":3884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960636497,"difficulty":0.0039363503}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Ricardo. Laura's card is shown to Laura. Laura's card is shown to Robin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Laura can now know whether Robin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ricardo","Laura","Robin"],"index":26021,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967773557,"difficulty":0.0032226443}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adrienne does not know whether or not everyone's forehead is muddy. It is publicly announced that Adrienne knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Albert can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Albert","Adrienne","Neva","Pearl"],"index":33748,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990032315,"difficulty":0.0009967685}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy. It is publicly announced that Cornell does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jennifer can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cornell","Jennifer","Mollie","Mary"],"index":23695,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976773858,"difficulty":0.0023226142}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"David can now know that Douglas can know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Stephanie","Douglas"],"index":24289,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983147383,"difficulty":0.0016852617}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Rachel can now know whether Mary can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rachel","Lola","Robert","Mary"],"index":18056,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994713664,"difficulty":0.0005286336}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether Judith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Melodie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Judith","Kimberly","Robin","Melodie"],"index":48676,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9726464748,"difficulty":0.0273535252}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Brooks's forehead is muddy. It is publicly announced that Trey's forehead is not muddy. It is publicly announced that Trey knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Brooks can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Trey","Brooks"],"index":57410,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9954658747,"difficulty":0.0045341253}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lu's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Betty can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kristi","Janice","Lu","Betty"],"index":35413,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987932444,"difficulty":0.0012067556}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know that Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebecca","James","Annie","Steven"],"index":12148,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976261258,"difficulty":0.0023738742}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenny's forehead is not muddy. It is publicly announced that Yvonne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Kenny can now know whether Mary can know whether Judy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Kenny","Judy","Yvonne"],"index":36603,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994509816,"difficulty":0.0005490184}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allen does not know whether Patricia is thirsty. It is publicly announced that Moses is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] Agenta knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Allen can now know that Kathryn can know that Allen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Allen","Moses","Patricia","Kathryn"],"index":44158,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9630960226,"difficulty":0.0369039774}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Richard can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mike","Mary","Richard","Eugene"],"index":12679,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993859529,"difficulty":0.0006140471}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kendall's card is shown to Janet. Janet's card is shown to Joshua. Kendall's card is shown to Joshua. Janet's card is shown to Kendall. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Janet picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kendall can now know whether Kendall picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janet","Joshua","Kendall"],"index":32995,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5234607458,"difficulty":1.5234607458}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karrie does not know whether or not everyone is thirsty. It is publicly announced that Karrie does not know whether Mark is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Norman can now know that Mark can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karrie","Mark","Norman"],"index":19196,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994959831,"difficulty":0.0005040169}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Rebecca. Rita's card is shown to Rebecca. Jeanette's card is shown to Rebecca. Patricia's card is shown to Jeanette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rebecca can now know whether Rita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Rebecca","Rita","Jeanette"],"index":41694,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9161158204,"difficulty":0.0838841796}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Hazel can now know whether Hazel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hazel","Arnold","Bertha"],"index":2437,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992868304,"difficulty":0.0007131696}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicole knows whether someone is thirsty. It is publicly announced that Marvin does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nicole can now know that Mary can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Nicole","Frances","Marvin"],"index":42615,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7197207808,"difficulty":0.2802792192}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nikki's forehead is muddy. It is publicly announced that Mary knows whether Nikki's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"David can now know that Mary can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Nikki","David","Carla"],"index":4187,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9859370589,"difficulty":0.0140629411}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is not thirsty. It is publicly announced that Daisy knows whether or not everyone is thirsty. It is publicly announced that John knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Patricia can now know that Daisy can know whether Chris is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daisy","Chris","John","Patricia"],"index":57762,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9784249067,"difficulty":0.0215750933}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Harold. Maureen's card is shown to Harold. Amanda's card is shown to Amanda. Maureen's card is shown to Amanda. Harold's card is shown to Maureen. Amanda's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Harold does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Maureen can now know whether Amanda can know whether Harold picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Amanda","Maureen","Jeffrey"],"index":40626,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983591437,"difficulty":0.0016408563}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terry's card is shown to Emily. Emily's card is shown to Earl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emily can now know that Emily picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Emily","Earl","Terry","Ruth"],"index":20060,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9884753227,"difficulty":0.0115246773}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Martin can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kimberley","Martin","Walter","Heidi"],"index":24432,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974453449,"difficulty":0.0025546551}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hope knows whether or not nobody's forehead is muddy. It is publicly announced that Hope knows whether Hope's forehead is muddy. It is publicly announced that Gary's forehead is muddy. It is publicly announced that Lela knows whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Theodore can now know that Gary can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Hope","Lela","Theodore"],"index":62249,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985656142,"difficulty":0.0014343858}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ernestine can now know that Nicole can know that Ernestine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ernestine","Ronnie","Nicole","Maria"],"index":44065,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983119965,"difficulty":0.0016880035}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esther's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Esther can now know that Sarah can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Esther","Sarah","Joseph"],"index":55111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994414449,"difficulty":0.0005585551}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Henry does not know whether Walter is thirsty. It is publicly announced that Walter does not know whether Letha is thirsty. It is publicly announced that Hector knows whether Hector is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether 3) ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Walter can now know whether Letha is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Henry","Hector","Letha"],"index":16081,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9886948466,"difficulty":0.0113051534}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cody's card is shown to Cody. Cody's card is shown to Charles. Charles's card is shown to Charles. Cody's card is shown to Russell. Russell's card is shown to Russell. It is publicly announced that someone picked a red card. It is publicly announced that Cody does not know whether Russell picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Alton can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cody","Charles","Alton","Russell"],"index":13713,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993724227,"difficulty":0.0006275773}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Mary can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","Edna"],"index":10394,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990347624,"difficulty":0.0009652376}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gail can now know that Reynaldo can know whether Winter is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gail","Scott","Winter","Reynaldo"],"index":8687,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9859469533,"difficulty":0.0140530467}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know whether Christopher can know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Christopher","Margaret"],"index":55357,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993164539,"difficulty":0.0006835461}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffery's card is shown to Jeffery. Joanne's card is shown to Joanne. Joan's card is shown to Joanne. Joanne's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Joan does not know whether Joan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Joan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffery","Joanne","Joan"],"index":33640,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990156889,"difficulty":0.0009843111}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacie knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Christian can now know whether Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stacie","Christian","Robert","Dominick"],"index":2780,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6675527096,"difficulty":0.3324472904}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Donald. Debra's card is shown to Shelley. Donald's card is shown to Tom. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether Shelley can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Donald","Shelley","Tom"],"index":56688,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993025064,"difficulty":0.0006974936}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlena does not know whether Jonathan is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Stephanie can now know whether Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jonathan","Mary","Charlena","Stephanie"],"index":13877,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8585101962,"difficulty":1.8585101962}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jim's card is shown to Jim. Jim's card is shown to Carrie. Emanuel's card is shown to Carrie. Jim's card is shown to Kelly. It is publicly announced that someone picked a red card. It is publicly announced that Jim does not know whether Emanuel picked a red card. It is publicly announced that Kelly knows whether or not everyone picked a red card. It is publicly announced that Jim does not know whether Carrie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jim can now know whether Kelly can know that Jim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jim","Carrie","Kelly","Emanuel"],"index":55411,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9301676154,"difficulty":0.0698323846}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry does not know whether Terry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Alonzo can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Alonzo","Edwina","Terry"],"index":46446,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Betty can now know whether Sherry can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Betty","Sherry"],"index":12838,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973171353,"difficulty":0.0026828647}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leticia's card is shown to Natalie. Leisha's card is shown to Natalie. Leisha's card is shown to Leticia. Leisha's card is shown to Leisha. It is publicly announced that someone picked a red card. It is publicly announced that Leisha does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Leisha can now know that Natalie can know whether Natalie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Natalie","Leticia","Leisha"],"index":20898,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5707316995,"difficulty":0.4292683005}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Monica knows whether Monica is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Monica can now know that Leola can know whether Monica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leola","Monica"],"index":45005,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9960064292,"difficulty":0.0039935708}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Joseph can now know whether Daniel can know that Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daniel","Joseph"],"index":39836,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9623739719,"difficulty":1.9623739719}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Margaret. Patrick's card is shown to Margaret. Patrick's card is shown to Patrick. Enrique's card is shown to Enrique. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know that Patrick can know that Enrique picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Patrick","Enrique"],"index":62510,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974907637,"difficulty":0.0025092363}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Helen can now know that Anna can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anna","Helen"],"index":40633,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9668880105,"difficulty":0.0331119895}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Debra's card is shown to Debra. Dan's card is shown to Debra. Mary's card is shown to Dan. Debra's card is shown to Dan. It is publicly announced that someone picked a red card. It is publicly announced that Debra picked a black card. It is publicly announced that Mary knows whether Mary picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Mary can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Debra","Dan"],"index":21663,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993979931,"difficulty":0.0006020069}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juliette does not know whether Anne is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Johnny can now know that Juliette can know that Juliette is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anne","Juliette","Johnny"],"index":40670,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9923694134,"difficulty":0.0076305866}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lauren knows whether or not everyone's forehead is muddy. It is publicly announced that Bret's forehead is muddy. It is publicly announced that Alexandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Bret can now know that Lauren's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bret","Lauren","Alexandra"],"index":43769,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.989948988,"difficulty":0.010051012}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eldon's card is shown to Thelma. Matthew's card is shown to Matthew. Eldon's card is shown to Matthew. Matthew's card is shown to Eldon. Eldon's card is shown to Eldon. It is publicly announced that someone picked a red card. It is publicly announced that Eldon picked a red card. It is publicly announced that Eldon does not know whether Thelma picked a red card. It is publicly announced that Eldon knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Matthew can now know whether Eldon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thelma","Matthew","Eldon"],"index":15282,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8817844987,"difficulty":0.1182155013}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melvin does not know whether Lisa is thirsty. It is publicly announced that Edward does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Edward can now know whether Sarita can know that Lisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sarita","Melvin","Edward","Lisa"],"index":19535,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9668287039,"difficulty":0.0331712961}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Lasonya's card is shown to Billy. Billy's card is shown to Lasonya. Howard's card is shown to Lasonya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Howard can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Billy","Howard","Lasonya"],"index":33821,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952072501,"difficulty":0.0047927499}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Cheryl. Mike's card is shown to Cheryl. Mike's card is shown to Mike. Stanley's card is shown to Mike. Anna's card is shown to Stanley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know that Cheryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Cheryl","Mike","Stanley"],"index":32030,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979026318,"difficulty":0.0020973682}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Caren is thirsty. It is publicly announced that Scott does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Scott can now know whether Scott is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Scott","Caren","Guillermo"],"index":20540,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979481101,"difficulty":0.0020518899}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen does not know whether or not everyone is thirsty. It is publicly announced that Karen does not know whether or not everyone is thirsty. It is publicly announced that Karen knows whether or not nobody is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Jason can now know that Karen can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Karen","Jason"],"index":9149,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990385771,"difficulty":0.0009614229}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cleo knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Li can now know that Cleo's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kelly","Carl","Cleo","Li"],"index":19716,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9381098151,"difficulty":0.0618901849}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Tina does not know whether Tina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Linda can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gail","Tina","Linda"],"index":44258,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992634654,"difficulty":0.0007365346}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose's forehead is not muddy. It is publicly announced that Jose knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jose can now know whether Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Micheal","Carol","Janette","Jose"],"index":23642,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.990950048,"difficulty":0.009049952}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Darlene. Scott's card is shown to Darlene. Darlene's card is shown to Scott. Tasha's card is shown to Tasha. It is publicly announced that someone picked a red card. It is publicly announced that Tasha picked a black card. It is publicly announced that Scott does not know whether Darlene picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Gary can now know whether Darlene can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Darlene","Scott","Tasha"],"index":30460,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994495511,"difficulty":0.0005504489}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest does not know whether Ernest's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Victor can now know that Ernest's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kandice","Ernest","Debra","Victor"],"index":29157,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.990085721,"difficulty":0.009914279}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kaylee knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Tiffany can now know that Kaylee is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kaylee","Sharon","Tiffany"],"index":63316,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9968485236,"difficulty":0.0031514764}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether Dan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Dan can now know that Jason can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dan","Scott","Jason","William"],"index":36208,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989832044,"difficulty":0.0010167956}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sandra can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kevin","Chris","Sandra"],"index":55445,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993028641,"difficulty":0.0006971359}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Buddy. Buddy's card is shown to Jaime. Jaime's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Johnny knows whether Johnny picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Johnny can now know whether Buddy can know whether Johnny picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnny","Buddy","Jaime","Donald"],"index":15841,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980573058,"difficulty":0.0019426942}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Bessie's forehead is muddy. It is publicly announced that Teresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Teresa can now know that Tracy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tracy","Teresa","Bessie","Jason"],"index":7825,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9866271615,"difficulty":0.0133728385}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Angel knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Angel can now know that Lorene can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Angel","Lorene"],"index":20869,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992169142,"difficulty":0.0007830858}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Teresa can now know that Judy can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Judy","Jessie","Teresa"],"index":24597,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995164871,"difficulty":0.0004835129}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty. It is publicly announced that Eloise is thirsty. It is publicly announced that Eloise is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! 3 ] Agentc knows that (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Eloise can now know that John can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Bobby","Eloise","John"],"index":27961,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994946718,"difficulty":0.0005053282}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Gladys can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gladys","James"],"index":50063,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985904098,"difficulty":0.0014095902}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doris knows whether or not everyone is thirsty. It is publicly announced that Jared is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Doris can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jared","Doris"],"index":373,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990388155,"difficulty":0.0009611845}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. Loretta's card is shown to Jessica. Leonel's card is shown to Jessica. Xavier's card is shown to Jessica. Xavier's card is shown to Leonel. Xavier's card is shown to Xavier. It is publicly announced that someone picked a red card. It is publicly announced that Xavier picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Leonel can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Loretta","Leonel","Xavier"],"index":23345,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990543723,"difficulty":0.0009456277}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Peter can now know that Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Julie","Marguerite","Peter"],"index":61720,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9922788143,"difficulty":0.0077211857}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not everyone's forehead is muddy. It is publicly announced that Deborah does not know whether Deborah's forehead is muddy. It is publicly announced that Karen does not know whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Deborah can now know whether Erin can know whether Karen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Erin","Deborah","Kenneth","Karen"],"index":22176,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980484247,"difficulty":0.0019515753}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Derrick can now know whether Derrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pamela","Tracy","Derrick"],"index":21520,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9590888023,"difficulty":0.0409111977}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karena knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Karena can now know whether William can know whether Larry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karena","William","Larry"],"index":45455,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993903637,"difficulty":0.0006096363}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyne knows whether Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Guadalupe can now know that Carolyne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carolyne","Pamela","Guadalupe"],"index":55156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980068803,"difficulty":0.0019931197}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherman's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Larry can now know that Larry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Sherman","Larry","Nora"],"index":2755,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9935046434,"difficulty":0.0064953566}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Kelly. Mark's card is shown to Anthony. Anthony's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card. It is publicly announced that Kelly does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Kelly can now know that Kelly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kelly","Anthony","Roy","Mark"],"index":58911,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9679570198,"difficulty":0.0320429802}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Maria is thirsty. It is publicly announced that Maria does not know whether William is thirsty. It is publicly announced that Julia does not know whether or not everyone is thirsty. It is publicly announced that Julia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Maria can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maria","Julia","William"],"index":14272,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9511452913,"difficulty":0.0488547087}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Doris can now know that Robert can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Tonisha","Doris"],"index":17366,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9632444382,"difficulty":0.0367555618}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether Luis is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Luis can now know that Fred can know that Fred is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Luis","Fred","Brenda"],"index":53212,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967777133,"difficulty":0.0032222867}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Rosa can now know that Dawn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Henry","Rosa","Dawn","Tamika"],"index":63157,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9788801074,"difficulty":0.0211198926}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jorge does not know whether William is thirsty. It is publicly announced that Virginia does not know whether Jorge is thirsty. It is publicly announced that Virginia does not know whether Jorge is thirsty. It is publicly announced that Rose knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows that (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jorge can now know that Virginia can know that Rose is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Rose","Virginia","Jorge"],"index":40416,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978273511,"difficulty":0.0021726489}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leigh does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Patricia can now know that John can know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Terry","Patricia","John","Leigh"],"index":2318,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9575183988,"difficulty":0.0424816012}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Byron's card is shown to Byron. Kevin's card is shown to Byron. Byron's card is shown to Kevin. Jesus's card is shown to Kevin. Byron's card is shown to Jesus. Kevin's card is shown to Jesus. Arthur's card is shown to Jesus. Byron's card is shown to Arthur. Kevin's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Byron does not know whether Arthur picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1,2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1,2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Jesus can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Byron","Kevin","Jesus","Arthur"],"index":59529,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994204044,"difficulty":0.0005795956}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Jason. Jason's card is shown to Mario. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Jason knows whether or not nobody picked a red card. It is publicly announced that Jason does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mario can now know that Jason can know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Mario","James"],"index":51390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9393590689,"difficulty":0.0606409311}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ismael's card is shown to Ismael. Ismael's card is shown to Andrew. Andrew's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Andrew picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Ismael can now know that Andrew can know whether Andrew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ismael","Andrew"],"index":37301,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.955082953,"difficulty":0.044917047}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Helen. Gerald's card is shown to Robert. Robert's card is shown to Robert. Robert's card is shown to Stephen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gerald can now know whether Gerald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Gerald","Robert","Stephen"],"index":29590,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.701459229,"difficulty":0.298540771}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Bobbie can now know that Raymond can know that Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raymond","Bobbie","Gary"],"index":9550,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977157116,"difficulty":0.0022842884}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Wesley can now know that Wesley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Ralph","Wesley"],"index":21491,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9931789637,"difficulty":0.0068210363}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelyn's card is shown to Bradley. Daniel's card is shown to Bradley. Bradley's card is shown to Angelyn. Nancy's card is shown to Angelyn. Daniel's card is shown to Angelyn. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Bradley can now know that Nancy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bradley","Angelyn","Nancy","Daniel"],"index":53124,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963105321,"difficulty":0.0036894679}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sammy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Sammy can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sammy","Mark","Jaime","Maria"],"index":33391,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9793599844,"difficulty":0.0206400156}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Michael. Wayne's card is shown to Matthew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Matthew can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Matthew","Wayne"],"index":4154,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966266155,"difficulty":0.0033733845}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shaneka knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Timothy can now know that Shaneka is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","George","Elsie","Shaneka"],"index":46393,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9260485768,"difficulty":0.0739514232}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty. It is publicly announced that David does not know whether Mary is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Dorothy knows whether Dorothy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dorothy can now know that David can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","Mary","David"],"index":61646,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941555262,"difficulty":0.0058444738}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darren is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Leslie can now know that Fleta can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leslie","Darren","Charles","Fleta"],"index":51723,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995069504,"difficulty":0.0004930496}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacob knows whether or not nobody is thirsty. It is publicly announced that Jacob does not know whether Dane is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Mary can now know whether Dane can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Patrick","Dane","Jacob"],"index":32590,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9623844624,"difficulty":0.0376155376}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie does not know whether Jamie's forehead is muddy. It is publicly announced that Helene knows whether Jamie's forehead is muddy. It is publicly announced that Lavina knows whether Lavina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jamie can now know whether Jamie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lavina","Jamie","Helene"],"index":60004,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8531602621,"difficulty":1.8531602621}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodore's card is shown to Theodore. Virginia's card is shown to Virginia. Theodore's card is shown to Flora. Virginia's card is shown to Flora. Alice's card is shown to Flora. Theodore's card is shown to Alice. Alice's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Flora does not know whether Flora picked a red card. It is publicly announced that Virginia does not know whether Flora picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Virginia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Theodore","Virginia","Flora","Alice"],"index":18360,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989728928,"difficulty":0.0010271072}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Catherine. George's card is shown to Catherine. Andreas's card is shown to Scott. George's card is shown to Scott. Catherine's card is shown to Andreas. George's card is shown to Andreas. Catherine's card is shown to George. Scott's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andreas can now know that Catherine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Scott","Andreas","George"],"index":9728,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988784194,"difficulty":0.0011215806}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that Donna can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donna","Mary","Ann"],"index":22899,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989020824,"difficulty":0.0010979176}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Chad can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Robert","Chad"],"index":9794,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986526966,"difficulty":0.0013473034}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerry's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Norma can now know whether Kerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Margaret","Kerry","Norma"],"index":66717,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994779229,"difficulty":0.0005220771}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ebony's card is shown to Ebony. Bryan's card is shown to Ebony. Ebony's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Bryan picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Bryan can now know whether Ebony can know whether Ebony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ebony","Bryan"],"index":53999,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9962902069,"difficulty":0.0037097931}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernestina's card is shown to Amber. Amber's card is shown to Emanuel. Loren's card is shown to Emanuel. Ernestina's card is shown to Emanuel. Amber's card is shown to Loren. Loren's card is shown to Loren. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Loren can now know whether Amber picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amber","Emanuel","Loren","Ernestina"],"index":52474,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8499743938,"difficulty":0.1500256062}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregg knows whether Virginia's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Virginia can now know that Virginia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Virginia","Gregg"],"index":52582,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9929559231,"difficulty":0.0070440769}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Juan does not know whether Kenneth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Kenneth can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Juan","Kenneth"],"index":26302,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955824018,"difficulty":0.0044175982}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Gonzalo. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Thomas knows whether someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Gonzalo can now know that Thomas can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gonzalo","Thomas"],"index":10844,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930231571,"difficulty":0.0069768429}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katheryn does not know whether Susana is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Katheryn can now know whether Michael can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eve","Susana","Michael","Katheryn"],"index":31517,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993971586,"difficulty":0.0006028414}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. Gregory's card is shown to Howard. Howard's card is shown to Howard. Jerome's card is shown to Howard. Gregory's card is shown to Jerome. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jerome can now know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregory","Howard","Jerome"],"index":18810,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954079986,"difficulty":0.0045920014}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cory knows whether Miguel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Cory can now know that Miguel can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Miguel","Fidel","Cory"],"index":40192,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992189407,"difficulty":0.0007810593}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Armando's card is shown to Armando. Mattie's card is shown to Armando. Charles's card is shown to Charles. Mattie's card is shown to Mattie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mattie can now know whether Armando can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Armando","Charles","Mattie"],"index":48769,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9444281459,"difficulty":1.9444281459}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Kevin can now know whether Judy can know whether Judy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Kevin","Judy"],"index":65055,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994533658,"difficulty":0.0005466342}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esmeralda knows whether Esmeralda's forehead is muddy. It is publicly announced that Jessica knows whether or not everyone's forehead is muddy. It is publicly announced that Eladia knows whether Esmeralda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jessica can now know that Eladia can know that Eladia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessica","Esmeralda","Eladia","Gary"],"index":18872,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9718027115,"difficulty":0.0281972885}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeff knows whether Carrie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Carrie can now know that Jeff's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jeff","Carrie"],"index":8165,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947502017,"difficulty":0.0052497983}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille does not know whether or not everyone's forehead is muddy. It is publicly announced that Everett knows whether Everett's forehead is muddy. It is publicly announced that Lucille knows whether Everett's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Everett can now know that Lucille can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lucille","Everett"],"index":14212,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5408039689,"difficulty":1.5408039689}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether Kyle is thirsty. It is publicly announced that Asa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] Agentb knows whether (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] 0","hypothesis":"Mark can now know whether Asa can know whether Tiffany is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kyle","Mark","Asa","Tiffany"],"index":63246,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991850257,"difficulty":0.0008149743}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis's forehead is muddy. It is publicly announced that Dennis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Isabel can now know whether Adam can know whether Isabel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dennis","Adam","Virginia","Isabel"],"index":51449,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994451404,"difficulty":0.0005548596}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harvey does not know whether Jason is thirsty. It is publicly announced that Clayton does not know whether Harvey is thirsty. It is publicly announced that Clayton does not know whether Jason is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Clayton can now know that Harvey can know whether Jason is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jason","Harvey","Clayton"],"index":60108,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9484823346,"difficulty":0.0515176654}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Franklin does not know whether Franklin's forehead is muddy. It is publicly announced that Adam knows whether Franklin's forehead is muddy. It is publicly announced that Adam does not know whether Adam's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Franklin can now know that Staci can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Staci","Briana","Adam","Franklin"],"index":65882,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994113445,"difficulty":0.0005886555}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Giselle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Giselle can now know whether William can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Aletha","William","Giselle"],"index":33911,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990916252,"difficulty":0.0009083748}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether someone's forehead is muddy. It is publicly announced that Vincent knows whether Vincent's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Rodolfo can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vincent","Rodolfo","Kathleen","John"],"index":17911,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992528558,"difficulty":0.0007471442}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy. It is publicly announced that Hugh knows whether Lillian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Hugh can now know whether Lillian can know that Hugh's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lillian","Hugh","Christopher","William"],"index":53877,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.96240592,"difficulty":1.96240592}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelby's card is shown to Shelby. Robert's card is shown to Shelby. Diane's card is shown to Diane. Robert's card is shown to Ann. Shelby's card is shown to Robert. Diane's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Shelby can know whether Ann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shelby","Diane","Ann","Robert"],"index":54227,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9936118722,"difficulty":0.0063881278}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Steve can now know whether Ralph can know that Steve is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amy","Ralph","Dorothy","Steve"],"index":52721,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9849164486,"difficulty":0.0150835514}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Christopher. Christopher's card is shown to Dennis. Alice's card is shown to Dennis. Dennis's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card. It is publicly announced that Christopher knows whether Alice picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Alice can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christopher","Dennis","Alice"],"index":23711,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994530082,"difficulty":0.0005469918}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carla knows whether Brenda's forehead is muddy. It is publicly announced that Andre's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] Agentc knows whether (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Andre can now know whether Carla can know whether Andre's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Ignacio","Andre","Carla"],"index":15637,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989430308,"difficulty":0.0010569692}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesus's card is shown to Harry. Harry's card is shown to Jesus. It is publicly announced that someone picked a red card. It is publicly announced that Jesus does not know whether or not everyone picked a red card. It is publicly announced that Jesus knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Jesus can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harry","Jesus"],"index":35961,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999456346,"difficulty":0.000543654}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tisha's card is shown to Deborah. Deborah's card is shown to Tisha. Judith's card is shown to Tisha. Alice's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether Deborah picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Deborah can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Tisha","Alice","Judith"],"index":62686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999422431,"difficulty":0.000577569}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcia knows whether Marcia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Marcia can now know whether Marcia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Ethel","Marcia","Georgia"],"index":54277,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994369149,"difficulty":0.0005630851}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know whether Andrew can know whether Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Andrew","Susan"],"index":64754,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8827683926,"difficulty":0.1172316074}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leisha's card is shown to Cynthia. Cynthia's card is shown to Maria. Leisha's card is shown to Maria. Francisca's card is shown to Maria. Cynthia's card is shown to Francisca. It is publicly announced that someone picked a red card. It is publicly announced that Leisha does not know whether Leisha picked a red card. It is publicly announced that Leisha does not know whether Maria picked a red card. It is publicly announced that Cynthia knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Leisha can now know that Maria can know that Cynthia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Maria","Leisha","Francisca"],"index":36862,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953586459,"difficulty":0.0046413541}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jess knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Katrina can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Manuel","Jess","Katrina"],"index":58973,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987855554,"difficulty":0.0012144446}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mae's card is shown to Ann. Ronald's card is shown to Warren. Mae's card is shown to Ronald. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mae can now know whether Mae picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ann","Mae","Warren","Ronald"],"index":24268,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8035194278,"difficulty":1.8035194278}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abraham knows whether Wanda's forehead is muddy. It is publicly announced that Jennifer knows whether Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Abraham can now know whether Jennifer can know that Wanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Abraham","Wanda","Jennifer"],"index":11782,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994719625,"difficulty":0.0005280375}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Letha knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"William can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Letha","Derek","William","Adam"],"index":33822,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989337325,"difficulty":0.0010662675}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Timothy can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","James","Timothy","Robert"],"index":66381,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9854758382,"difficulty":0.0145241618}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcus knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Estelle can now know that Estelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Estelle","Lisa","Marcus"],"index":61468,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983901978,"difficulty":0.0016098022}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillie's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] 0","hypothesis":"Robert can now know that Lillie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Lillie"],"index":45536,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994981289,"difficulty":0.0005018711}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Alexandra can now know that Alexandra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Richard","Alexandra","Margaret"],"index":25334,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9910556078,"difficulty":0.0089443922}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Mary can now know whether Kimberly can know whether Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Kimberly","Mary","Ashley"],"index":18196,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9871361256,"difficulty":0.0128638744}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy. It is publicly announced that Ashley does not know whether Ashley's forehead is muddy. It is publicly announced that Ashley knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"George can now know whether James can know whether Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","George","Ashley"],"index":8283,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990253448,"difficulty":0.0009746552}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernardo's forehead is muddy. It is publicly announced that Bernardo knows whether someone's forehead is muddy. It is publicly announced that Margaret's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Bernardo can now know whether Margaret can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Margaret","Bernardo"],"index":8218,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994268417,"difficulty":0.0005731583}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darren's card is shown to Darren. Thelma's card is shown to Darren. Ashley's card is shown to Ashley. Thelma's card is shown to Ashley. Ashley's card is shown to Charles. Charles's card is shown to Charles. Darren's card is shown to Thelma. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Thelma picked a red card. It is publicly announced that Darren does not know whether Ashley picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Thelma can now know whether Ashley can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darren","Ashley","Charles","Thelma"],"index":47462,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8424884677,"difficulty":0.1575115323}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Martha can know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jimmy","John","Michael","Martha"],"index":61852,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9950232506,"difficulty":0.0049767494}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerrie does not know whether Ruth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jerrie can now know that Ruth can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruth","Jerrie","Penny","Karl"],"index":63420,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989829659,"difficulty":0.0010170341}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Melody. Manuel's card is shown to Melody. Manuel's card is shown to Manuel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruby can now know whether Summer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melody","Ruby","Manuel","Summer"],"index":36826,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977688789,"difficulty":0.0022311211}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felipa's card is shown to Felipa. Barbara's card is shown to Felipa. Janet's card is shown to Felipa. Felipa's card is shown to Barbara. Barbara's card is shown to Barbara. Janet's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Felipa knows whether Felipa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Barbara can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Felipa","Barbara","Janet"],"index":27383,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9181787968,"difficulty":0.0818212032}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Nancy can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nancy","Nicholas"],"index":17162,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994062185,"difficulty":0.0005937815}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick does not know whether Frederick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Frederick can now know whether Elizabeth can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Matt","Dale","Frederick"],"index":3440,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994091988,"difficulty":0.0005908012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jack knows whether Jack is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jack can now know that Elizabeth can know that Jack is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","Thomas","Jack"],"index":49835,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9841002226,"difficulty":0.0158997774}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Nathan can now know that Mary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nathan","Mary"],"index":930,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980760813,"difficulty":0.0019239187}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know that Robert can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","David","Dale","Anissa"],"index":38826,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993952513,"difficulty":0.0006047487}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Rod can now know that Tony can know whether Tony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Rod","Tony","Martha"],"index":56215,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993087053,"difficulty":0.0006912947}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marguerite does not know whether Marguerite's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Marguerite can now know whether Larry can know that Marguerite's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Larry","Marguerite"],"index":52737,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9820128083,"difficulty":0.0179871917}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dan knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"David can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Dan","Thomas","Carl"],"index":8857,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986612797,"difficulty":0.0013387203}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin's forehead is muddy. It is publicly announced that Jonathan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Charles can now know that Justin can know that Jonathan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Jonathan","Gabriel","Justin"],"index":62294,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9939981699,"difficulty":0.0060018301}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nakia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Nina can now know that Nakia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sharon","Nakia","Angel","Nina"],"index":12461,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981100559,"difficulty":0.0018899441}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilma can now know that Susan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wilma","Donald","Susan","Carrie"],"index":63108,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988252521,"difficulty":0.0011747479}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"James can now know whether Fred can know whether Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Fred"],"index":46785,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994016886,"difficulty":0.0005983114}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denise's card is shown to Myron. Myron's card is shown to Myron. Denise's card is shown to Joseph. Myron's card is shown to Joseph. Denise's card is shown to Cassandra. Myron's card is shown to Cassandra. It is publicly announced that someone picked a red card. It is publicly announced that Myron does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Denise can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Denise","Myron","Joseph","Cassandra"],"index":14655,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993363023,"difficulty":0.0006636977}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dustin can now know that Rebecca can know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Muriel","Rebecca","Mark","Dustin"],"index":29294,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959647655,"difficulty":0.0040352345}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Carla can now know that Angela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Rachel","Carla"],"index":26226,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978222847,"difficulty":0.0021777153}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nicolette can now know that Shari can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shari","Jeffery","Nicolette"],"index":18842,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992215633,"difficulty":0.0007784367}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellie does not know whether Ellie's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"John can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Ellie","Joann","Robert"],"index":64615,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9907706976,"difficulty":0.0092293024}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Harriette can now know that Michael can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harriette","Michael","Shirley"],"index":5629,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989357591,"difficulty":0.0010642409}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Adam's card is shown to Charlotte. Kathleen's card is shown to Adam. Charlotte's card is shown to Adam. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlotte can now know that Kathleen can know whether Kathleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Barbara","Charlotte","Adam"],"index":57238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9822339416,"difficulty":0.0177660584}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Adam can now know that Elsie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Adam","Aaron","Gregory","Elsie"],"index":3525,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987624884,"difficulty":0.0012375116}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Melanie. Sharon's card is shown to Joe. Shirley's card is shown to Sharon. Joe's card is shown to Sharon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melanie can now know whether Joe can know whether Melanie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Melanie","Joe","Sharon"],"index":47592,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9976142645,"difficulty":0.0023857355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Colin can now know whether Jeffrey is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Colin","Jeffrey","Chris"],"index":59213,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9937756062,"difficulty":0.0062243938}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joy does not know whether or not everyone is thirsty. It is publicly announced that Joy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joy can now know that Marsha can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joy","Jonathan","Paul","Marsha"],"index":51674,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994360805,"difficulty":0.0005639195}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer knows whether someone is thirsty. It is publicly announced that Marcus does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Michael can now know that Marcus can know that Marcus is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Jennifer","Marcus"],"index":64674,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9853402972,"difficulty":0.0146597028}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eunice knows whether Chester's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Eunice can now know whether Chester can know whether Chester's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Eunice","Angela","Chester"],"index":30099,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.588880837,"difficulty":1.588880837}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Virginia can now know that Carl can know that Virginia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Virginia","Paul","Carl"],"index":59882,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9962136149,"difficulty":0.0037863851}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candace's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Leslie can now know whether Candace can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leslie","Florence","Candace"],"index":56248,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9573446512,"difficulty":0.0426553488}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Kendra. John's card is shown to Kendra. Christine's card is shown to Christine. Kendra's card is shown to John. Christine's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kendra can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kendra","Christine","John"],"index":26646,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963394403,"difficulty":0.0036605597}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Michael can now know that Harry can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Mildred","Michael","Harry"],"index":52886,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9903139472,"difficulty":0.0096860528}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rachael does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Rachael knows whether someone is thirsty. It is publicly announced that Rachael knows whether Rachael is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Angela can now know whether Rachael can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rachael","Angela"],"index":39852,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999442637,"difficulty":0.000557363}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judi does not know whether or not everyone's forehead is muddy. It is publicly announced that Judi does not know whether or not everyone's forehead is muddy. It is publicly announced that Stan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Stan can now know that Judi can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stan","Judi"],"index":61539,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.999083519,"difficulty":0.000916481}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mai's card is shown to Theresa. Theresa's card is shown to Mai. Mai's card is shown to Mai. It is publicly announced that someone picked a red card. It is publicly announced that Mai knows whether Mai picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Theresa can now know that Mai picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Theresa","Mai"],"index":64693,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9348800778,"difficulty":0.0651199222}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Julia can now know that Carlos can know that Julia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julia","Carlos","Judith","Angela"],"index":53493,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9923914075,"difficulty":0.0076085925}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Robert's card is shown to Michael. Michael's card is shown to Michael. Robert's card is shown to Justin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Justin can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Michael","Justin"],"index":4043,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993853569,"difficulty":0.0006146431}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Omar knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joanna can now know that Omar can know whether Omar's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Omar","Joanna","Irina"],"index":44948,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994382262,"difficulty":0.0005617738}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Robert can now know that Patricia can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Robert","Nolan"],"index":7664,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975734353,"difficulty":0.0024265647}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vicenta does not know whether or not everyone's forehead is muddy. It is publicly announced that Manuela knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kevin can now know that Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kevin","Vicenta","Manuela","Margaret"],"index":42035,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8138466477,"difficulty":1.8138466477}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy. It is publicly announced that Barbara's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agentd knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Susan can now know that Howard can know whether Howard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Howard","Mary","Susan"],"index":50968,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7271411419,"difficulty":0.2728588581}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether Derrick is thirsty. It is publicly announced that Lee is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Melissa can now know that Lee can know whether Melissa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lee","Melissa","Arthur","Derrick"],"index":7556,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7296750546,"difficulty":1.7296750546}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jon's forehead is muddy. It is publicly announced that Isaac's forehead is not muddy. It is publicly announced that Jon knows whether Isaac's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Hugh can now know that Isaac's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Isaac","Jon","Hugh"],"index":25100,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9739198089,"difficulty":0.0260801911}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holly's card is shown to Holly. Holly's card is shown to Gregory. Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that Gregory knows whether Gregory picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Holly can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Holly","Gregory"],"index":30785,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994551539,"difficulty":0.0005448461}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bessie knows whether or not nobody is thirsty. It is publicly announced that David does not know whether Bessie is thirsty. It is publicly announced that Bessie is thirsty. It is publicly announced that Elisabeth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Adrienne can now know whether David can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Adrienne","Elisabeth","Bessie"],"index":22319,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990028739,"difficulty":0.0009971261}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Hazel. Sally's card is shown to Opal. Sally's card is shown to Sally. Opal's card is shown to Virginia. It is publicly announced that someone picked a red card. It is publicly announced that Sally does not know whether or not everyone picked a red card. It is publicly announced that Hazel picked a black card. It is publicly announced that Sally does not know whether Opal picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sally can now know whether Opal can know that Hazel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hazel","Opal","Sally","Virginia"],"index":32964,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9216912389,"difficulty":0.0783087611}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Jose. Bernice's card is shown to Michael. Jose's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bernice can now know that Jose can know that Bernice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bernice","Jose","Michael"],"index":9997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997538805,"difficulty":0.002461195}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Shawn's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Shawn can now know that Nancy can know that Shawn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Shawn","Nancy"],"index":60485,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9458244443,"difficulty":0.0541755557}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jason can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Audrey","Jason","William","Alicia"],"index":23491,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989733696,"difficulty":0.0010266304}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie knows whether someone is thirsty. It is publicly announced that James does not know whether Rose is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"James can now know that Willie can know whether Rose is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rose","Willie","James"],"index":46534,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9959938526,"difficulty":0.0040061474}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Mary can now know that Judy can know whether Laura's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Edward","Laura","Judy"],"index":64810,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993726611,"difficulty":0.0006273389}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry knows whether Sherry's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Danny can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sherry","William","Danny","Dulce"],"index":13091,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9910934567,"difficulty":0.0089065433}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Marjorie. Marjorie's card is shown to David. David's card is shown to David. Sandy's card is shown to David. Mildred's card is shown to David. David's card is shown to Sandy. Marjorie's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Sandy does not know whether Marjorie picked a red card. It is publicly announced that Marjorie knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Mildred can now know whether Sandy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marjorie","David","Sandy","Mildred"],"index":33286,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994130135,"difficulty":0.0005869865}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abraham knows whether Emily's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Kayla can now know whether Emily can know that Kayla's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorthea","Kayla","Emily","Abraham"],"index":30094,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9885918498,"difficulty":0.0114081502}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheryl knows whether Thomas's forehead is muddy. It is publicly announced that Sheryl's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Sheryl can now know that Juan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Juan","Thomas","Sheryl"],"index":4469,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997071743,"difficulty":0.002928257}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Otis can now know whether Margie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Evelyn","Winifred","Otis","Margie"],"index":45395,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9449050426,"difficulty":0.0550949574}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa does not know whether Emily is thirsty. It is publicly announced that Emily does not know whether Brian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jo can now know whether Brian can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jo","Teresa","Brian","Emily"],"index":15510,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994279742,"difficulty":0.0005720258}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcus does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Lois can now know that Marcus can know that Christina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lois","Marcus","Christina","Ardis"],"index":35313,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9149824977,"difficulty":0.0850175023}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joy does not know whether or not everyone is thirsty. It is publicly announced that Joy does not know whether Jeanette is thirsty. It is publicly announced that Jeanette knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jenifer can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeanette","Joy","Jenifer"],"index":8638,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. Brian's card is shown to Daniel. Aaron's card is shown to Angie. It is publicly announced that someone picked a red card. It is publicly announced that Aaron picked a black card. It is publicly announced that Angie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 4 ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 4 ] 0","hypothesis":"Daniel can now know that Angie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Aaron","Brian","Angie"],"index":42046,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7831219435,"difficulty":1.7831219435}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eula's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Eula can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tammy","Eula"],"index":63922,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993844032,"difficulty":0.0006155968}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Joseph. John's card is shown to John. John's card is shown to Carol. Carol's card is shown to Carol. Carol's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","John","Carol","Charles"],"index":67668,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980177879,"difficulty":0.0019822121}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Bernard can now know that Bernard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Bernard","Janice"],"index":5674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9900348783,"difficulty":0.0099651217}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delilah knows whether or not everyone's forehead is muddy. It is publicly announced that Delilah knows whether someone's forehead is muddy. It is publicly announced that Delilah knows whether Delilah's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Delilah can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Delilah","Audrey"],"index":64708,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999338448,"difficulty":0.000661552}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juana knows whether someone is thirsty. It is publicly announced that Essie knows whether Juana is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Juana can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Juana","Essie"],"index":35046,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9731043577,"difficulty":1.9731043577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester does not know whether Lester's forehead is muddy. It is publicly announced that Norma knows whether Lester's forehead is muddy. It is publicly announced that Norma does not know whether Norma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Norma can now know that Lester can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gail","Heather","Norma","Lester"],"index":13528,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989456534,"difficulty":0.0010543466}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis does not know whether Louis's forehead is muddy. It is publicly announced that Nancy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Nancy can now know that Louis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Erik","Louis"],"index":14942,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7138931155,"difficulty":0.2861068845}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Tania can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Rosalba","Tania","Ashley"],"index":316,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9111839533,"difficulty":1.9111839533}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jackson can now know that Linda can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Linda","Michelle","Jackson"],"index":9373,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989225268,"difficulty":0.0010774732}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that Sherry knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Benjamin can now know that Charles can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Mary","Benjamin","Sherry"],"index":13004,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990620017,"difficulty":0.0009379983}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Donald can now know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aaron","Donald","Patricia","Ted"],"index":40218,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9913535714,"difficulty":0.0086464286}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Brenda can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Brenda","Kevin","Julie"],"index":55477,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989669323,"difficulty":0.0010330677}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norbert knows whether Ronald's forehead is muddy. It is publicly announced that Iva's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Iva can now know that Iva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Iva","Norbert","Ronald"],"index":65692,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.994387567,"difficulty":0.005612433}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty. It is publicly announced that Mary does not know whether Marilyn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mary can now know that Barbara can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Marilyn","Vivian","Barbara"],"index":26992,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942031503,"difficulty":0.0057968497}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dolly does not know whether Domonique is thirsty. It is publicly announced that Dolly does not know whether Domonique is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dolly can now know whether Domonique can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dolly","Domonique"],"index":45890,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9845095277,"difficulty":1.9845095277}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Fannie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alexander can now know that Carol can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fannie","John","Alexander","Carol"],"index":67573,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992415905,"difficulty":0.0007584095}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Mary is thirsty. It is publicly announced that Mark knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"John can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Mark","Greg","John"],"index":41608,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994221926,"difficulty":0.0005778074}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clinton knows whether Lillie's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lillie can now know that Clinton can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Lillie","Clinton"],"index":30534,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9933545589,"difficulty":0.0066454411}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roxanne's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Gary can now know whether Roxanne can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Roxanne","Gary"],"index":24765,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999409318,"difficulty":0.000590682}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Patty can now know that Gary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alfred","Patty","Gary","Jon"],"index":67321,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7203609943,"difficulty":0.2796390057}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that Brent can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Brent","Barney"],"index":7876,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993864298,"difficulty":0.0006135702}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michelle knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Walter can now know that Michelle can know whether Walter is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juan","Walter","Michelle"],"index":22014,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5398873687,"difficulty":1.5398873687}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Dennis can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rueben","Albert","Dennis"],"index":36853,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990103245,"difficulty":0.0009896755}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Flora's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Flora can now know that Lori can know whether Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lori","Flora"],"index":19845,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9810055494,"difficulty":0.0189944506}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Krista's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Krista can now know that Bruce can know that Harold's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Harold","Krista","Bruce"],"index":1659,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9864729643,"difficulty":0.0135270357}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyle knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Shelly can now know that Samuel can know that Shelly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Samuel","Shelly","Kyle"],"index":8559,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979083538,"difficulty":0.0020916462}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Orlando's card is shown to Orlando. Alexander's card is shown to Orlando. Orlando's card is shown to Alexander. It is publicly announced that someone picked a red card. It is publicly announced that Alexander does not know whether Alexander picked a red card. It is publicly announced that Orlando knows whether Alexander picked a red card. It is publicly announced that Orlando knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Orlando can now know that Alexander can know whether Alexander picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Orlando","Alexander"],"index":48663,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9517096877,"difficulty":1.9517096877}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Allen can now know that Jaime can know that Karl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karl","Jaime","Allen","Kelly"],"index":47953,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9858019948,"difficulty":0.0141980052}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Nancy. Nancy's card is shown to Kristopher. Ma's card is shown to Kristopher. Kristopher's card is shown to Kristopher. Nancy's card is shown to Andrew. Andrew's card is shown to Andrew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ma can now know that Kristopher can know whether Kristopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Ma","Kristopher","Andrew"],"index":61565,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6078113914,"difficulty":0.3921886086}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether Larry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Larry can now know that Luz can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Wendy","Luz","Steven"],"index":44306,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993698001,"difficulty":0.0006301999}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Genoveva knows whether Irma's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Genoveva can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Irma","Genoveva"],"index":45198,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992040992,"difficulty":0.0007959008}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"James can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Rachel","James"],"index":34451,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989134073,"difficulty":0.0010865927}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valerie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Valerie can now know that Leila can know whether Benedict's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Valerie","Kelly","Leila","Benedict"],"index":21017,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993655086,"difficulty":0.0006344914}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Nancy can now know that Todd is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Elizabeth","Todd"],"index":60740,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9796034694,"difficulty":0.0203965306}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lashawn can now know that Marian can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeanne","Alice","Lashawn","Marian"],"index":65537,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993274212,"difficulty":0.0006725788}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jane's card is shown to Jane. Ralph's card is shown to Robert. Robert's card is shown to Ralph. Ralph's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Ralph knows whether or not nobody picked a red card. It is publicly announced that Ralph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! 3 ] 0","hypothesis":"Jane can now know that Ralph can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jane","Robert","Ralph"],"index":13289,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994459748,"difficulty":0.0005540252}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Rosalind can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rosalind","Florence","Charles"],"index":45489,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993978739,"difficulty":0.0006021261}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know whether Anthony can know that Lloyd's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laverna","Michelle","Anthony","Lloyd"],"index":67000,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994157553,"difficulty":0.0005842447}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Beverly. Louis's card is shown to Louis. Etta's card is shown to Louis. Beverly's card is shown to Christopher. Beverly's card is shown to Etta. Etta's card is shown to Etta. It is publicly announced that someone picked a red card. It is publicly announced that Louis does not know whether Beverly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,4 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Beverly can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beverly","Louis","Christopher","Etta"],"index":660,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990481734,"difficulty":0.0009518266}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Amanda can now know whether Susan can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amanda","Stacey","John","Susan"],"index":23211,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9408034086,"difficulty":1.9408034086}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geoffrey knows whether or not nobody's forehead is muddy. It is publicly announced that Carolyn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] 0","hypothesis":"Lori can now know that Lori's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lori","Errol","Geoffrey","Carolyn"],"index":57629,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978340268,"difficulty":0.0021659732}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shawn knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Candy can now know whether Shawn can know whether Candy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shawn","Joshua","Candy"],"index":26026,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990757704,"difficulty":0.0009242296}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jo can now know that Deborah can know that Deborah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cindy","Jo","Deborah"],"index":50308,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985449314,"difficulty":0.0014550686}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Robert does not know whether Connie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Judy can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Connie","Judy","Robert"],"index":30377,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994938374,"difficulty":0.0005061626}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Leona's card is shown to Leona. Jennifer's card is shown to Mary. Leona's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leona can now know whether Mary can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Leona","Mary"],"index":14052,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993353486,"difficulty":0.0006646514}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Jose knows whether Jose is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Eric can now know whether Jose can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eric","Jose"],"index":11589,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994434714,"difficulty":0.0005565286}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cecilia can now know that Michael can know that Cecilia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Theodore","Shelby","Cecilia"],"index":14038,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985153079,"difficulty":0.0014846921}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy. It is publicly announced that Donna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Donna can now know that Lauren can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donna","Lauren"],"index":18684,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987164736,"difficulty":0.0012835264}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Gwendolyn can now know that Rita can know whether Gwendolyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rita","Gwendolyn","Ruth"],"index":64112,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993358254,"difficulty":0.0006641746}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Timothy knows whether someone is thirsty. It is publicly announced that Kurtis does not know whether Timothy is thirsty. It is publicly announced that Kurtis knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Kurtis can now know that Ruben is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ruben","Kurtis","Timothy"],"index":24875,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982958436,"difficulty":0.0017041564}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lyle knows whether Lyle is thirsty. It is publicly announced that Cecil knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Cecil can now know that Lyle is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cecil","Lyle"],"index":29221,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9701429605,"difficulty":1.9701429605}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe's forehead is muddy. It is publicly announced that Joe knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Evelyn can now know that Joe can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joe","Sophie","Evelyn","George"],"index":23926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989688396,"difficulty":0.0010311604}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dawn knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Dawn can now know that Sally can know that Keisha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dawn","Sally","Keisha"],"index":18863,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973881841,"difficulty":0.0026118159}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Edna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Mary can now know that Edna can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Edna"],"index":8114,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999435842,"difficulty":0.000564158}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Elizabeth. Robert's card is shown to Elizabeth. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card. It is publicly announced that Jessica knows whether Jessica picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Elizabeth can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Jessica","Robert"],"index":24893,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9868946075,"difficulty":0.0131053925}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether Alfred's forehead is muddy. It is publicly announced that Maria does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Alfred can now know whether Maria can know whether Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maria","Alfred"],"index":6271,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8979691863,"difficulty":0.1020308137}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vera knows whether or not everyone's forehead is muddy. It is publicly announced that Vera does not know whether Vera's forehead is muddy. It is publicly announced that Stacie knows whether Stacie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Stacie can now know that Vera can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Vera","Mary","Stacie"],"index":30185,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9777588844,"difficulty":0.0222411156}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tom knows whether someone's forehead is muddy. It is publicly announced that Vicki knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Christian can now know whether Tom can know that Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tom","Vicki","Timothy","Christian"],"index":22426,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9536316991,"difficulty":0.0463683009}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Paul can now know whether Nancy can know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Paul","John","Charles"],"index":48461,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994138479,"difficulty":0.0005861521}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Garrett does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Garrett can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Garrett","Ruth","Robert"],"index":33301,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8177073598,"difficulty":0.1822926402}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joey's card is shown to Joey. Loren's card is shown to Joey. Joey's card is shown to Loren. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joey picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Joey can now know that Loren can know that Joey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joey","Loren"],"index":24557,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7714239955,"difficulty":0.2285760045}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Kathy. Albert's card is shown to William. Kathy's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathy","William","Michael","Albert"],"index":29794,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993084669,"difficulty":0.0006915331}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ruth can now know whether Rosalie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bette","Ruth","Rosalie","Deborah"],"index":37652,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993034601,"difficulty":0.0006965399}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Una does not know whether Julie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Una can now know that Jenny can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Una","Jenny","Mary"],"index":27564,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979293346,"difficulty":0.0020706654}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether or not everyone is thirsty. It is publicly announced that Terri does not know whether Valda is thirsty. It is publicly announced that Terri does not know whether Valda is thirsty. It is publicly announced that Terri does not know whether Darcie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Darcie can now know whether Terri can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darcie","Terri","Thomas","Valda"],"index":19029,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9959540367,"difficulty":0.0040459633}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina's forehead is not muddy. It is publicly announced that Carmen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Tina can now know whether Shonta can know whether Tina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carmen","Betty","Tina","Shonta"],"index":48744,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Beatrice. Beatrice's card is shown to Theresa. Theresa's card is shown to Rich. Rich's card is shown to Rich. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Beatrice","Theresa","Rich"],"index":44266,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948923588,"difficulty":0.0051076412}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Evelyn can now know that Rickie can know whether Rickie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rickie","Evelyn"],"index":45713,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5164720416,"difficulty":1.5164720416}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristina does not know whether or not everyone's forehead is muddy. It is publicly announced that Kristina knows whether Richard's forehead is muddy. It is publicly announced that Kristina does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Luis","Kristina","Mary"],"index":8230,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6653118134,"difficulty":1.6653118134}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nick knows whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Gary can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frances","Gary","Pam","Nick"],"index":52984,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986421466,"difficulty":0.0013578534}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Sarah","Tammy","Joshua"],"index":842,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983702302,"difficulty":0.0016297698}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel's forehead is muddy. It is publicly announced that Andrew knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Ursula can now know whether Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andrew","Ursula","Daniel","Irma"],"index":57368,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991633892,"difficulty":0.0008366108}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amalia's card is shown to Amalia. Enrique's card is shown to Amalia. Carmen's card is shown to Amalia. Carmen's card is shown to Enrique. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amalia can now know whether Carmen can know whether Amalia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amalia","Enrique","Carmen"],"index":5505,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9965054989,"difficulty":0.0034945011}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Benjamin's card is shown to Benjamin. Phyllis's card is shown to Phyllis. It is publicly announced that someone picked a red card. It is publicly announced that Phyllis does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Benjamin can now know that Phyllis can know that Phyllis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Benjamin","Phyllis"],"index":14672,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5222741961,"difficulty":1.5222741961}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Mildred is thirsty. It is publicly announced that Thomas knows whether or not nobody is thirsty. It is publicly announced that Thomas does not know whether Jacqueline is thirsty. It is publicly announced that Thomas does not know whether Jacqueline is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Thomas can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jacqueline","Mildred","Thomas","Janice"],"index":10863,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961948395,"difficulty":0.0038051605}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julia is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Wallace can now know whether Carmen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carmen","Julia","Wallace"],"index":61903,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972157478,"difficulty":0.0027842522}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Warren's card is shown to Jeremy. Warren's card is shown to Warren. It is publicly announced that someone picked a red card. It is publicly announced that Warren knows whether Jeremy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Warren can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeremy","Warren"],"index":2931,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994328618,"difficulty":0.0005671382}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven knows whether Steven is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Joshua can now know whether Steven can know that Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Gary","Steven"],"index":48619,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9953315854,"difficulty":1.9953315854}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Patricia. Patricia's card is shown to Mary. Dale's card is shown to Mary. Patricia's card is shown to Dale. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Dale picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Patricia can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Mary","Dale"],"index":31127,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919141531,"difficulty":0.0080858469}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Al does not know whether or not everyone is thirsty. It is publicly announced that Al does not know whether Peter is thirsty. It is publicly announced that Peter does not know whether Julie is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Al can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julie","Al","Peter"],"index":24205,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9970518351,"difficulty":0.0029481649}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debbie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Doris can now know that Patricia can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Debbie","Patricia"],"index":10117,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993187189,"difficulty":0.0006812811}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Shane's forehead is muddy. It is publicly announced that Steven's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shane knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Shane can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francisco","Shane","Steven"],"index":59218,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998990953,"difficulty":0.001009047}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Norman. Norman's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Kenneth's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know whether Norman picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norman","Lena","Kenneth","Matthew"],"index":67535,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9233053923,"difficulty":0.0766946077}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Heather can now know that Evelyn can know whether Evelyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Evelyn","Shannon","Heather"],"index":3650,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979541302,"difficulty":0.0020458698}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether or not everyone's forehead is muddy. It is publicly announced that Mark does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mark can now know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Donald","Mark"],"index":65469,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9655148387,"difficulty":0.0344851613}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie does not know whether Marjorie's forehead is muddy. It is publicly announced that Kathi knows whether or not nobody's forehead is muddy. It is publicly announced that Kathi knows whether Kathi's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Kathi can now know that Marjorie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marjorie","Kathi"],"index":41774,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964851141,"difficulty":0.0035148859}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kyle knows whether or not everyone is thirsty. It is publicly announced that Kyle knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Kyle can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mildred","Kyle"],"index":13145,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9750863314,"difficulty":0.0249136686}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell knows whether Robert's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy. It is publicly announced that Russell knows whether Russell's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Russell","Robert"],"index":50438,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989500642,"difficulty":0.0010499358}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Patricia can now know whether David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","David","Patricia","Catherine"],"index":55900,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9812597632,"difficulty":0.0187402368}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Karen. Karen's card is shown to Arthur. Arthur's card is shown to Arthur. Karen's card is shown to Daniel. Arthur's card is shown to Daniel. Karen's card is shown to Robin. Robin's card is shown to Robin. It is publicly announced that someone picked a red card. It is publicly announced that Arthur picked a black card. It is publicly announced that Arthur does not know whether Robin picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Karen can now know whether Robin can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Arthur","Daniel","Robin"],"index":26351,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992903471,"difficulty":0.0007096529}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Chad's card is shown to John. Jennifer's card is shown to Chad. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether Chad picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Chad can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","John","Chad"],"index":39835,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9756161571,"difficulty":0.0243838429}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Robyn can now know that Dale can know that Howard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frieda","Robyn","Howard","Dale"],"index":27994,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965311885,"difficulty":0.0034688115}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joline knows whether Joline's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ronnie can now know that Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joline","Ronnie","Christopher","Rebecca"],"index":13840,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953725934,"difficulty":0.0046274066}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jarod's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Amy can now know whether Maria can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jarod","Amy","Maria"],"index":33503,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994893074,"difficulty":0.0005106926}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandy's card is shown to Christina. Brandy's card is shown to Brandy. James's card is shown to Brandy. Christina's card is shown to Lisa. Lisa's card is shown to Lisa. Christina's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christina","Brandy","Lisa","James"],"index":34574,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989976287,"difficulty":0.0010023713}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott does not know whether Joshua is thirsty. It is publicly announced that Scott does not know whether Joshua is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Joshua can now know that Joshua is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joshua","Scott"],"index":16700,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9425221086,"difficulty":0.0574778914}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kara does not know whether Kara's forehead is muddy. It is publicly announced that Kara does not know whether Kara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kara","Mary","Noelia","Jeanette"],"index":62961,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9814172387,"difficulty":0.0185827613}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Ivy can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Constance","Dolores","Lillian","Ivy"],"index":38054,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8662167788,"difficulty":1.8662167788}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Arthur. Arthur's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether Deborah picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Deborah can now know whether Arthur can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arthur","Deborah"],"index":66587,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9826418161,"difficulty":0.0173581839}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Alejandro. Alejandro's card is shown to Linda. William's card is shown to Irene. It is publicly announced that someone picked a red card. It is publicly announced that Linda picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"William can now know that Irene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Alejandro","Linda","Irene"],"index":64192,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9903820157,"difficulty":0.0096179843}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Robin can now know whether David can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Billy","Timothy","David"],"index":57144,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993376136,"difficulty":0.0006623864}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"John can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arnold","John","Kevin","Thomas"],"index":2957,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994844198,"difficulty":0.0005155802}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antonio knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that Richard can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Antonio","Michael","Richard"],"index":12920,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999355495,"difficulty":0.000644505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether or not nobody's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that Nancy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] Agentd knows whether (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"Nancy can now know whether James can know that Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Scott","Matthew","Nancy"],"index":24475,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9036155343,"difficulty":0.0963844657}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy. It is publicly announced that Molly knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Larry can now know whether Molly can know whether Larry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Molly","Larry"],"index":31967,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6689173579,"difficulty":0.3310826421}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Patrick can now know whether Kelly can know whether Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rick","Patrick","Virginia","Kelly"],"index":62319,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9946770668,"difficulty":0.0053229332}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jeremy can now know that Gina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeremy","Julie","Gina","Miguel"],"index":52271,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978291392,"difficulty":0.0021708608}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Christopher. Christopher's card is shown to Katherine. Donald's card is shown to Katherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barry can now know whether Barry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barry","Christopher","Donald","Katherine"],"index":48702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99084723,"difficulty":0.00915277}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Eric. Eric's card is shown to Alfredo. Alfredo's card is shown to Carol. Carol's card is shown to Carol. Carol's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eric can now know that Carol can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Alfredo","Carol","Mary"],"index":15593,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998056829,"difficulty":0.001943171}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marie can now know that Lisa can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Matthew","Marie","Lisa","Ron"],"index":48365,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988645315,"difficulty":0.0011354685}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Jose can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Valerie","Jose","Sandra"],"index":11064,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989000559,"difficulty":0.0010999441}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] 0","hypothesis":"Hannah can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Willie","John","Hannah"],"index":13308,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992795587,"difficulty":0.0007204413}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eddie does not know whether Mayme is thirsty. It is publicly announced that Ryan does not know whether or not everyone is thirsty. It is publicly announced that Hipolito does not know whether Mayme is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Hipolito can now know whether Ryan can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eddie","Hipolito","Mayme","Ryan"],"index":43060,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9967905879,"difficulty":0.0032094121}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Melvin knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Kenneth can now know that Melvin can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Melvin","Kenneth"],"index":31546,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9661208391,"difficulty":0.0338791609}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Cindy. Craig's card is shown to Craig. Craig's card is shown to Dusty. It is publicly announced that someone picked a red card. It is publicly announced that Craig knows whether or not everyone picked a red card. It is publicly announced that Cindy does not know whether Dusty picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Craig can now know whether Dusty can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cindy","Craig","Dusty","Warren"],"index":15901,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994564652,"difficulty":0.0005435348}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raisa can now know that Peter can know that Peter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Peter","Amanda","Raisa"],"index":53895,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959689379,"difficulty":0.0040310621}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jessica can now know that Jessica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Jessica","John","Donald"],"index":57494,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977849126,"difficulty":0.0022150874}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Sherry can now know that Dorcas can know whether Sherry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorcas","Sherry","Shirley"],"index":27180,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994052649,"difficulty":0.0005947351}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon does not know whether Brandon's forehead is muddy. It is publicly announced that Thomas does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Chad can now know whether Thomas can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brandon","Thomas","Chad"],"index":18730,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9894082546,"difficulty":0.0105917454}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Edward. Mark's card is shown to Edward. Joan's card is shown to Joan. Joan's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Edward picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Joan can now know whether Mark can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Joan","Mark"],"index":57572,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.990426898,"difficulty":0.009573102}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cindy knows whether someone's forehead is muddy. It is publicly announced that Cindy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Cindy can now know that Robert can know that Cindy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alba","Edith","Robert","Cindy"],"index":45796,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7295799255,"difficulty":1.7295799255}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Geraldine does not know whether Lora is thirsty. It is publicly announced that Tracy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] 0","hypothesis":"Tracy can now know that Lora can know that Tracy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracy","Mary","Lora","Geraldine"],"index":47110,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9064897299,"difficulty":1.9064897299}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"James can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["May","Margaret","James","Dorothy"],"index":43401,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995243549,"difficulty":0.0004756451}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Anne. Maxine's card is shown to Anne. Mario's card is shown to Anne. Maxine's card is shown to Maxine. Mario's card is shown to Maxine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anne can now know that Maxine can know whether Anne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anne","Maxine","Mario"],"index":39848,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7353191376,"difficulty":1.7353191376}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Anthony can now know whether Joshua's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Anthony","Betty","Joshua"],"index":24221,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993454814,"difficulty":0.0006545186}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Judith is thirsty. It is publicly announced that Erica does not know whether Rosemarie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Maria can now know that Erica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Rosemarie","Judith","Erica"],"index":57647,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977668524,"difficulty":0.0022331476}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nita does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Steven can now know that Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nita","Lashawn","Earlene","Steven"],"index":67025,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9172246456,"difficulty":0.0827753544}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is thirsty. It is publicly announced that Larry does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Larry can now know that David can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Allison","Larry","David"],"index":16064,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8768516183,"difficulty":0.1231483817}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether Henry's forehead is muddy. It is publicly announced that Mark knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Tony can now know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Henry","Mary","Mark","Tony"],"index":63387,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965083003,"difficulty":0.0034916997}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luz is thirsty. It is publicly announced that Damian knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Damian can now know that Christopher can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Damian","Sara","Luz","Christopher"],"index":38100,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999037385,"difficulty":0.000962615}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renee knows whether or not nobody's forehead is muddy. It is publicly announced that Brock knows whether Renee's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Renee can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Renee","Brock"],"index":44901,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990125895,"difficulty":0.0009874105}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth's forehead is not muddy. It is publicly announced that Kimberly knows whether Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ruth can now know that Myrtle can know that Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","Sarah","Ruth","Myrtle"],"index":28879,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977060556,"difficulty":0.0022939444}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Patrick can now know that Brian can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clarence","Brian","Patrick","Edward"],"index":13383,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989597797,"difficulty":0.0010402203}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jennifer can now know whether Charles can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Charles"],"index":50919,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993790388,"difficulty":0.0006209612}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ian's card is shown to Richard. Theresa's card is shown to Richard. Richard's card is shown to Raymond. Ian's card is shown to Raymond. Ian's card is shown to Ian. Richard's card is shown to Theresa. Ian's card is shown to Theresa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Theresa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Raymond","Ian","Theresa"],"index":20775,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999380827,"difficulty":0.000619173}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"Robert can now know whether Tim can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","David","Walter","Tim"],"index":25863,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994474053,"difficulty":0.0005525947}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha does not know whether Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Martha can now know that Dino can know that Dino is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Dino","Jennifer","Paula"],"index":51382,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967033267,"difficulty":0.0032966733}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eduardo's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eduardo's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Edith can now know that Eduardo can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eduardo","Winston","Edith"],"index":64285,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994493127,"difficulty":0.0005506873}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether or not nobody's forehead is muddy. It is publicly announced that Harry's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Harry can now know whether Pamela can know that Pamela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Harry","Pamela"],"index":6830,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993133545,"difficulty":0.0006866455}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Whitney's card is shown to Corey. Alva's card is shown to Sonia. Whitney's card is shown to Alva. Alva's card is shown to Whitney. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sonia can now know whether Alva can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Corey","Sonia","Alva","Whitney"],"index":60684,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.954164207,"difficulty":0.045835793}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Estell does not know whether Gloria is thirsty. It is publicly announced that Estell does not know whether Richard is thirsty. It is publicly announced that Gloria does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Susan can now know whether Susan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Susan","Estell","Gloria"],"index":32777,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9631984234,"difficulty":0.0368015766}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristopher's card is shown to Cristopher. Cristopher's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Cristopher does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Cristopher can now know that Thomas can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cristopher","Thomas"],"index":3041,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.750846386,"difficulty":1.750846386}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"John can now know that Susan can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","John","Susan","Maricela"],"index":57724,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982652068,"difficulty":0.0017347932}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Beth can now know that Joshua can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Caitlin","Beth","Joshua"],"index":2358,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.980034709,"difficulty":0.019965291}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Julie. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Margaret does not know whether Julie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Julie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Julie","Margaret"],"index":44368,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9924371839,"difficulty":1.9924371839}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Gladys is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Valerie can now know whether Gladys can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Valerie","Gladys"],"index":31637,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993194342,"difficulty":0.0006805658}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Veronica. Dana's card is shown to Veronica. Veronica's card is shown to John. Dana's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Joan can now know that Veronica can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Veronica","John","Joan","Dana"],"index":9495,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993054867,"difficulty":0.0006945133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vincent knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Mary can now know whether Katie can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katie","Vincent","Gloria","Mary"],"index":3015,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9334154129,"difficulty":0.0665845871}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francoise does not know whether Francoise's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Francoise can now know whether Elizabeth can know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Stella","Francoise","Mark"],"index":60400,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9578416944,"difficulty":0.0421583056}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kent knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kent can now know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Yvonne","Kent"],"index":14433,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937129617,"difficulty":0.0062870383}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas does not know whether Joe is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Joe can now know that Joshua can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Douglas","Joe"],"index":46891,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967932105,"difficulty":0.0032067895}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Robert. Barry's card is shown to Robert. Angela's card is shown to Angela. Barry's card is shown to Angela. Barry's card is shown to Barry. Larry's card is shown to Barry. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Barry can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Angela","Barry","Larry"],"index":23868,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9971985817,"difficulty":0.0028014183}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether Ronald is thirsty. It is publicly announced that Elizabeth knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Adam can now know that Elizabeth can know that Ronald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Elizabeth","Adam"],"index":39390,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9817883968,"difficulty":0.0182116032}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Thelma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Thelma can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thelma","Christopher","Paul","Alejandra"],"index":49945,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993988276,"difficulty":0.0006011724}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Samuel. Phillip's card is shown to Phillip. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Samuel can now know whether Phillip can know whether Phillip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Samuel","Phillip"],"index":66055,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9902627468,"difficulty":0.0097372532}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald does not know whether Ronald's forehead is muddy. It is publicly announced that Stephen knows whether Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kelly can now know whether Candelaria can know whether Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Candelaria","Kelly","Stephen","Ronald"],"index":129,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9975097179,"difficulty":0.0024902821}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that Myrtle knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Charles can now know whether Jaqueline can know that Myrtle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jaqueline","David","Charles","Myrtle"],"index":14312,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999473393,"difficulty":0.000526607}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey does not know whether Myra is thirsty. It is publicly announced that Myra does not know whether Jeffrey is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Rachel can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffrey","Myra","Rachel"],"index":51750,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967703819,"difficulty":0.0032296181}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Ronald can now know whether Jason can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Joshua","Linda","Jason"],"index":7871,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999438107,"difficulty":0.000561893}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kent's card is shown to Loretta. It is publicly announced that someone picked a red card. It is publicly announced that Floyd picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Floyd can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Floyd","Kent","Bonnie","Loretta"],"index":66814,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990436435,"difficulty":0.0009563565}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eugene can now know that Eugene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronnie","Mary","Eugene","Lakisha"],"index":66981,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996209383,"difficulty":0.003790617}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna does not know whether or not everyone's forehead is muddy. It is publicly announced that Sue knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Pearl can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Susan","Sue","Pearl"],"index":38210,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999483943,"difficulty":0.000516057}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Betty is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Betty can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Mary","William","Sarah"],"index":4618,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983258843,"difficulty":0.0016741157}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sadie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Barbara can now know that Sadie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jon","Dawn","Sadie","Barbara"],"index":47581,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994495511,"difficulty":0.0005504489}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lottie's card is shown to Michael. Michael's card is shown to Linda. Lottie's card is shown to Linda. Linda's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Lottie","Linda"],"index":38238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9923189282,"difficulty":0.0076810718}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Robert can now know that Eugene can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Lisa","Eugene","Robert"],"index":31572,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994068146,"difficulty":0.0005931854}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Cindy can now know whether Andrew can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","Reginald","Paul","Cindy"],"index":38021,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993159771,"difficulty":0.0006840229}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Dan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Matthew can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Sherri","William","Dan"],"index":2814,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992955923,"difficulty":0.0007044077}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to Daphne. Daphne's card is shown to Daphne. Jon's card is shown to Daphne. Earl's card is shown to Earl. Steven's card is shown to Jon. It is publicly announced that someone picked a red card. It is publicly announced that Daphne knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Earl can now know whether Jon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Daphne","Earl","Jon"],"index":11079,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919717312,"difficulty":0.0080282688}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Sonya's card is shown to Mark. Melissa's card is shown to Mark. Patty's card is shown to Melissa. Mark's card is shown to Melissa. Sonya's card is shown to Melissa. Melissa's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know whether Patty can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patty","Mark","Sonya","Melissa"],"index":40666,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9931897521,"difficulty":0.0068102479}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Odis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Barbara can now know that Joy can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joy","Barbara","Odis"],"index":42497,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993797541,"difficulty":0.0006202459}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis does not know whether Kirk is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Joshua does not know whether Dennis is thirsty. It is publicly announced that Dennis does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Mark can now know that Dennis can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Kirk","Dennis","Joshua"],"index":1193,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981074333,"difficulty":0.0018925667}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Teresa. Tom's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Teresa can now know whether Tom picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Teresa","James","Tom"],"index":9615,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9621303678,"difficulty":0.0378696322}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Megan knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"David can now know whether Megan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Megan","David","Mark"],"index":22830,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992043376,"difficulty":0.0007956624}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melinda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Carl can now know whether Theodore can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Melinda","Theodore","George"],"index":10766,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993776679,"difficulty":0.0006223321}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Robert can now know that Barbara can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barbara","Robert"],"index":26003,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7309081554,"difficulty":1.7309081554}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether Cecilia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Larry can now know that Kara can know that Marla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kara","Larry","Marla","Cecilia"],"index":61097,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981440306,"difficulty":0.0018559694}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Maria's forehead is muddy. It is publicly announced that Gary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Gary can now know whether Ben can know that Ben's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Gary","Ben"],"index":37545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990907907,"difficulty":0.0009092093}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virgil knows whether Bernard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Derrick can now know whether Virgil can know whether Karin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karin","Virgil","Derrick","Bernard"],"index":19676,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999401927,"difficulty":0.000598073}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Scott can know whether Bryce's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Bryce","Wilson","Scott"],"index":58920,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999384284,"difficulty":0.000615716}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eileen knows whether Eileen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Cynthia can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cynthia","Eileen"],"index":17120,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989908338,"difficulty":0.0010091662}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Ethel can now know whether Gladys is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ethel","Andrew","Gladys","David"],"index":39587,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973934889,"difficulty":0.0026065111}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adelina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"David can now know whether Ellen can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Adelina","Wendy","Ellen"],"index":55938,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9976214767,"difficulty":0.0023785233}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Patricia can now know that Michael can know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Amanda","Patricia","Mary"],"index":51524,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9721158147,"difficulty":0.0278841853}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cara does not know whether Cara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Marty can now know that Cara can know that Cara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Cara","Marty","Linda"],"index":656,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9922657609,"difficulty":0.0077342391}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Julie can now know that Albert can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Albert","Julie","Linda"],"index":8942,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988627434,"difficulty":0.0011372566}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Annie can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Annie","Theresa"],"index":17835,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993854761,"difficulty":0.0006145239}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Walter's card is shown to Dawn. William's card is shown to Walter. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dawn can now know that William can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Dawn","Walter"],"index":16348,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990234375,"difficulty":0.0009765625}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarita knows whether Carolyn's forehead is muddy. It is publicly announced that Carolyn knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Carolyn can now know whether Sarita can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carolyn","Sarita"],"index":62731,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993658662,"difficulty":0.0006341338}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Velvet knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"John can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Dan","Velvet"],"index":24564,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989412427,"difficulty":0.0010587573}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dawn knows whether Vera's forehead is muddy. It is publicly announced that Vera knows whether Vera's forehead is muddy. It is publicly announced that Dawn knows whether Dawn's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dawn can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dawn","Vera"],"index":22159,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989569187,"difficulty":0.0010430813}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frederick is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Kathy can now know whether Debra can know that Debra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frederick","Debra","Kathy"],"index":6143,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.537959218,"difficulty":1.537959218}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Clarence's card is shown to Angela. Angela's card is shown to Carl. Angela's card is shown to Clarence. Clarence's card is shown to Clarence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clarence can now know whether Angela can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Carl","Clarence"],"index":31621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994143248,"difficulty":0.0005856752}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Cheryl can now know whether William can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Patricia","Cheryl"],"index":15954,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992745519,"difficulty":0.0007254481}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rose's card is shown to Muriel. Christine's card is shown to Teresa. Christine's card is shown to Christine. Teresa's card is shown to Rose. It is publicly announced that someone picked a red card. It is publicly announced that Christine does not know whether or not everyone picked a red card. It is publicly announced that Muriel picked a black card. It is publicly announced that Christine does not know whether Teresa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Teresa can now know that Muriel can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Muriel","Teresa","Christine","Rose"],"index":20267,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998247385,"difficulty":0.001752615}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Collin does not know whether Tambra is thirsty. It is publicly announced that Collin does not know whether Melvin is thirsty. It is publicly announced that Collin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] 0","hypothesis":"Melvin can now know whether Tambra can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Collin","Tambra","Melvin"],"index":6420,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6819115281,"difficulty":0.3180884719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Donna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Richard can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","John","Lillie","Richard"],"index":11040,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969171286,"difficulty":0.0030828714}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Debra can now know that Florine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Debra","Sean","Florine"],"index":7236,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988459349,"difficulty":0.0011540651}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raul knows whether or not everyone's forehead is muddy. It is publicly announced that Paula's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Joyce can now know that Paula's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Marsha","Paula","Raul"],"index":60390,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9746704102,"difficulty":0.0253295898}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemarie's card is shown to Rosemarie. Ruby's card is shown to David. David's card is shown to Ruby. Ruby's card is shown to Ruby. Rosemarie's card is shown to Jack. It is publicly announced that someone picked a red card. It is publicly announced that Jack knows whether Rosemarie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Jack can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rosemarie","David","Ruby","Jack"],"index":14645,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994423985,"difficulty":0.0005576015}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jeffrey can now know that Henry can know that Jeffrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Jeffrey","Henry"],"index":23414,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953006506,"difficulty":0.0046993494}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know that Dawn can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dawn","Leslie","Cindy","Elizabeth"],"index":18355,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999265492,"difficulty":0.000734508}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet does not know whether Janet's forehead is muddy. It is publicly announced that Janet does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Janet can now know whether Patrick can know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janet","Charles","Aja","Patrick"],"index":14318,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5939885378,"difficulty":1.5939885378}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Meredith's card is shown to Kathryn. Kathryn's card is shown to Meredith. Meredith's card is shown to Meredith. It is publicly announced that someone picked a red card. It is publicly announced that Kathryn does not know whether Kathryn picked a red card. It is publicly announced that Kathryn does not know whether Kathryn picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kathryn can now know whether Meredith can know that Meredith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathryn","Meredith"],"index":62416,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8764243722,"difficulty":0.1235756278}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa's forehead is muddy. It is publicly announced that Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] Agentc knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Melissa can now know that Constance can know that Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roxanne","Margaret","Melissa","Constance"],"index":66204,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8219467998,"difficulty":0.1780532002}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Sandra can now know whether Jennifer can know whether Chris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Chris","Barbara","Sandra"],"index":34265,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993770719,"difficulty":0.0006229281}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether or not everyone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Martha can now know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Martha","Kenneth"],"index":33765,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9897073507,"difficulty":0.0102926493}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Deborah can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Clarence","Camilla","Charlott"],"index":34384,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99925071,"difficulty":0.00074929}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Beverly. Sherri's card is shown to Beverly. Sherri's card is shown to Sherri. It is publicly announced that someone picked a red card. It is publicly announced that Beverly knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Beverly can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Beverly","Sherri"],"index":2368,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994261265,"difficulty":0.0005738735}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Christine can now know that Joel can know whether Joel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christine","Diane","Joel","Hubert"],"index":64937,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993711114,"difficulty":0.0006288886}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phoebe knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Valery can now know whether Tomasa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vincent","Phoebe","Valery","Tomasa"],"index":55406,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9950054288,"difficulty":0.0049945712}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Richard knows whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Richard can now know that Timothy can know that Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Timothy","Kenneth"],"index":60058,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9787852764,"difficulty":0.0212147236}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brianna does not know whether Ashley is thirsty. It is publicly announced that Ashley does not know whether Viola is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Viola can now know that Katheryn can know that Brianna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Viola","Katheryn","Ashley","Brianna"],"index":7574,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981520772,"difficulty":0.0018479228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Matthew can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brandon","Jean","Matthew","Robin"],"index":9920,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985861778,"difficulty":0.0014138222}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jo can now know that Jo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jay","Christopher","Jo","Justin"],"index":57603,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9944835305,"difficulty":0.0055164695}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Edward can now know that Robin can know that Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robin","Edward"],"index":32303,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983385801,"difficulty":0.0016614199}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samantha knows whether Suzanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Cornelia can now know whether Suzanne can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Suzanne","Cornelia","Samantha","Lois"],"index":38224,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9738219976,"difficulty":0.0261780024}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luisa's card is shown to Luisa. Kari's card is shown to Luisa. Kari's card is shown to Paula. Kari's card is shown to Rick. Luisa's card is shown to Kari. It is publicly announced that someone picked a red card. It is publicly announced that Luisa knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Luisa can now know whether Kari can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Luisa","Paula","Rick","Kari"],"index":63379,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993702769,"difficulty":0.0006297231}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Monica can now know that Frank can know that Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Louis","Elizabeth","Monica","Frank"],"index":58355,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963929057,"difficulty":0.0036070943}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Martha can now know whether Dorothy can know whether Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Martha","Dorothy"],"index":8726,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994607687,"difficulty":0.005392313}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marsha knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Howard can now know that James can know whether Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Howard","Marsha","James","Joseph"],"index":18111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993548989,"difficulty":0.0006451011}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Nicholas knows whether Walter is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Walter can now know that Walter is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Walter","Nicholas"],"index":58683,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9953958392,"difficulty":0.0046041608}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy. It is publicly announced that Alice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Linda can now know that Dino can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Willie","Dino","Linda","Alice"],"index":9722,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99418962,"difficulty":0.00581038}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Debora's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Sherry can now know whether Debora can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sherry","Helen","Debora"],"index":37950,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993268251,"difficulty":0.0006731749}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Megan can now know that William can know that Megan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Megan","John"],"index":14199,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984236956,"difficulty":0.0015763044}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita does not know whether Irene is thirsty. It is publicly announced that Kimberly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agentd knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Irene can now know that Anita can know whether Irene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dillon","Kimberly","Anita","Irene"],"index":54669,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8603672385,"difficulty":1.8603672385}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Lisa can now know that Jesus can know whether Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Lisa","Jesus"],"index":41654,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.994084537,"difficulty":0.005915463}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cheryl does not know whether Dorothy is thirsty. It is publicly announced that Dorothy does not know whether Ann is thirsty. It is publicly announced that Ann does not know whether Cheryl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Ann can now know that Cheryl can know whether Dorothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Cheryl","Ann","Dorothy"],"index":55818,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954102635,"difficulty":0.0045897365}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Dennis. Dennis's card is shown to Leonora. Leonora's card is shown to Leonora. Robin's card is shown to Leonora. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leonora can now know that Robin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Leonora","Robin"],"index":59390,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965788722,"difficulty":0.0034211278}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ana can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gary","Ana","Beatrice"],"index":7650,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998960495,"difficulty":0.001039505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dustin does not know whether Helen is thirsty. It is publicly announced that Karen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agentd knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Helen can now know whether Glenn can know that Glenn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Glenn","Karen","Dustin","Helen"],"index":55358,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9362395406,"difficulty":0.0637604594}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlene does not know whether Lawrence is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Lawrence can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lawrence","Charlene"],"index":43425,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9935008883,"difficulty":1.9935008883}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margo's card is shown to Guy. Margo's card is shown to Margo. William's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Margo can now know whether William can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Guy","Margo","William"],"index":61738,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993928671,"difficulty":0.0006071329}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wayne knows whether Wayne is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kathy can now know that Wayne can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anna","Wayne","Kathy","Bert"],"index":35722,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994619489,"difficulty":0.0005380511}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether or not everyone is thirsty. It is publicly announced that John is thirsty. It is publicly announced that Jason does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jason can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Jason","John","Kimberly"],"index":18486,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8305569887,"difficulty":0.1694430113}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. George's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Betty can now know that George can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Betty","George"],"index":1028,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990369081,"difficulty":0.0009630919}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Laurence can now know whether Laurence's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rosario","Laurence","Suzanne"],"index":62386,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9900615215,"difficulty":0.0099384785}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Lavern's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lavern can now know that Lavern's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peter","Mary","Lavern","Charles"],"index":52062,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959132075,"difficulty":0.0040867925}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that George does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Margaret can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Margaret","George"],"index":34279,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994524121,"difficulty":0.0005475879}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leslie knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Leslie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leah","Martha","Alvin","Leslie"],"index":28904,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989237189,"difficulty":0.0010762811}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Christopher can now know that Minnie can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Minnie","Don","Michael","Christopher"],"index":14278,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977185726,"difficulty":0.0022814274}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Randall can now know whether George can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","John","Randall","Ellen"],"index":47471,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9893432856,"difficulty":0.0106567144}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey knows whether Troy is thirsty. It is publicly announced that Jeffrey knows whether Troy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Troy can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeffrey","Troy"],"index":36793,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995019436,"difficulty":0.0004980564}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrew's card is shown to Andrew. Andrew's card is shown to Rita. Marie's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Marie does not know whether Rita picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Marie can now know whether Andrew can know whether Andrew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Marie","Rita"],"index":42789,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983432293,"difficulty":0.0016567707}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernice's card is shown to Bernice. Shauna's card is shown to Bernice. Bernice's card is shown to Brooks. Brooks's card is shown to Brooks. Shauna's card is shown to Brooks. Bernice's card is shown to Shauna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shauna can now know that Brooks can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bernice","Brooks","Shauna"],"index":2396,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993213415,"difficulty":0.0006786585}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kay is thirsty. It is publicly announced that Linda does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Kay can now know that Virginia can know whether Aileen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Virginia","Kay","Aileen","Linda"],"index":3667,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9847466946,"difficulty":0.0152533054}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Matthew. Ronald's card is shown to Matthew. Frank's card is shown to Frank. Matthew's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Matthew can now know whether Frank can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Frank","Ronald"],"index":22570,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993690848,"difficulty":0.0006309152}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cheryl does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mary can now know that Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cheryl","Mary","Sydney","Stephen"],"index":65845,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.967697978,"difficulty":0.032302022}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilbert knows whether Tracie's forehead is muddy. It is publicly announced that Wilbert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Tracie can now know that Wilbert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tracie","Wilbert"],"index":6255,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990216494,"difficulty":0.0009783506}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wesley knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Wesley can now know whether Jerry can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chris","Jerry","Wesley"],"index":57072,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993461967,"difficulty":0.0006538033}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Kristen is thirsty. It is publicly announced that Paul knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Patrick can now know whether Kristen can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Patrick","Kristen","Paul"],"index":36422,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994353652,"difficulty":0.0005646348}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Travis does not know whether Breanna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Travis can now know that Natalie can know whether Natalie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Claudette","Travis","Natalie","Breanna"],"index":15385,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5088604689,"difficulty":0.4911395311}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Branda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Gloria can now know that Adrianna can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Adrianna","Frances","Branda"],"index":44234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987353683,"difficulty":0.0012646317}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl does not know whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Alexander can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rachel","Alexander","Carl"],"index":57677,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9795655012,"difficulty":0.0204344988}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kira's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Kira can now know whether Joshua can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Loretta","Kira","Joshua"],"index":60144,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994377494,"difficulty":0.0005622506}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harry does not know whether Crystal is thirsty. It is publicly announced that Anthony does not know whether Harry is thirsty. It is publicly announced that Anthony does not know whether Crystal is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Crystal can now know whether Anthony can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harry","Anthony","Crystal"],"index":29403,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9879604578,"difficulty":0.0120395422}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Liz does not know whether Theresa is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Lavern can now know whether Theresa can know that Theresa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Liz","Theresa","Lavern"],"index":62522,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8882434964,"difficulty":1.8882434964}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herman's card is shown to Herman. Herman's card is shown to Glenn. Glenn's card is shown to Glenn. Herman's card is shown to Betty. Betty's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Herman does not know whether Glenn picked a red card. It is publicly announced that Glenn does not know whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Geneva can now know whether Glenn can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Herman","Glenn","Geneva","Betty"],"index":39192,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994452596,"difficulty":0.0005547404}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Malvina's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Malvina can now know whether Mark can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mark","Malvina"],"index":23282,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992815852,"difficulty":0.0007184148}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herbert does not know whether Herbert's forehead is muddy. It is publicly announced that Eugene's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Eugene can now know that Herbert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Herbert","Eugene"],"index":67190,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985837936,"difficulty":0.0014162064}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geraldine's card is shown to Geraldine. Jose's card is shown to Rickey. Jose's card is shown to Jose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rickey can now know whether Jay can know that Jay picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jay","Geraldine","Rickey","Jose"],"index":2539,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9918968081,"difficulty":1.9918968081}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know whether Michael can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vicente","Michael","David","Ingrid"],"index":35974,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994342923,"difficulty":0.0005657077}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosemary does not know whether Michael is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Rosemary can now know whether Michael can know that Sheila is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosemary","Michael","Sheila"],"index":20736,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.994625628,"difficulty":0.005374372}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evelyn's card is shown to Marcela. Marcela's card is shown to Adrian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marcela can now know whether Adrian can know that Adrian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marcela","Adrian","Evelyn"],"index":14417,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8591666222,"difficulty":1.8591666222}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawna knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"John can now know that Shawna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shawna","Juanita","Robert","John"],"index":32302,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8757976294,"difficulty":0.1242023706}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angel knows whether or not everyone's forehead is muddy. It is publicly announced that Geraldine does not know whether Geraldine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Angel can now know whether Keith's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Keith","Angel","Robin","Geraldine"],"index":2207,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991551638,"difficulty":0.0008448362}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessie's card is shown to Jessie. Jessie's card is shown to Christopher. Jessie's card is shown to Arthur. Christopher's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Jessie knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jessie can now know that Arthur can know that Jessie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jessie","Christopher","Arthur"],"index":37292,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9684479237,"difficulty":0.0315520763}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dana does not know whether Elizabeth is thirsty. It is publicly announced that Karen does not know whether Cecille is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Cecille can now know whether Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Elizabeth","Cecille","Dana"],"index":32003,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965797067,"difficulty":0.0034202933}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virgil knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Maria can now know whether Bobby can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bobby","Virgil","Maria"],"index":58282,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993324876,"difficulty":0.0006675124}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Toby knows whether Toby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Danielle can now know whether Toby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Danielle","Toby","Vicky","Cheryl"],"index":24941,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994550347,"difficulty":0.0005449653}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tim's card is shown to Brian. Brian's card is shown to Brian. Jason's card is shown to Brian. Brian's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brian can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tim","Brian","Jason"],"index":14414,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993615746,"difficulty":0.0006384254}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmie knows whether Ramiro's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jimmie can now know that Joseph can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jimmie","Virgil","Ramiro","Joseph"],"index":16901,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989613295,"difficulty":0.0010386705}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl is not thirsty. It is publicly announced that Genevieve knows whether Carl is thirsty. It is publicly announced that Carl does not know whether Jason is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Genevieve can now know that Jason is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Genevieve","Lisa","Jason","Carl"],"index":13958,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9917959571,"difficulty":0.0082040429}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know that Lee can know whether Yang's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Yang","Lee","Melba"],"index":22257,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993501306,"difficulty":0.0006498694}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Denise's card is shown to John. Mary's card is shown to Denise. Kevin's card is shown to Kevin. Denise's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Denise","Kevin","Mary"],"index":63730,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959378242,"difficulty":0.0040621758}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Amelia can now know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Amelia","William"],"index":39704,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992189407,"difficulty":0.0007810593}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory's forehead is muddy. It is publicly announced that Andrew knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kristine can now know whether Kristine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Kristine","Deana","Gregory"],"index":24726,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.990162015,"difficulty":0.009837985}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Ellen can now know whether Darnell can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bonnie","Darnell","Ellen","Jane"],"index":16037,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994279742,"difficulty":0.0005720258}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bryan's card is shown to Bryan. Martha's card is shown to Bryan. Alfred's card is shown to Bryan. Alfred's card is shown to Martha. Bryan's card is shown to Alfred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bryan can now know that Alfred can know whether Martha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bryan","Martha","Alfred"],"index":28198,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9786325097,"difficulty":0.0213674903}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Herbert. Herbert's card is shown to Howard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Howard can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Herbert","Howard","Justin"],"index":66585,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994142056,"difficulty":0.0005857944}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victor's card is shown to Victor. Daniel's card is shown to James. Keith's card is shown to Daniel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know that James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Victor","James","Daniel"],"index":3164,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989970326,"difficulty":0.0010029674}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentd knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Bradley can now know whether Donald can know that Bradley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Ruth","Donald","Bradley"],"index":26440,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9573514462,"difficulty":0.0426485538}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that Benito's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Robert","Janet","Benito"],"index":5151,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978074431,"difficulty":0.0021925569}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether Susan is thirsty. It is publicly announced that Mike is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Mike can now know whether Susan can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mike","William","Carol","Susan"],"index":24816,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991964698,"difficulty":0.0008035302}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Percy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Percy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peter","Percy","Glenda","Luke"],"index":8813,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986231327,"difficulty":0.0013768673}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Vincent can now know whether Lawrence can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vincent","Lawrence"],"index":3521,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994437099,"difficulty":0.0005562901}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremiah knows whether someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jeremiah knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Mary can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Jeremiah"],"index":63618,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993120432,"difficulty":0.0006879568}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Dolores can now know that Kelly can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Kelly","Ruby","Dolores"],"index":34038,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986643791,"difficulty":0.0013356209}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Debbi can now know that Luisa can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debbi","William","Luisa","Brittany"],"index":19997,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993821383,"difficulty":0.0006178617}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vickie does not know whether Charlotte is thirsty. It is publicly announced that Vickie does not know whether or not everyone is thirsty. It is publicly announced that Vickie does not know whether or not everyone is thirsty. It is publicly announced that Charlotte is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Vickie can now know that Charlotte can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charlotte","Vickie"],"index":32968,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989932179,"difficulty":0.0010067821}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Margaret can now know whether Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Margaret","William"],"index":4198,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992752671,"difficulty":0.0007247329}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Megan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Kenneth can now know that Megan can know that Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Gary","Megan"],"index":67463,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978377223,"difficulty":0.0021622777}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Williams can now know whether Chad can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Williams","Chad"],"index":51,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994155169,"difficulty":0.0005844831}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Howard can now know that Tracy can know that Tracy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heather","Arthur","Tracy","Howard"],"index":60423,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959277511,"difficulty":0.0040722489}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"David can now know whether Laurel can know that Laurel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Laurel","Arthur"],"index":24978,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992867112,"difficulty":0.0007132888}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is not thirsty. It is publicly announced that John does not know whether Madeline is thirsty. It is publicly announced that Kathryn knows whether Kathryn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Madeline can now know whether Tom can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Madeline","Kathryn","Tom"],"index":19028,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9026928544,"difficulty":1.9026928544}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan does not know whether Jonathan's forehead is muddy. It is publicly announced that Jonathan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Doloris can now know whether Doloris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Doloris","Jonathan"],"index":21226,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7347258925,"difficulty":0.2652741075}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Micah does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Harry can now know that Linda can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Linda","Harry","Micah"],"index":21183,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987336993,"difficulty":0.0012663007}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yolanda knows whether or not nobody is thirsty. It is publicly announced that Yolanda does not know whether Amy is thirsty. It is publicly announced that George knows whether or not everyone is thirsty. It is publicly announced that Amy knows whether Amy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Yolanda can now know that George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yolanda","George","Amy"],"index":11604,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9695945382,"difficulty":0.0304054618}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ella's card is shown to Robert. Latonya's card is shown to Robert. Mandi's card is shown to Ella. Ella's card is shown to Latonya. Robert's card is shown to Mandi. It is publicly announced that someone picked a red card. It is publicly announced that Ella does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Latonya can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Ella","Latonya","Mandi"],"index":66161,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9771313071,"difficulty":0.0228686929}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Wallace. Sharon's card is shown to Robert. Wallace's card is shown to Sharon. Sharon's card is shown to Sharon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sharon can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wallace","Robert","Sharon","Mary"],"index":23132,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984915257,"difficulty":0.0015084743}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Matthew. Matthew's card is shown to Suzanne. Suzanne's card is shown to Suzanne. It is publicly announced that someone picked a red card. It is publicly announced that Suzanne picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Matthew can now know whether Suzanne can know that Suzanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Matthew","Suzanne"],"index":26946,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9836747646,"difficulty":0.0163252354}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Julie can now know whether Craig can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julie","Craig","Robert"],"index":56228,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9951283932,"difficulty":0.0048716068}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherri's card is shown to Austin. Austin's card is shown to Sherri. Sherri's card is shown to Sherri. Austin's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that Austin does not know whether Austin picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Sherri can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Austin","Sherri","Lisa"],"index":14025,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994519353,"difficulty":0.0005480647}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgia's forehead is not muddy. It is publicly announced that Lawrence's forehead is muddy. It is publicly announced that Lawrence's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Lawrence can now know that Georgia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pamela","Lawrence","Georgia"],"index":18008,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9442533255,"difficulty":0.0557466745}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ed knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Thomas can now know whether Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Ed","Sandy","Fred"],"index":6734,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993938208,"difficulty":0.0006061792}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brad does not know whether or not everyone is thirsty. It is publicly announced that Patrick knows whether someone is thirsty. It is publicly announced that Patrick is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Juliana can now know whether Juliana is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juliana","Patrick","Brad","Paula"],"index":35683,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9879798889,"difficulty":0.0120201111}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miyoko knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Robert can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Miyoko","Robert","Jacqueline"],"index":288,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9961613417,"difficulty":0.0038386583}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allen is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Allen can now know whether Nina can know that Martha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Allen","Nina","Martha"],"index":27185,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.98900491,"difficulty":1.98900491}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy. It is publicly announced that Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentb knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Richard can now know whether Henry can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Richard","Michael","Henry"],"index":11573,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994783998,"difficulty":0.0005216002}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason does not know whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"William can now know whether Elizabeth can know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Elizabeth","Kris","Jason"],"index":60651,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9074090123,"difficulty":0.0925909877}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Joel knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Joel can now know that Francis can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joel","Francis","Carolyn"],"index":13014,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998840034,"difficulty":0.001159966}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jorge knows whether or not everyone is thirsty. It is publicly announced that Maxine is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Maxine can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Maxine","Jorge"],"index":31976,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994807839,"difficulty":0.0005192161}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvia knows whether Darline's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know that Darline can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sylvia","Mary","Darline","Michael"],"index":23196,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7837672234,"difficulty":1.7837672234}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Joseph's card is shown to Adan. Joyce's card is shown to Adan. Joyce's card is shown to Scott. Scott's card is shown to Joyce. Joyce's card is shown to Joyce. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Adan can now know whether Joyce can know that Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Adan","Scott","Joyce"],"index":24694,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9546125531,"difficulty":1.9546125531}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Carol. Carol's card is shown to Amy. Clara's card is shown to Amy. Amy's card is shown to Clara. It is publicly announced that someone picked a red card. It is publicly announced that Carol knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Clara can now know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Amy","Clara"],"index":27075,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9539158344,"difficulty":0.0460841656}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ida's card is shown to Angela. Angela's card is shown to Lenard. Lenard's card is shown to Lenard. Lenard's card is shown to Ida. It is publicly announced that someone picked a red card. It is publicly announced that Ida picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Angela can now know that Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Lenard","Ida"],"index":37997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9134801626,"difficulty":0.0865198374}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Florine. Jared's card is shown to Teresa. Jonathan's card is shown to Teresa. Jonathan's card is shown to Jared. Teresa's card is shown to Jonathan. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan does not know whether Jared picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jonathan can now know that Jared can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Florine","Teresa","Jared","Jonathan"],"index":4752,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994101524,"difficulty":0.0005898476}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce knows whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Rosendo can now know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Dianna","Rosendo","Elizabeth"],"index":54215,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949620962,"difficulty":0.0050379038}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Johnnie can now know that Anna can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnnie","Anna","John"],"index":29288,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992210865,"difficulty":0.0007789135}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurie knows whether Roseanne's forehead is muddy. It is publicly announced that Raymond's forehead is not muddy. It is publicly announced that Raymond knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Laurie can now know that Roseanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laurie","Raymond","Roseanne"],"index":16500,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957183003,"difficulty":0.0042816997}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Barbara. Michael's card is shown to Darwin. Darwin's card is shown to Darwin. Darwin's card is shown to Katrina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Darwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Michael","Darwin","Katrina"],"index":19881,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958070517,"difficulty":0.0041929483}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Victoria does not know whether Helen is thirsty. It is publicly announced that Sandi does not know whether Victoria is thirsty. It is publicly announced that Sandi does not know whether Helen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Sandi can now know whether Victoria can know whether Helen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Victoria","Sandi","Helen"],"index":42891,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990974665,"difficulty":0.0009025335}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlie's card is shown to Charles. Charles's card is shown to Eric. Max's card is shown to Eric. Charles's card is shown to Max. It is publicly announced that someone picked a red card. It is publicly announced that Charlie knows whether Charles picked a red card. It is publicly announced that Eric does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Charles can now know that Eric can know that Eric picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Charlie","Eric","Max"],"index":67012,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6902606487,"difficulty":0.3097393513}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerardo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Gerardo can now know that Krystina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gerardo","Krystina","Pamela"],"index":49828,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9892436266,"difficulty":0.0107563734}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eric can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffrey","Jose","Henry","Eric"],"index":28373,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989275336,"difficulty":0.0010724664}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kerry's card is shown to Kerry. George's card is shown to George. Gretchen's card is shown to Gretchen. It is publicly announced that someone picked a red card. It is publicly announced that Gretchen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Gretchen can now know that Kerry can know whether Kerry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kerry","George","Gretchen"],"index":27678,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8397693634,"difficulty":0.1602306366}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rod's card is shown to Randall. Randall's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rod can now know that Randall can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rod","Randall","David"],"index":53258,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987083673,"difficulty":0.0012916327}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Stacey does not know whether Stacey's forehead is muddy. It is publicly announced that Stacey does not know whether Stacey's forehead is muddy. It is publicly announced that Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Judith can now know that Judith's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeffrey","Stacey","Judith"],"index":28740,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958549142,"difficulty":0.0041450858}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lina can now know whether Beverly can know whether Judy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beverly","Lina","Judy"],"index":40155,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990775585,"difficulty":0.0009224415}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl does not know whether Connie is thirsty. It is publicly announced that Connie does not know whether Carl is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Carl can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carl","Connie","Evelyn"],"index":4537,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998950839,"difficulty":0.001049161}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janet can now know whether Constance can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janet","Noreen","Bobbie","Constance"],"index":37672,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993398786,"difficulty":0.0006601214}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know whether David can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Cynthia","David","John"],"index":37779,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978426695,"difficulty":0.0021573305}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Kevin can now know whether Ronald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronald","Kevin","John"],"index":4240,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993184805,"difficulty":0.0006815195}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is not thirsty. It is publicly announced that Matt is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"James can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Annette","Melissa","James","Matt"],"index":34029,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999022603,"difficulty":0.000977397}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kathy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Anthony","Kathy"],"index":64631,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998941958,"difficulty":0.001058042}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miranda knows whether or not nobody's forehead is muddy. It is publicly announced that Miranda knows whether Miranda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Hank can now know whether Miranda can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Miranda","Hank"],"index":38882,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993786812,"difficulty":0.0006213188}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is muddy. It is publicly announced that Christopher's forehead is muddy. It is publicly announced that Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agentb knows whether (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Jessica can now know whether Beverly can know whether Jessica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Jessica","Lola","Beverly"],"index":50766,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998735249,"difficulty":0.001264751}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael is thirsty. It is publicly announced that Gregory does not know whether or not everyone is thirsty. It is publicly announced that Gregory does not know whether Loretta is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Gregory can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Geraldine","Loretta","Michael","Gregory"],"index":53501,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990756512,"difficulty":0.0009243488}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Franklin. Emily's card is shown to Emily. Franklin's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Franklin's card is shown to Nicole. Emily's card is shown to Nicole. It is publicly announced that someone picked a red card. It is publicly announced that Nicole knows whether someone picked a red card. It is publicly announced that Kenneth does not know whether Nicole picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] Agenta knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Franklin can now know whether Kenneth can know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Franklin","Emily","Kenneth","Nicole"],"index":64888,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6208515167,"difficulty":0.3791484833}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad knows whether Chad's forehead is muddy. It is publicly announced that Cynthia knows whether Ryan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Sarah can now know that Ryan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ryan","Cynthia","Sarah","Chad"],"index":39279,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989379048,"difficulty":0.0010620952}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jung can now know that Patti can know that Jung's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Drew","Patti","Jung","Leroy"],"index":28685,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982690811,"difficulty":0.0017309189}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eleanor","Joann","Michael"],"index":16892,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962790608,"difficulty":0.0037209392}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terry can now know whether Wendy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terry","Wendy","Jose","Edward"],"index":34576,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993106127,"difficulty":0.0006893873}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pamela does not know whether Dave is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Pamela can now know that Dave can know that Dave is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antonio","Pamela","Teresa","Dave"],"index":27865,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9860559702,"difficulty":0.0139440298}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Daron is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Joshua can now know whether Daron can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joshua","James","Iva","Daron"],"index":42287,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994114637,"difficulty":0.0005885363}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucille does not know whether Bonnie is thirsty. It is publicly announced that Rebecca does not know whether Bonnie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Lucille can now know whether Rebecca can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucille","Rebecca","Bonnie"],"index":28079,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994182587,"difficulty":0.0005817413}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lottie's card is shown to Lottie. Johnny's card is shown to Lottie. Lottie's card is shown to Johnny. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Johnny can now know that Lottie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lottie","Johnny"],"index":40379,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9820140004,"difficulty":1.9820140004}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darlene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Scott can now know that Trinidad can know that Darlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Trinidad","Darlene","Scott"],"index":1243,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976599216,"difficulty":0.0023400784}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melba knows whether Melba's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Melba can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Keith","Melba","Angel"],"index":62842,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989602566,"difficulty":0.0010397434}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard is thirsty. It is publicly announced that Kristen does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Luisa can now know whether Kristen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kristen","Richard","Sheldon","Luisa"],"index":2966,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9925242066,"difficulty":0.0074757934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley does not know whether Shirley's forehead is muddy. It is publicly announced that Jeff does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Shirley can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeff","Shirley","Sandra","Margaret"],"index":40637,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993875027,"difficulty":0.0006124973}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffany's card is shown to Gregory. Gregory's card is shown to Tiffany. It is publicly announced that someone picked a red card. It is publicly announced that Gregory knows whether Gregory picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Gregory can now know that Tiffany can know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gregory","Tiffany"],"index":66110,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9307919741,"difficulty":1.9307919741}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Casey's forehead is muddy. It is publicly announced that Theresa does not know whether Theresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Casey can now know whether Justin can know whether Casey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Casey","James","Theresa","Justin"],"index":18400,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989904761,"difficulty":0.0010095239}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Miguel can know that Miguel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bernadette","Miguel","Janet","Linda"],"index":25357,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951068163,"difficulty":0.0048931837}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that Elaine can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brenda","Elaine","Joseph"],"index":34074,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989174604,"difficulty":0.0010825396}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marla's forehead is not muddy. It is publicly announced that Marilee knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Marla can now know whether Marla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marla","Marilee","Martha"],"index":9336,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994607568,"difficulty":0.0005392432}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Warren's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Robert can now know that Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lynda","Robert","Susan","Warren"],"index":62743,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977346659,"difficulty":0.0022653341}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Tracey. Tracey's card is shown to Willie. Willie's card is shown to Willie. Willie's card is shown to Alan. Alan's card is shown to Alan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Willie can now know that Tracey can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tracey","Willie","Alan"],"index":26215,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988887906,"difficulty":0.0011112094}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Gordon can now know that Jennifer can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Carlos","Gordon","Jennifer"],"index":10771,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989485145,"difficulty":0.0010514855}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know whether George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jennifer","George","Francis","Robert"],"index":10234,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986718893,"difficulty":0.0013281107}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gearldine does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gearldine can now know whether Larry can know whether Larry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cornelia","Gearldine","Vanessa","Larry"],"index":63564,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9946886301,"difficulty":0.0053113699}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether David's forehead is muddy. It is publicly announced that Amy knows whether Amy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know that Allison can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Allison","Amy","David"],"index":46353,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991875291,"difficulty":0.0008124709}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Charlotte can now know that John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlotte","Sarah","John","Kimberly"],"index":145,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5128901601,"difficulty":0.4871098399}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Elizabeth can now know that Joshua can know that Opal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ranae","Opal","Joshua","Elizabeth"],"index":36064,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975367785,"difficulty":0.0024632215}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Anne can now know that Fred can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anne","Fred"],"index":5418,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993107319,"difficulty":0.0006892681}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Wanda can now know whether Joseph can know that Wanda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wanda","James","Joseph"],"index":17633,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9226888418,"difficulty":0.0773111582}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Joseph knows whether Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Stephen can now know that Kerry can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Kerry","Stephen"],"index":36807,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9975067973,"difficulty":0.0024932027}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly knows whether Kelly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Thomas can now know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Kelly","Thomas","Beth"],"index":43147,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993525147,"difficulty":0.0006474853}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Britt does not know whether Emily is thirsty. It is publicly announced that Emily does not know whether Britt is thirsty. It is publicly announced that Shawna does not know whether or not everyone is thirsty. It is publicly announced that Emily does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Britt can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emily","Britt","Shawna"],"index":15782,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994438291,"difficulty":0.0005561709}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betsy's card is shown to Betsy. Margaret's card is shown to Betsy. Stephanie's card is shown to Margaret. Stephanie's card is shown to Stephanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know that Stephanie can know whether Betsy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betsy","Margaret","Stephanie"],"index":1005,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9173128009,"difficulty":0.0826871991}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gwendolyn knows whether someone is thirsty. It is publicly announced that Casey does not know whether Gwendolyn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Gwendolyn can now know whether Walter can know that Christopher is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Gwendolyn","Casey","Walter"],"index":53321,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9946979284,"difficulty":0.0053020716}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristen's card is shown to Kristen. Charles's card is shown to Kristen. Kristen's card is shown to Charles. Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Kristen knows whether or not nobody picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Kristen can now know whether Charles can know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kristen","Charles"],"index":2137,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9963645339,"difficulty":0.0036354661}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie does not know whether or not everyone's forehead is muddy. It is publicly announced that Carrie's forehead is muddy. It is publicly announced that Carrie knows whether Arlene's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Arlene can now know whether Carrie can know that Carrie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carrie","Arlene"],"index":4380,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9340125918,"difficulty":0.0659874082}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Keith. Ciera's card is shown to Cynthia. Keith's card is shown to Ciera. Fred's card is shown to Ciera. Keith's card is shown to Fred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ciera can now know whether Keith can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Cynthia","Ciera","Fred"],"index":43593,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992575049,"difficulty":0.0007424951}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raul is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Jesse can now know whether Brandon can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brandon","Jesse","Raul"],"index":46523,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994755387,"difficulty":0.0005244613}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lakendra knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Andrew can now know that Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Gretchen","Lakendra","Lawrence"],"index":42955,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975825548,"difficulty":0.0024174452}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Christine can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vera","Christine"],"index":26813,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992563128,"difficulty":0.0007436872}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Todd. Martin's card is shown to Martin. Martin's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Todd can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Todd","Martin","Robert"],"index":65087,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981439114,"difficulty":0.0018560886}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cherie's card is shown to Cherie. Brenda's card is shown to Cherie. Cherie's card is shown to Brenda. Morris's card is shown to Brenda. Cherie's card is shown to Morris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brenda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cherie","Brenda","Morris"],"index":63252,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943828583,"difficulty":0.0056171417}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Kimberly. Kimberly's card is shown to Harry. Harry's card is shown to Harry. Kimberly's card is shown to Elizabeth. Harry's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Harry does not know whether or not everyone picked a red card. It is publicly announced that Kimberly does not know whether Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Elizabeth can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kimberly","Harry","Elizabeth"],"index":35282,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994438291,"difficulty":0.0005561709}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Cheryle can now know whether Daniel can know whether Ben is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cheryle","Ben","Daniel"],"index":25285,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992889166,"difficulty":0.0007110834}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aaron knows whether Jody's forehead is muddy. It is publicly announced that Barbara knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Michael can now know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Aaron","Jody","Barbara"],"index":39365,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975940585,"difficulty":0.0024059415}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amber's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Kent can now know that Charles can know that Amber's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amber","Kent","Charles"],"index":59694,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971938133,"difficulty":0.0028061867}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Ronald can now know whether Lynn can know whether Lynn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patrica","Lynn","Ronald","Robyn"],"index":31938,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989250302,"difficulty":0.0010749698}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jonathan's card is shown to Martha. Martha's card is shown to Jonathan. Jonathan's card is shown to Renee. Donna's card is shown to Donna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jonathan can now know that Renee can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Martha","Jonathan","Renee","Donna"],"index":19529,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993728995,"difficulty":0.0006271005}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose knows whether Rose's forehead is muddy. It is publicly announced that Rose knows whether Rose's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Rose can now know that Marcia can know that Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dana","Marcia","Rose","Evelyn"],"index":14244,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944217801,"difficulty":0.0055782199}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Micheal does not know whether Jackie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jackie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Micheal","Margaret","Jackie"],"index":36384,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990013242,"difficulty":0.0009986758}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy. It is publicly announced that Calvin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] 0","hypothesis":"Marc can now know that Calvin can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marc","Mary","Calvin"],"index":29368,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990697503,"difficulty":0.0009302497}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Anna can now know that Richard can know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chad","Richard","Dale","Anna"],"index":52998,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982740879,"difficulty":0.0017259121}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Mary can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tonya","Daniel","Nancy","Mary"],"index":36151,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995063543,"difficulty":0.0004936457}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jesus can now know that Geraldine can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesus","Harold","Robert","Geraldine"],"index":8220,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991945624,"difficulty":0.0008054376}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerry does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Jennifer can now know that Jerry can know that Melvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Melvin","Jerry","Mitchell"],"index":12718,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9054604769,"difficulty":0.0945395231}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lyle is thirsty. It is publicly announced that Ruth is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(3) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Ruth can now know that Lyle can know that Morgan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Morgan","Lyle","Ruth"],"index":36622,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965890646,"difficulty":0.0034109354}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Robert's card is shown to Amanda. Amanda's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that Amanda knows whether Amanda picked a red card. It is publicly announced that Robert does not know whether Amanda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Robert can now know whether Amanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Amanda"],"index":32801,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9209545851,"difficulty":1.9209545851}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Rosalyn can now know whether Patricia can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Shawn","Rosalyn"],"index":28325,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994295239,"difficulty":0.0005704761}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ralph does not know whether Timothy is thirsty. It is publicly announced that Timothy does not know whether Eric is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Kenneth can now know that Eric can know whether Ralph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Ralph","Eric","Timothy"],"index":43674,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979071617,"difficulty":0.0020928383}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence does not know whether Florence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Florence can now know whether Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christal","Brenda","Florence","Shawna"],"index":31773,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989996552,"difficulty":0.0010003448}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chris's card is shown to Chris. Donovan's card is shown to Pamela. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Chris can now know whether Donovan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donovan","Chris","Pamela"],"index":54947,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994245768,"difficulty":0.0005754232}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Harold. Douglas's card is shown to Harold. Harold's card is shown to Douglas. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Douglas can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harold","Douglas","John"],"index":45143,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980825186,"difficulty":0.0019174814}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terrie's card is shown to Terrie. Terrie's card is shown to Rebecca. Rebecca's card is shown to Rebecca. Wayne's card is shown to Rebecca. Terrie's card is shown to Barbara. Barbara's card is shown to Barbara. Barbara's card is shown to Wayne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,4 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terrie can now know whether Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terrie","Rebecca","Barbara","Wayne"],"index":7954,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970266223,"difficulty":0.0029733777}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janna does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Sandra can now know that Joan can know that Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janna","Joan","Cynthia","Sandra"],"index":11322,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8673769236,"difficulty":0.1326230764}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Ingrid can now know that Ingrid is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ingrid","David","Mike","Abby"],"index":32335,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9930024743,"difficulty":0.0069975257}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille's forehead is muddy. It is publicly announced that Cedric knows whether Lucille's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Cecil can now know that Norma can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cedric","Lucille","Cecil","Norma"],"index":902,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987239242,"difficulty":0.0012760758}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor's forehead is muddy. It is publicly announced that Thomas knows whether Victor's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Victor can now know that Joseph can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Willie","Joseph","Victor","Thomas"],"index":30729,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9924382567,"difficulty":0.0075617433}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank does not know whether Sha is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Sha can now know that Mary can know that Dorothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sha","Dorothy","Frank","Mary"],"index":24722,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.974303484,"difficulty":0.025696516}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samuel does not know whether Mary is thirsty. It is publicly announced that Guillermo does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Albert","Samuel","Mary","Guillermo"],"index":31515,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995192289,"difficulty":0.0004807711}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lashonda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Margaret can now know that Denise can know whether Lillie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Denise","Lashonda","Lillie"],"index":61295,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993884563,"difficulty":0.0006115437}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Normand's card is shown to Sherri. Verna's card is shown to Sherri. Maria's card is shown to Normand. Normand's card is shown to Normand. Normand's card is shown to Verna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know whether Normand can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sherri","Maria","Normand","Verna"],"index":53376,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992620349,"difficulty":0.0007379651}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Dorothy can now know that Kenneth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Dorothy","Kenneth"],"index":7202,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7240114212,"difficulty":1.7240114212}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Helen. Christopher's card is shown to Helen. Christopher's card is shown to Carl. Carl's card is shown to Christopher. Carol's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Carl does not know whether Carol picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Helen can now know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Carl","Christopher","Carol"],"index":40779,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5289462209,"difficulty":0.4710537791}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfredo knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"John can now know that Alfredo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Alfredo","Della","Patrick"],"index":27062,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981449842,"difficulty":0.0018550158}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nicholas can now know whether David can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Hector","Michael","Nicholas"],"index":40931,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999334991,"difficulty":0.000665009}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether or not everyone's forehead is muddy. It is publicly announced that Barbara knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Johnnie can now know that Barbara can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Johnnie","Barbara"],"index":40358,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984046817,"difficulty":0.0015953183}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Matthew can now know that Patsy can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Patsy","Joseph","Janet"],"index":40209,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993300438,"difficulty":0.0006699562}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristopher knows whether or not everyone's forehead is muddy. It is publicly announced that Edward's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Kristopher can now know that Edward can know whether Kristopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kristopher","Edward"],"index":66756,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993991852,"difficulty":0.0006008148}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Van's card is shown to Pam. Arnold's card is shown to Pam. Mark's card is shown to Van. Arnold's card is shown to Van. Pam's card is shown to Mark. Mark's card is shown to Mark. Arnold's card is shown to Arnold. It is publicly announced that someone picked a red card. It is publicly announced that Arnold does not know whether Van picked a red card. It is publicly announced that Mark does not know whether Van picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3,4 Agentc:1,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mark can now know whether Van picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pam","Van","Mark","Arnold"],"index":16387,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8225349784,"difficulty":1.8225349784}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alma's forehead is not muddy. It is publicly announced that Carlotta knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Alma can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alma","Carlotta","Joan"],"index":59236,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998886764,"difficulty":0.001113236}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy. It is publicly announced that Phyllis knows whether or not nobody's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Brian can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terry","Brian","Phyllis"],"index":8100,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986750484,"difficulty":0.0013249516}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tommie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tommie can now know that Henry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Henry","Tommie","Scott","Jae"],"index":7714,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982193112,"difficulty":0.0017806888}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew does not know whether Sharon is thirsty. It is publicly announced that Jean knows whether someone is thirsty. It is publicly announced that Jean does not know whether Matthew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jean can now know that Martin can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Jean","Sharon","Martin"],"index":46661,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992985725,"difficulty":0.0007014275}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynn knows whether someone's forehead is muddy. It is publicly announced that Joel knows whether Joel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Timothy can now know that Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joel","Timothy","Lynn","Daniel"],"index":38773,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997672379,"difficulty":0.002327621}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Waneta can now know that Michael can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daryl","Waneta","Michael","Leroy"],"index":64442,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993815422,"difficulty":0.0006184578}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy. It is publicly announced that Amy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Ricky can now know that Amy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ricky","Amy","James"],"index":58600,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9837393165,"difficulty":0.0162606835}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Elizabeth can now know whether William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kimberly","William","Elizabeth"],"index":23496,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967575669,"difficulty":0.0032424331}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Karrie can now know whether Karrie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marie","Karen","Karrie"],"index":5220,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9812399745,"difficulty":0.0187600255}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Melissa is thirsty. It is publicly announced that Kendrick is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Kendrick can now know that Kendrick is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kendrick","Milton","Robert","Melissa"],"index":4866,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7588525414,"difficulty":1.7588525414}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vera's forehead is muddy. It is publicly announced that Vera knows whether or not nobody's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Vera can now know that Thomas can know whether Vera's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Beth","Vera"],"index":63294,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989727736,"difficulty":0.0010272264}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrea knows whether Andrea is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Gene can now know whether Andrea is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gene","Andrea"],"index":26137,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9733974934,"difficulty":1.9733974934}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Simon's card is shown to Sylvia. Sylvia's card is shown to Simon. Simon's card is shown to Israel. Sylvia's card is shown to John. Simon's card is shown to John. Israel's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Simon can now know that Simon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sylvia","Simon","Israel","John"],"index":66830,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949982166,"difficulty":0.0050017834}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gwendolyn is not thirsty. It is publicly announced that Gwendolyn is not thirsty. It is publicly announced that Patrick does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Patrick can now know that Gwendolyn can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Patrick","Robert","Gwendolyn"],"index":66866,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994920492,"difficulty":0.0005079508}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale does not know whether Dale's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Tyron can now know that Dale can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dale","Tyron","David","Chad"],"index":56149,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973697662,"difficulty":0.0026302338}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronda knows whether Ronda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ronda can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Zachary","Ruben","Ronda","Margaret"],"index":12963,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989793897,"difficulty":0.0010206103}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Minnie knows whether Francis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Cindy can now know whether Minnie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Francis","Cindy","Minnie","Joesph"],"index":59586,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999204576,"difficulty":0.000795424}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jewell knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Gertrude can now know that Krista can know whether Jewell is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gertrude","Krista","Jewell"],"index":31148,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.604126215,"difficulty":1.604126215}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Tom. Jenny's card is shown to Tom. Gilbert's card is shown to Tom. Tom's card is shown to Jenny. Gilbert's card is shown to Jenny. Gilbert's card is shown to Gilbert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gilbert can now know that Jenny picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tom","Jenny","Gilbert"],"index":59880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976041913,"difficulty":0.0023958087}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annemarie is not thirsty. It is publicly announced that Rodney knows whether Annemarie is thirsty. It is publicly announced that Annemarie does not know whether Justin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Rodney can now know that Rodney is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rodney","David","Justin","Annemarie"],"index":1259,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9845530987,"difficulty":0.0154469013}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annamaria's card is shown to Larhonda. Larhonda's card is shown to Alice. Cameron's card is shown to Annamaria. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Alice can now know that Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cameron","Larhonda","Alice","Annamaria"],"index":43583,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9874271154,"difficulty":0.0125728846}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joan can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Joan","Mark"],"index":1538,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974449873,"difficulty":0.0025550127}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kenneth","John","Jeff"],"index":22024,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994914532,"difficulty":0.0005085468}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geoffrey's card is shown to Karen. Karen's card is shown to Christina. Christina's card is shown to Christina. Geoffrey's card is shown to Christina. Christina's card is shown to Geoffrey. Geoffrey's card is shown to Geoffrey. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Geoffrey can now know whether Christina can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Christina","Geoffrey"],"index":4941,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9872374535,"difficulty":1.9872374535}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Willie can now know that Edward can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Willie","Barbara","Edward"],"index":40407,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989738464,"difficulty":0.0010261536}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vinita knows whether Vinita's forehead is muddy. It is publicly announced that Susan knows whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Susan can now know that Vinita can know whether Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesse","Susan","Vinita","Timothy"],"index":35801,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993529916,"difficulty":0.0006470084}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Victoria knows whether Emma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jared can now know whether Emma can know whether Emma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emma","Jared","Victoria","Sheila"],"index":7105,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993507266,"difficulty":0.0006492734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy knows whether someone is thirsty. It is publicly announced that Anthony does not know whether Michael is thirsty. It is publicly announced that Donna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Timothy can now know whether Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Timothy","Anthony","Michael"],"index":25352,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.992749691,"difficulty":0.007250309}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katrina knows whether Herman's forehead is muddy. It is publicly announced that Herman does not know whether Herman's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ralph can now know whether Herman can know whether Ralph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ralph","Katrina","Herman"],"index":49611,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9955244064,"difficulty":0.0044755936}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steve knows whether Annemarie's forehead is muddy. It is publicly announced that Annemarie does not know whether Annemarie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Annemarie can now know that Steve can know that Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melissa","Steve","Annemarie"],"index":62151,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.992104888,"difficulty":0.007895112}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cory knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jonnie can now know that Cory can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ryan","Cory","Jonnie"],"index":12256,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990129471,"difficulty":0.0009870529}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emma's card is shown to Kristin. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Emma can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emma","Kristin","Matthew","Mary"],"index":36130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9927353859,"difficulty":0.0072646141}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phil is thirsty. It is publicly announced that Gabriela does not know whether or not everyone is thirsty. It is publicly announced that Phil does not know whether Irving is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Phil can now know whether Stephen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Irving","Stephen","Phil","Gabriela"],"index":21019,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9890089631,"difficulty":0.0109910369}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ethelyn does not know whether or not everyone's forehead is muddy. It is publicly announced that Ethelyn does not know whether Ethelyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Robin","James","Ethelyn"],"index":36634,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.540179193,"difficulty":1.540179193}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Chase. Adam's card is shown to Virginia. Robert's card is shown to Virginia. Chase's card is shown to Adam. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Adam picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Adam can now know that Chase can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chase","Virginia","Adam","Robert"],"index":23437,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9844167829,"difficulty":0.0155832171}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Franklin does not know whether Maria is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (1&2&3&4) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (1&2&3&4) ] 0","hypothesis":"Lola can now know whether Franklin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kay","Lola","Maria","Franklin"],"index":319,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9968596697,"difficulty":0.0031403303}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Yvonne can now know that Yvonne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yvonne","Frederick","Kenton"],"index":44729,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997163713,"difficulty":0.002836287}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hugh knows whether someone is thirsty. It is publicly announced that Pam does not know whether Hugh is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jessica can now know that Julian can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julian","Hugh","Pam","Jessica"],"index":62267,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990217686,"difficulty":0.0009782314}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Thomas can now know that Guillermo can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Guillermo","Thomas"],"index":31425,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991880059,"difficulty":0.0008119941}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Juan. Esther's card is shown to Summer. Ralph's card is shown to Summer. Juan's card is shown to Ralph. It is publicly announced that someone picked a red card. It is publicly announced that Juan knows whether Juan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Summer can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Summer","Esther","Ralph"],"index":56925,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994503856,"difficulty":0.0005496144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angela does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Angela can now know that Lisa can know whether Lisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Delilah","Lisa","Angela","Judith"],"index":43005,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9042547941,"difficulty":0.0957452059}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Brian. James's card is shown to Brian. William's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","William","James"],"index":36295,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988667965,"difficulty":0.0011332035}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Stephanie. Harold's card is shown to Harold. Harold's card is shown to Virginia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harold can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephanie","Harold","Virginia","Mattie"],"index":54375,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994083643,"difficulty":0.0005916357}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Jose's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Theodore can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Theodore","Robbie","Linda"],"index":50755,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989816546,"difficulty":0.0010183454}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Mark. Joseph's card is shown to Mark. Cynthia's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Cynthia","Mark","Joseph"],"index":9858,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989743233,"difficulty":0.0010256767}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annie's card is shown to Barbara. Heather's card is shown to Barbara. Ray's card is shown to Annie. Barbara's card is shown to Annie. Heather's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ray can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ray","Barbara","Annie","Heather"],"index":13196,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977807403,"difficulty":0.0022192597}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard is thirsty. It is publicly announced that Gregory does not know whether Kathleen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Richard can now know whether Kathleen can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Gregory","Kathleen"],"index":30984,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9889007807,"difficulty":0.0110992193}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] 0","hypothesis":"Michael can now know whether Patricia can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Michael","Joseph","Robert"],"index":6658,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8648311496,"difficulty":0.1351688504}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gayle's forehead is muddy. It is publicly announced that Monica's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] Agentd knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Paulette can now know whether Gayle can know that Gayle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Gayle","Monica","Paulette"],"index":25763,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9818442464,"difficulty":0.0181557536}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bonnie knows whether Bonnie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bonnie can now know that Eva is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Bonnie","Emily","Eva"],"index":9571,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972376823,"difficulty":0.0027623177}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shu's card is shown to Shu. Tracy's card is shown to Shu. Shu's card is shown to Mary. Shu's card is shown to Tracy. Tracy's card is shown to Tracy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shu can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shu","Mary","Tracy"],"index":8841,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999361217,"difficulty":0.000638783}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Eva can now know that Andrea can know that Eva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Eva","Richard","Andrea"],"index":17606,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983614087,"difficulty":0.0016385913}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Bradley can now know whether Connie can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Connie","Bradley","John","Thurman"],"index":6918,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999245286,"difficulty":0.000754714}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tamara does not know whether Kathryn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Anna can now know that Kathryn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathryn","Anna","Tamara"],"index":43770,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977408648,"difficulty":0.0022591352}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether or not everyone is thirsty. It is publicly announced that Nancy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Alan can now know that Nancy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Alan","Albert"],"index":63844,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984897375,"difficulty":0.0015102625}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether James is thirsty. It is publicly announced that Harvey knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Margaret can now know that Harvey can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Rebecca","James","Harvey"],"index":27189,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989670515,"difficulty":0.0010329485}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tom knows whether or not nobody's forehead is muddy. It is publicly announced that Lynette knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Tom can now know that Tom's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Lynette","Tom"],"index":32790,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967785478,"difficulty":0.0032214522}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 1 ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 1 ] 0","hypothesis":"Marie can now know that Scott can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Scott","Marie","James"],"index":66398,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9654624462,"difficulty":0.0345375538}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernice does not know whether or not everyone is thirsty. It is publicly announced that Bernice knows whether Bernice is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Laura can now know that Bernice can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laura","Bernice","Chelsea"],"index":22535,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995071888,"difficulty":0.0004928112}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly does not know whether Beverly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Carl can now know that Beverly can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Lauren","Beverly","Joan"],"index":20744,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994164705,"difficulty":0.0005835295}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Brenda can now know that Jason can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brenda","Michael","John","Jason"],"index":50395,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983866215,"difficulty":0.0016133785}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether Vincent is thirsty. It is publicly announced that Glenn does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Anthony can now know whether Cynthia can know whether Glenn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vincent","Glenn","Cynthia","Anthony"],"index":41042,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991680384,"difficulty":0.0008319616}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Hazel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentd knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"David can now know whether Joshua can know that Joshua's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hazel","Mike","Joshua","David"],"index":18446,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992989302,"difficulty":0.0007010698}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cruz's card is shown to Cruz. Kathleen's card is shown to Cruz. Jarod's card is shown to Cruz. Cruz's card is shown to Kathleen. Jane's card is shown to Jane. Cruz's card is shown to Jarod. Jane's card is shown to Jarod. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kathleen can now know that Jarod picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cruz","Kathleen","Jane","Jarod"],"index":46159,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970865846,"difficulty":0.0029134154}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Angela can now know that Elizabeth can know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paula","Elizabeth","Clayton","Angela"],"index":55,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937798381,"difficulty":0.0062201619}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Nellie. John's card is shown to Lisette. Nellie's card is shown to Lisette. Lisette's card is shown to Lisette. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nellie can now know whether John can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Nellie","Lisette"],"index":13505,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994049072,"difficulty":0.0005950928}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Deborah. Claudia's card is shown to Beth. Deborah's card is shown to Claudia. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Deborah can now know whether Beth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deborah","Beth","Claudia","Joann"],"index":53629,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9494460821,"difficulty":0.0505539179}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to James. Jason's card is shown to Jason. James's card is shown to Joey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carlos","James","Jason","Joey"],"index":48308,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989796281,"difficulty":0.0010203719}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Robert. Robert's card is shown to Elizabeth. Elizabeth's card is shown to Christine. Clarence's card is shown to Christine. Christine's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth knows whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Robert can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Elizabeth","Christine","Clarence"],"index":58037,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.987187624,"difficulty":0.012812376}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Edwin can now know that William can know that Edwin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Renea","William","Edwin","Marilyn"],"index":62458,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8755258918,"difficulty":0.1244741082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adam knows whether or not nobody's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that Adam's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"Adam can now know whether David can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","William","Donald","Adam"],"index":51858,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993364215,"difficulty":0.0006635785}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Larry can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Mary","Wayne","Larry"],"index":29632,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983080626,"difficulty":0.0016919374}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Paul. Harold's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Harold knows whether Paul picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Paul can now know whether Harold can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Harold"],"index":17525,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994282126,"difficulty":0.0005717874}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Adam. Morris's card is shown to Adam. Morris's card is shown to Morris. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Morris does not know whether or not everyone picked a red card. It is publicly announced that Morris does not know whether Adam picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Adam can now know whether Morris can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Adam","Morris"],"index":12951,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994545579,"difficulty":0.0005454421}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Willa can now know that Pearl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pearl","Juan","Willa","Mark"],"index":354,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967088699,"difficulty":0.0032911301}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen does not know whether or not everyone's forehead is muddy. It is publicly announced that Troy knows whether Troy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Troy can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Troy","Stephen"],"index":66683,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994848967,"difficulty":0.0005151033}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know whether Margaret can know that Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Ruby","Margaret","Celine"],"index":27145,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9800137281,"difficulty":0.0199862719}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Justin. Arthur's card is shown to Justin. Justin's card is shown to Charles. Robert's card is shown to Charles. Arthur's card is shown to Charles. Robert's card is shown to Robert. Arthur's card is shown to Robert. Justin's card is shown to Arthur. Arthur's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 Agentc:3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 Agentc:3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Arthur can now know whether Arthur picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Justin","Charles","Robert","Arthur"],"index":15871,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7921651006,"difficulty":0.2078348994}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Angie can now know that Sue can know whether Dudley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angie","Sue","Dudley"],"index":414,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993523955,"difficulty":0.0006476045}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald does not know whether Stephanie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Stephanie can now know whether Adam can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephanie","Adam","Donald"],"index":41166,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993713498,"difficulty":0.0006286502}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian does not know whether Anthony is thirsty. It is publicly announced that Doug is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agentc knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Karen can now know whether Anthony can know that Doug is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doug","Brian","Karen","Anthony"],"index":159,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9909404516,"difficulty":0.0090595484}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sara does not know whether Harold is thirsty. It is publicly announced that Sara does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Janet can now know that Darlene can know whether Sara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janet","Sara","Darlene","Harold"],"index":26520,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6590534449,"difficulty":1.6590534449}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Marvin can now know whether Marvin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marvin","Stephan","Bonita","Larry"],"index":39815,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9938509464,"difficulty":0.0061490536}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karla does not know whether or not everyone's forehead is muddy. It is publicly announced that Karla does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Brian can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Karla","Brian"],"index":55778,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999425292,"difficulty":0.000574708}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Enid's card is shown to Enid. Kenneth's card is shown to Enid. Enid's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Enid's card is shown to Alice. Kenneth's card is shown to Alice. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Enid","Kenneth","Alice","Daniel"],"index":59840,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994069338,"difficulty":0.0005930662}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herbert's card is shown to Herbert. Michael's card is shown to Michael. Darren's card is shown to Michael. Michael's card is shown to Darren. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Herbert can now know whether Herbert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Herbert","Michael","Darren"],"index":1713,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6965878606,"difficulty":0.3034121394}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendi does not know whether Wendi's forehead is muddy. It is publicly announced that Laura knows whether or not everyone's forehead is muddy. It is publicly announced that Laura knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Wendi can now know whether Wendi's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wendi","Laura"],"index":45781,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9356975555,"difficulty":0.0643024445}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patrick can now know whether Jonathan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patrick","Natalie","Lee","Jonathan"],"index":7486,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992753863,"difficulty":0.0007246137}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicholas's card is shown to Nicholas. Anthony's card is shown to Nicholas. Lisa's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Anthony picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Lisa can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Nicholas","Anthony"],"index":3780,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994577765,"difficulty":0.0005422235}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Tonya. Tonya's card is shown to David. David's card is shown to David. Tonya's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tonya can now know that David can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tonya","David","William"],"index":7587,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999329567,"difficulty":0.000670433}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cheryl can now know whether Kelly can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cheryl","Kelly","Richard"],"index":3184,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9931573272,"difficulty":0.0068426728}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhonda knows whether or not nobody's forehead is muddy. It is publicly announced that Winston knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Samuel can now know that Samuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Samuel","Winston","Rhonda"],"index":48222,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980623126,"difficulty":0.0019376874}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Calvin can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Calvin","Martha"],"index":5347,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9734924436,"difficulty":0.0265075564}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lillian does not know whether Gayle is thirsty. It is publicly announced that Lillian does not know whether or not everyone is thirsty. It is publicly announced that Lillian does not know whether or not everyone is thirsty. It is publicly announced that Gayle is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] Agentb knows that (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Lillian can now know that Gayle can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gayle","Lillian"],"index":62096,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9979008436,"difficulty":1.9979008436}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Verna's card is shown to Verna. Antoinette's card is shown to Antoinette. Ann's card is shown to Antoinette. Ann's card is shown to Ann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Verna can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Verna","Antoinette","Ann"],"index":38860,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944617152,"difficulty":0.0055382848}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Linda can now know whether Jeff can know whether Elizabeth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Elizabeth","Jeff"],"index":27307,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991764426,"difficulty":0.0008235574}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Melissa can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Chris","Esther","Robert","Melissa"],"index":28176,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999268353,"difficulty":0.000731647}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kendrick does not know whether or not everyone's forehead is muddy. It is publicly announced that Genevieve's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Genevieve can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Genevieve","Blanche","Leonard","Kendrick"],"index":11511,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9071831107,"difficulty":0.0928168893}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. James's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether someone picked a red card. It is publicly announced that Paul does not know whether Paul picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Paul can now know that James can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Paul","Jerry"],"index":1130,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9743697047,"difficulty":0.0256302953}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacey does not know whether or not everyone's forehead is muddy. It is publicly announced that Susan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Stacey can now know whether Susan can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stacey","Susan"],"index":2177,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994404912,"difficulty":0.0005595088}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Helen can now know whether Michael can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louise","Michael","Helen","Margot"],"index":38752,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992496371,"difficulty":0.0007503629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roger does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Leigh can now know that Roger's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leigh","Debra","Roger","Bryant"],"index":57073,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6816095114,"difficulty":1.6816095114}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rita does not know whether Frank is thirsty. It is publicly announced that Scott does not know whether Rita is thirsty. It is publicly announced that Scott does not know whether Frank is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rita can now know that Frank can know that Rita is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rita","Scott","Frank"],"index":53242,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9906747937,"difficulty":0.0093252063}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] 0","hypothesis":"Nicholas can now know that David can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","David","Robert","Nicholas"],"index":63582,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992741942,"difficulty":0.0007258058}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Audrey knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Audrey can now know whether Amy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Audrey","Amy","Mary"],"index":4310,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993552566,"difficulty":0.0006447434}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rosa can now know whether Jon can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosa","Jon","Nancy"],"index":30061,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993910789,"difficulty":0.0006089211}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva does not know whether Eva's forehead is muddy. It is publicly announced that Bobby knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Betty can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Eva","Bobby"],"index":67193,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995058775,"difficulty":0.0004941225}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dalton is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Angela can now know whether Ricardo can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ricardo","Dalton","Angela","William"],"index":39225,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995114803,"difficulty":0.0004885197}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard knows whether Leonard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Paula can now know whether Leonard can know whether Paula's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paula","Edith","Leonard"],"index":2409,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994143248,"difficulty":0.0005856752}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Patricia can now know that Ellen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Theresa","Ellen","Patricia"],"index":3588,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988381267,"difficulty":0.0011618733}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether Rodney's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Lois can now know that Forrest can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Evelyn","Rodney","Forrest","Lois"],"index":15260,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994137287,"difficulty":0.0005862713}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Irma can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gerald","Robert","Irma"],"index":38948,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9917587638,"difficulty":0.0082412362}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edith knows whether Edith is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Assunta can now know that Jordon can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Assunta","Edith","Frank","Jordon"],"index":13563,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994876385,"difficulty":0.0005123615}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"David can now know whether Jason can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Jason","Marianne"],"index":377,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976230264,"difficulty":0.0023769736}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Suzette knows whether or not everyone is thirsty. It is publicly announced that Suzette knows whether Nancy is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Suzette can now know whether Nancy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nancy","Suzette"],"index":37741,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9367608428,"difficulty":1.9367608428}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Edward is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Edward can now know whether Robert can know that Gloria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Edward","Gloria"],"index":37577,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.995125711,"difficulty":0.004874289}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan knows whether Terry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Alan can now know whether Dawn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dawn","Terry","Alan","Estella"],"index":12202,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993999004,"difficulty":0.0006000996}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Constance's card is shown to Kevin. Constance's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that Kevin can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","James","Constance"],"index":36558,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993534684,"difficulty":0.0006465316}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether someone is thirsty. It is publicly announced that Jerilyn does not know whether David is thirsty. It is publicly announced that Jerilyn is thirsty. It is publicly announced that Todd does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] (Agentd knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Todd can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Letha","Jerilyn","David","Todd"],"index":56816,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988069534,"difficulty":0.0011930466}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ira's card is shown to James. Shirley's card is shown to James. Ira's card is shown to Ira. James's card is shown to Shirley. Shirley's card is shown to Shirley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shirley can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Ira","Shirley"],"index":46264,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989861846,"difficulty":0.0010138154}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether Pamela's forehead is muddy. It is publicly announced that Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 1 ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 1 ] 0","hypothesis":"Pamela can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ruth","Pamela"],"index":21616,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999297142,"difficulty":0.000702858}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Chris can now know that Lucy can know that Kristina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chris","Kristina","Shelby","Lucy"],"index":9805,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997567296,"difficulty":0.002432704}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether Jason's forehead is muddy. It is publicly announced that Kimberly's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Jason can now know whether Kimberly can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Jason","Kimberly"],"index":14541,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994472861,"difficulty":0.0005527139}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelley does not know whether Shelley's forehead is muddy. It is publicly announced that Titus does not know whether Titus's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gary can now know whether Titus can know whether Titus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Shelley","Titus"],"index":40094,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9060081244,"difficulty":0.0939918756}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fabian knows whether Brooke's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Jerry can now know that Albina can know that Jerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brooke","Albina","Jerry","Fabian"],"index":53882,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983704686,"difficulty":0.0016295314}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Derrick does not know whether Marjorie is thirsty. It is publicly announced that Kathy does not know whether Barbie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Barbie can now know that Derrick can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathy","Derrick","Marjorie","Barbie"],"index":48857,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990149736,"difficulty":0.0009850264}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane's forehead is not muddy. It is publicly announced that Christopher's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Eunice can now know that Jane can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Jane","Eunice"],"index":49559,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99899441,"difficulty":0.00100559}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentd knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Joseph can now know whether Anthony can know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Dorothy","Cheryl","Joseph"],"index":26915,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8887031078,"difficulty":0.1112968922}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey does not know whether Jeffrey's forehead is muddy. It is publicly announced that Jeffrey does not know whether Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Misty can now know that Nan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Preston","Jeffrey","Misty","Nan"],"index":66369,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956834316,"difficulty":0.0043165684}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ramona does not know whether or not everyone is thirsty. It is publicly announced that Patricia knows whether Ramona is thirsty. It is publicly announced that John does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Patricia can now know that Ramona can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Ramona","John"],"index":35451,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.976257205,"difficulty":0.023742795}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Ronald's card is shown to Michael. Peter's card is shown to Ronald. Ronald's card is shown to Alison. Alison's card is shown to Peter. Peter's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Ronald does not know whether Alison picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Michael can now know that Ronald can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Ronald","Alison","Peter"],"index":32163,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993420243,"difficulty":0.0006579757}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellen does not know whether Miguel is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Brandy can now know that Ellen can know whether Miguel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brandy","Ellen","Miguel"],"index":9435,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941913486,"difficulty":0.0058086514}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether John's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Elizabeth can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Janet","Christopher","John"],"index":30438,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8478855491,"difficulty":0.1521144509}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to Michael. Michael's card is shown to Janice. Janice's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card. It is publicly announced that Nellie does not know whether Nellie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Nellie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nellie","Michael","Janice"],"index":42724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994613528,"difficulty":0.0005386472}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Daniel. Harry's card is shown to Thomas. Daniel's card is shown to Shellie. Harry's card is shown to Shellie. Thomas's card is shown to Harry. Harry's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Harry picked a red card. It is publicly announced that Daniel does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Daniel can now know that Thomas can know whether Shellie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Thomas","Shellie","Harry"],"index":24424,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7385239005,"difficulty":0.2614760995}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ronald","Michael","David"],"index":59029,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994955063,"difficulty":0.0005044937}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Robert's card is shown to Anthony. Robert's card is shown to Stephanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Stephanie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Robert","Stephanie"],"index":53566,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9896019101,"difficulty":0.0103980899}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Annie knows whether Annie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Anthony can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Annie","Anthony"],"index":65910,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993917942,"difficulty":0.0006082058}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robyn does not know whether Jean is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Amos does not know whether Jean is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Jean can now know that Ryan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jean","Robyn","Ryan","Amos"],"index":12933,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977954626,"difficulty":0.0022045374}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Michelle can now know that Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Maryam","Michelle"],"index":11136,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9500538707,"difficulty":1.9500538707}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steve's card is shown to Lynne. Lynne's card is shown to Caitlyn. Caitlyn's card is shown to Caitlyn. Steve's card is shown to Caitlyn. Caitlyn's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Lynne can now know that Steve picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynne","Caitlyn","Steve"],"index":16888,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9634224772,"difficulty":0.0365775228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa does not know whether John is thirsty. It is publicly announced that Teresa is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(3) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kellie can now know whether Gladys can know that Kellie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kellie","Gladys","Teresa","John"],"index":20218,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8920419216,"difficulty":0.1079580784}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Mark can now know that Jason can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jason","Mark"],"index":17896,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9961267114,"difficulty":0.0038732886}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alonzo does not know whether or not everyone is thirsty. It is publicly announced that Alonzo knows whether Alonzo is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lonnie can now know whether Alonzo can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lonnie","Alonzo"],"index":44671,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999463737,"difficulty":0.000536263}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Jonathan can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tanya","Jerry","Jonathan"],"index":18836,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991835952,"difficulty":0.0008164048}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Alfred knows whether someone is thirsty. It is publicly announced that Kevin does not know whether Alfred is thirsty. It is publicly announced that Kevin knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Kevin can now know that Alfred is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["April","Kevin","Alfred"],"index":46753,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9944722056,"difficulty":0.0055277944}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Brandon can now know whether Victoria can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandon","Victoria","Mary","Gary"],"index":58897,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987183809,"difficulty":0.0012816191}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joan knows whether Joan is thirsty. It is publicly announced that Harold does not know whether Shanika is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Harold can now know whether Joan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joan","Harold","Shanika"],"index":28699,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9866924882,"difficulty":0.0133075118}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Wesley can now know whether Marty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wesley","Marty","Courtney"],"index":8147,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994171858,"difficulty":0.0005828142}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Grant knows whether or not everyone's forehead is muddy. It is publicly announced that Alice knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Alice can now know whether Grant can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harriet","Grant","James","Alice"],"index":17324,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994650483,"difficulty":0.0005349517}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy knows whether someone's forehead is muddy. It is publicly announced that Eva knows whether or not nobody's forehead is muddy. It is publicly announced that Eva knows whether Judy's forehead is muddy. It is publicly announced that Rosetta knows whether Rosetta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Judy can now know whether Rosetta can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Judy","Rosetta","Eva"],"index":66728,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992884398,"difficulty":0.0007115602}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexander knows whether Brian's forehead is muddy. It is publicly announced that Preston knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Preston can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Alexander","Brian","Preston"],"index":16861,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993937016,"difficulty":0.0006062984}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elena knows whether or not nobody's forehead is muddy. It is publicly announced that Elena does not know whether Elena's forehead is muddy. It is publicly announced that Elena knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Cathy can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cathy","Elena","Donald"],"index":34678,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982459545,"difficulty":0.0017540455}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that George does not know whether Trey is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lucille can now know that Lucille is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lucille","Joe","Trey","George"],"index":44675,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9959113598,"difficulty":0.0040886402}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Theresa can now know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tammy","Theresa","Jason","Mike"],"index":37003,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970399737,"difficulty":0.0029600263}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Kim. Pamela's card is shown to Kim. Rita's card is shown to Kelly. Rita's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Kim picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Kelly can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kim","Pamela","Kelly","Rita"],"index":6611,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8386051059,"difficulty":1.8386051059}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether David is thirsty. It is publicly announced that Frances does not know whether Julie is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know that Julie can know whether Julie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","David","Elizabeth","Julie"],"index":15455,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.969040215,"difficulty":0.030959785}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Benjamin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Darryl can now know whether Alberto can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alberto","Darryl","Augusta","Benjamin"],"index":38969,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8197836876,"difficulty":1.8197836876}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Kevin. Sandra's card is shown to Sandra. Stephanie's card is shown to Sandra. Kevin's card is shown to Stephanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sandra can now know that Kevin can know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Sandra","Stephanie"],"index":48747,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.852321744,"difficulty":0.147678256}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Filiberto's card is shown to Filiberto. Filiberto's card is shown to Virginia. Virginia's card is shown to Virginia. Virginia's card is shown to Joyce. It is publicly announced that someone picked a red card. It is publicly announced that Joyce knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Virginia can now know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Filiberto","Virginia","Joyce"],"index":67310,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9908969998,"difficulty":0.0091030002}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan does not know whether Derek is thirsty. It is publicly announced that Susan is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Derek can now know whether Susan can know that Derek is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Derek","Latoya","Susan"],"index":3421,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9658265114,"difficulty":0.0341734886}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Darrin is thirsty. It is publicly announced that Michelle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agenta knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Barbara can now know that Darrin can know that Darrin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Michelle","Joseph","Darrin"],"index":40764,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9594858289,"difficulty":0.0405141711}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gordon's card is shown to Carol. Gordon's card is shown to Gordon. It is publicly announced that someone picked a red card. It is publicly announced that Carol picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Carol can now know that Gordon can know whether Gordon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carol","Gordon"],"index":55822,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8953787088,"difficulty":0.1046212912}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Shawn knows whether Rufus's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Shawn can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Shawn","Rufus"],"index":58044,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992984533,"difficulty":0.0007015467}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delia's card is shown to Haywood. Haywood's card is shown to Freddie. Freddie's card is shown to Freddie. Haywood's card is shown to Delia. Freddie's card is shown to Delia. It is publicly announced that someone picked a red card. It is publicly announced that Freddie knows whether Freddie picked a red card. It is publicly announced that Haywood does not know whether Freddie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Delia can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Haywood","Freddie","Delia"],"index":19611,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990391731,"difficulty":0.0009608269}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amelia does not know whether Amelia's forehead is muddy. It is publicly announced that Jesus knows whether or not everyone's forehead is muddy. It is publicly announced that Jesus knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jesus can now know that Jesus's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Amelia","Jesus"],"index":57070,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9642754197,"difficulty":1.9642754197}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to David. Katherine's card is shown to David. David's card is shown to Robert. Robert's card is shown to Robert. Katherine's card is shown to Robert. David's card is shown to Katherine. Christopher's card is shown to Katherine. Christopher's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Katherine picked a red card. It is publicly announced that Christopher does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"David can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Robert","Katherine","Christopher"],"index":38859,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9822922945,"difficulty":0.0177077055}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Jason can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jason","Susan"],"index":24121,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993578792,"difficulty":0.0006421208}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tera's forehead is not muddy. It is publicly announced that Christopher's forehead is muddy. It is publicly announced that Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Fred can now know that Tera's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Fred","Christopher","Tera"],"index":23517,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9207100868,"difficulty":0.0792899132}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kayla's card is shown to Kayla. Edward's card is shown to Kayla. Kayla's card is shown to Edward. Edward's card is shown to Edward. Edward's card is shown to Noreen. Noreen's card is shown to Noreen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kayla can now know whether Edward can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kayla","Edward","Noreen"],"index":34816,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994155169,"difficulty":0.0005844831}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice knows whether Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Michael can now know that Deanna can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deanna","Casey","Michael","Janice"],"index":55272,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993624091,"difficulty":0.0006375909}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to John. John's card is shown to Larry. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether Larry picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"John can now know whether Larry can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Larry"],"index":67155,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999432385,"difficulty":0.000567615}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Kristine can now know that Kristine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marisela","Kristine","Christina"],"index":22412,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980923533,"difficulty":0.0019076467}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Bonnie can now know whether Anthony can know that Anthony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Glenn","Anthony"],"index":21784,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994010925,"difficulty":0.0005989075}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Evelyn knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Evelyn can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ethel","Murray","Evelyn"],"index":21181,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989314675,"difficulty":0.0010685325}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Vanessa. Lawrence's card is shown to Thomas. Vanessa's card is shown to James. Vanessa's card is shown to Lawrence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vanessa can now know that Thomas can know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vanessa","Thomas","James","Lawrence"],"index":64924,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983935952,"difficulty":0.0016064048}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Jean is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Monty can now know whether Jean can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Monty","Jean","Richard"],"index":38885,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994395375,"difficulty":0.0005604625}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tonya is not thirsty. It is publicly announced that Tonya does not know whether David is thirsty. It is publicly announced that Jeffrey does not know whether Hazel is thirsty. It is publicly announced that Jeffrey does not know whether Hazel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Tonya can now know that David can know that Tonya is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","David","Tonya","Hazel"],"index":43159,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964953065,"difficulty":0.0035046935}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Violette does not know whether Tonya is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Tonya can now know whether David can know that Violette is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Violette","Jeanne","Tonya","David"],"index":22720,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9904158115,"difficulty":0.0095841885}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether John is thirsty. It is publicly announced that Candice does not know whether John is thirsty. It is publicly announced that Candice does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Barbara can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","John","Candice"],"index":42396,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9940146804,"difficulty":0.0059853196}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Martha can now know that Russell is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carson","Travis","Russell","Martha"],"index":29097,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.994125843,"difficulty":0.005874157}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Nancy. Tamara's card is shown to Nancy. Nancy's card is shown to Melissa. Melissa's card is shown to Melissa. Nancy's card is shown to Tamara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nancy can now know whether Tamara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Melissa","Tamara"],"index":34548,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.984870851,"difficulty":1.984870851}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest does not know whether Ernest's forehead is muddy. It is publicly announced that Harold's forehead is not muddy. It is publicly announced that Ernest's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] 0","hypothesis":"Ernest can now know whether Harold can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ernest","Thomas","Harold"],"index":6512,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9640278816,"difficulty":0.0359721184}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether Nicholas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Lola can now know that Anna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lola","Nicholas","Anna"],"index":40789,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980899692,"difficulty":0.0019100308}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Diane can now know whether Deon can know that Diane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Diane","Deon"],"index":19696,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994263649,"difficulty":0.0005736351}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Burton's card is shown to Marc. Burton's card is shown to Burton. Joel's card is shown to Burton. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marc can now know that Burton can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marc","Burton","Joel"],"index":51809,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9859765768,"difficulty":0.0140234232}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keisha knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Keisha can now know that Keisha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jane","Alvin","Keisha"],"index":43278,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957736135,"difficulty":0.0042263865}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna does not know whether William is thirsty. It is publicly announced that Cleo is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] 0","hypothesis":"Abe can now know whether Donna can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Donna","Cleo","Abe"],"index":58900,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994859695,"difficulty":0.0005140305}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edwin does not know whether Darlene is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Darlene can now know whether Edwin can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edwin","Kristen","Michele","Darlene"],"index":52456,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994008541,"difficulty":0.0005991459}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"James can now know that Lottie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Lottie","James","Mark"],"index":44920,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993367791,"difficulty":0.0006632209}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Mary can now know that Wendy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wendy","Darby","Mary","Sara"],"index":29832,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9932890534,"difficulty":0.0067109466}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neal knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Edward can now know whether Kathleen can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","Edward","Leslie","Neal"],"index":63603,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992803931,"difficulty":0.0007196069}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen does not know whether Carmen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Carmen can now know that Evelyn can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gregory","Carmen","Helen","Evelyn"],"index":12723,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9897376895,"difficulty":0.0102623105}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Paula can now know that Wilfred can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joanna","Wilfred","Paula","Alice"],"index":38147,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989320636,"difficulty":0.0010679364}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris does not know whether Doris's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] Agentb knows whether (Agentd knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Thomas can now know whether Matthew can know whether Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jane","Thomas","Doris","Matthew"],"index":62406,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8453311324,"difficulty":1.8453311324}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeannie knows whether someone's forehead is muddy. It is publicly announced that May does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jeannie can now know that May can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeannie","Rafael","May"],"index":57232,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6789226532,"difficulty":0.3210773468}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether or not nobody's forehead is muddy. It is publicly announced that Billy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Patricia can now know whether Billy can know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Billy","Patricia"],"index":24930,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994513392,"difficulty":0.0005486608}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Williams can now know whether Refugio can know that Refugio's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruby","Williams","Edward","Refugio"],"index":30155,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5893384218,"difficulty":1.5893384218}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Craig does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Craig can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Craig","Robert","Misty","Richard"],"index":56483,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994695783,"difficulty":0.0005304217}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debra is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Shaunna can now know that Debra can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terry","Debra","Shaunna","James"],"index":11407,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994811416,"difficulty":0.0005188584}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. Lela's card is shown to James. James's card is shown to Erin. Erin's card is shown to Lela. Lela's card is shown to Lela. It is publicly announced that someone picked a red card. It is publicly announced that James picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Erin can now know whether Erin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Erin","Lela"],"index":30891,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8353001475,"difficulty":1.8353001475}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothea's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Barbara can now know that Dorothea can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dorothea","Barbara"],"index":38125,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989485145,"difficulty":0.0010514855}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Keith can now know that Sherlyn can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sherlyn","Keith","Thomas"],"index":20359,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998726666,"difficulty":0.001273334}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Brian can now know whether Gloria can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alejandro","Gloria","Alicia","Brian"],"index":51047,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994138479,"difficulty":0.0005861521}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Andrew is thirsty. It is publicly announced that David does not know whether Andrew is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Andrew can now know that Andrew is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Andrew","Margaret","David"],"index":16013,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6725891232,"difficulty":0.3274108768}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Gary can now know that John can know that Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gary","Philip","John"],"index":17505,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9954746366,"difficulty":0.0045253634}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne knows whether someone's forehead is muddy. It is publicly announced that Doris knows whether Yvonne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Yvonne can now know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Juan","Doris","Helen","Yvonne"],"index":28309,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979585409,"difficulty":0.0020414591}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lee does not know whether Alexander is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Jeffrey is thirsty. It is publicly announced that Lee knows whether Jeffrey is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] (Agentd knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Alexander can now know that Lee is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruben","Jeffrey","Lee","Alexander"],"index":6430,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9507995844,"difficulty":0.0492004156}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Elva can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Elva","Justin","Ashley"],"index":15207,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989330173,"difficulty":0.0010669827}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerry does not know whether or not everyone is thirsty. It is publicly announced that Patricia does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Edyth can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Edyth","Gerry"],"index":35886,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990453124,"difficulty":0.0009546876}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose does not know whether Rose's forehead is muddy. It is publicly announced that Agnes's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know whether Charlyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Agnes","Rose","Charlyn"],"index":25118,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993590713,"difficulty":0.0006409287}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] 0","hypothesis":"Linda can now know whether Virginia can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Virginia"],"index":59495,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994774461,"difficulty":0.0005225539}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nick's forehead is muddy. It is publicly announced that Claudine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Claudine","Mark","Robert","Nick"],"index":34106,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9826892614,"difficulty":0.0173107386}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether Dexter's forehead is muddy. It is publicly announced that George knows whether Dexter's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Dexter can now know that Jeremiah can know whether Jeremiah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Dexter","Robert","Jeremiah"],"index":60038,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992709756,"difficulty":0.0007290244}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether Kathy can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Charles","William","Kathy"],"index":60832,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993348718,"difficulty":0.0006651282}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfonso knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agenta knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Dustin can now know whether Raymond can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dustin","Alfonso","Raymond"],"index":33478,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993056059,"difficulty":0.0006943941}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Serena knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Bobbie can now know whether Serena can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Serena","Kathy","Bobbie","Don"],"index":2011,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993506074,"difficulty":0.0006493926}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angie does not know whether Shanna is thirsty. It is publicly announced that Shanna does not know whether Herbert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Shanna can now know whether Herbert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Herbert","Roger","Shanna","Angie"],"index":50128,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973799586,"difficulty":0.0026200414}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin knows whether Evelyn's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Evelyn can now know whether Erin can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Evelyn","Erin"],"index":54532,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991990924,"difficulty":0.0008009076}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose knows whether Jose is thirsty. It is publicly announced that Van does not know whether Jose is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Jose can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jose","Van"],"index":57681,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990022779,"difficulty":0.0009977221}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is not muddy. It is publicly announced that Donna knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Donna can now know that Catherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Paul","Catherine"],"index":16942,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982541203,"difficulty":0.0017458797}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Rosemary"],"index":10329,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990577102,"difficulty":0.0009422898}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Mamie's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Michael can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Michael","Barbara","Mamie"],"index":25269,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989510775,"difficulty":0.0010489225}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Frank knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Brandon can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Frank","Brandon"],"index":6376,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953527451,"difficulty":0.0046472549}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Laura can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dave","William","Laura"],"index":17330,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9842564464,"difficulty":0.0157435536}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerome's card is shown to Jerome. Dennis's card is shown to Jerome. Jerome's card is shown to Henry. Dennis's card is shown to Dennis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dennis can now know whether Henry can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jerome","Henry","Dennis"],"index":60621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990926981,"difficulty":0.0009073019}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hector's forehead is muddy. It is publicly announced that Hector knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"David can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Hector","David"],"index":46349,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5027677417,"difficulty":0.4972322583}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Ken's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jay can now know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ken","Michael","James","Jay"],"index":54703,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993876219,"difficulty":0.0006123781}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charisse's card is shown to Charles. Charles's card is shown to Charisse. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Charisse","Crystal"],"index":38046,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988926053,"difficulty":0.0011073947}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Charles can now know whether William can know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ellen","Charles","William","Douglas"],"index":5732,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9648262858,"difficulty":0.0351737142}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nathan can now know that James can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nathan","Hugh","James","Mary"],"index":12602,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9820682406,"difficulty":0.0179317594}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Christopher can now know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Larry"],"index":40030,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9956710339,"difficulty":0.0043289661}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sandra can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jean","Sandra","Marc","Ellis"],"index":47692,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9909877181,"difficulty":0.0090122819}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Brian is thirsty. It is publicly announced that Russell knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Mary can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Brian","Russell"],"index":7344,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965726137,"difficulty":0.0034273863}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Jo can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Oscar","Jo","Michael","Mary"],"index":62763,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966308475,"difficulty":0.0033691525}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Angela's card is shown to David. Angela's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Emely does not know whether David picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Brenda does not know whether Brenda picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Brenda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emely","Brenda","David","Angela"],"index":67139,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9785917401,"difficulty":0.0214082599}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Brenda can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rosalind","Richard","Brenda"],"index":34575,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9982593656,"difficulty":0.0017406344}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catherine's card is shown to Catherine. Catherine's card is shown to Evelyn. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn picked a red card. It is publicly announced that Evelyn knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Evelyn can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Catherine","Evelyn"],"index":31006,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994674325,"difficulty":0.0005325675}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Britany. Britany's card is shown to Frank. Deann's card is shown to Deann. Deann's card is shown to Lauren. It is publicly announced that someone picked a red card. It is publicly announced that Lauren does not know whether Frank picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Frank can now know whether Britany can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Britany","Frank","Deann","Lauren"],"index":5419,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994207621,"difficulty":0.0005792379}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maxwell's card is shown to Gerald. Gerald's card is shown to Maxwell. Maxwell's card is shown to Maxwell. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Gerald can now know that Maxwell can know that Gerald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gerald","Maxwell"],"index":11216,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961107373,"difficulty":0.0038892627}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. John's card is shown to William. Florence's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","John","Florence"],"index":14238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.992349267,"difficulty":0.007650733}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Maria can now know that David can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["David","Maria"],"index":37822,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6440511942,"difficulty":1.6440511942}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Eneida can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Eneida","Anne","Mary"],"index":63662,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987953901,"difficulty":0.0012046099}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jesse can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jesse","Raymond","Thomas"],"index":53748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986664057,"difficulty":0.0013335943}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathleen is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Sharyn can now know that Andrew can know that Andrew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharyn","Kathleen","Andrew"],"index":55534,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.949729979,"difficulty":0.050270021}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle knows whether someone's forehead is muddy. It is publicly announced that Ruth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] 0","hypothesis":"Danielle can now know whether Ava can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ava","Danielle","Ruth"],"index":18542,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994484782,"difficulty":0.0005515218}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbra knows whether or not everyone's forehead is muddy. It is publicly announced that Susan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Leann can now know that Barbra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leann","Wanda","Susan","Barbra"],"index":60298,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975935817,"difficulty":0.0024064183}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raul does not know whether Viola is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Shane can now know whether Viola can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daryl","Viola","Raul","Shane"],"index":4070,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9944552779,"difficulty":0.0055447221}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erick does not know whether Edna is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Erick can now know that Edna can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathy","Erick","Edna"],"index":48129,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970567226,"difficulty":0.0029432774}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Robin. Elizabeth's card is shown to Robin. Graciela's card is shown to Elizabeth. Robin's card is shown to Graciela. Robin's card is shown to Rudolph. Elizabeth's card is shown to Rudolph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Graciela can now know whether Graciela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robin","Elizabeth","Graciela","Rudolph"],"index":39790,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6741012931,"difficulty":0.3258987069}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lowell's forehead is muddy. It is publicly announced that Lowell's forehead is muddy. It is publicly announced that Carlos's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Carlos can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicole","Cynthia","Carlos","Lowell"],"index":11570,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985845089,"difficulty":0.0014154911}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Dwight. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dwight can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dwight","Carl","Kathleen"],"index":50460,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989798665,"difficulty":0.0010201335}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mauricio's card is shown to Lora. Lora's card is shown to Mauricio. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Lora can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lora","Mauricio"],"index":42486,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.988319397,"difficulty":0.011680603}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michelle does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know that Heidi can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michelle","Robert","Heidi"],"index":14320,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5467476845,"difficulty":1.5467476845}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda knows whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Linda can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Howard","Linda","Brett"],"index":30996,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994629025,"difficulty":0.0005370975}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Michel can now know that Callie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michel","Callie","Debra"],"index":40652,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988697171,"difficulty":0.0011302829}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kareem's card is shown to Kareem. Patricia's card is shown to Patricia. Joyce's card is shown to Steven. Kareem's card is shown to Steven. Patricia's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joyce can now know that Kareem can know whether Kareem picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Kareem","Patricia","Steven"],"index":4320,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.641346395,"difficulty":1.641346395}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Jean can now know that Sue can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sue","Jean","Leo"],"index":34366,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994347692,"difficulty":0.0005652308}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Shirley's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! 1 ] 0","hypothesis":"Joe can now know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Shirley","Joe"],"index":5484,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9924585223,"difficulty":0.0075414777}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marlin can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Valarie","Mamie","Marlin"],"index":7446,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994953871,"difficulty":0.0005046129}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elnora is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Louis can now know that Michale can know whether Elnora is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louis","Elnora","Michale"],"index":17078,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9528241158,"difficulty":0.0471758842}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Dean's card is shown to Robert. Jason's card is shown to Jason. Dean's card is shown to Dean. It is publicly announced that someone picked a red card. It is publicly announced that Dean does not know whether Robert picked a red card. It is publicly announced that Jason does not know whether Raul picked a red card. It is publicly announced that Dean knows whether someone picked a red card. It is publicly announced that Dean does not know whether Raul picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (Agenta knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Dean can now know whether Robert can know that Raul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Jason","Dean","Raul"],"index":45973,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8648099303,"difficulty":0.1351900697}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jason's card is shown to Clay. Jason's card is shown to Adela. Adela's card is shown to Joshua. Adela's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clay can now know that Joshua picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clay","Adela","Joshua","Jason"],"index":32279,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983831644,"difficulty":0.0016168356}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judy's card is shown to Mark. Mark's card is shown to Kathleen. Judy's card is shown to Kathleen. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Kathleen can now know that Mark can know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Kathleen","Judy"],"index":29074,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5493003726,"difficulty":0.4506996274}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. William's card is shown to Susan. Ethan's card is shown to Susan. Ethan's card is shown to Ethan. Ethan's card is shown to Ann. Ann's card is shown to Ann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susan can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Susan","Ethan","Ann"],"index":62521,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8941711187,"difficulty":1.8941711187}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos knows whether Robert's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"Katie can now know whether Robert can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katie","Donald","Robert","Carlos"],"index":12677,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994601607,"difficulty":0.0005398393}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Latoya knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Alberta can now know that Latoya can know that Alberta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alberta","Latoya","Ashley"],"index":13828,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.966177702,"difficulty":0.033822298}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amber is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Julie can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Don","Julie","Amber"],"index":49963,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995085001,"difficulty":0.0004914999}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ethel's card is shown to David. Ethel's card is shown to Ethel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"David can now know that Ethel can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Ethel"],"index":21863,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994012117,"difficulty":0.0005987883}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Renee is thirsty. It is publicly announced that Linda knows whether someone is thirsty. It is publicly announced that Linda does not know whether Maria is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jonathan can now know that Linda can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Linda","Renee","Jonathan"],"index":27578,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989732504,"difficulty":0.0010267496}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jason knows whether or not nobody's forehead is muddy. It is publicly announced that Jason knows whether Carolyn's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jason can now know that Carolyn can know that Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carolyn","Jason"],"index":44487,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9952118397,"difficulty":0.0047881603}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Joshua. Ann's card is shown to Francisco. Joshua's card is shown to Ann. Ann's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Ann picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Ann can now know whether Joshua can know whether Francisco picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joshua","Francisco","Ann"],"index":65879,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989460111,"difficulty":0.0010539889}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy. It is publicly announced that Eddy knows whether someone's forehead is muddy. It is publicly announced that Eddy knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Eddy can now know whether John can know whether Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Eddy","John"],"index":64488,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989689589,"difficulty":0.0010310411}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lois's card is shown to Lois. Gwendolyn's card is shown to Gwendolyn. It is publicly announced that someone picked a red card. It is publicly announced that Lois does not know whether or not everyone picked a red card. It is publicly announced that Gwendolyn knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Gwendolyn can now know whether Lois can know that Gwendolyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lois","Gwendolyn"],"index":42821,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8349606991,"difficulty":0.1650393009}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antonia knows whether someone's forehead is muddy. It is publicly announced that Antonia knows whether someone's forehead is muddy. It is publicly announced that Dave knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Antonia can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dave","Antonia"],"index":9621,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994562268,"difficulty":0.0005437732}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Georgann can now know that Leif's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Gordon","Georgann","Leif"],"index":6531,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9943984151,"difficulty":0.0056015849}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Javier's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Denise can now know that Michael can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Javier","Denise"],"index":39556,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994334579,"difficulty":0.0005665421}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dianne knows whether Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Dianne can now know that Brian can know that Judson's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alexander","Judson","Dianne","Brian"],"index":32165,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973978996,"difficulty":0.0026021004}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carolyn does not know whether or not everyone is thirsty. It is publicly announced that Carolyn does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Barry can now know that Carolyn can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barry","Carolyn"],"index":41711,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994944334,"difficulty":0.0005055666}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Drew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Dolores can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Dolores","Linda","Drew"],"index":4670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988627434,"difficulty":0.0011372566}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Thomas. Rebecca's card is shown to Lynn. Kendra's card is shown to Kendra. Thomas's card is shown to Rebecca. It is publicly announced that someone picked a red card. It is publicly announced that Lynn does not know whether Thomas picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Thomas picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Thomas can now know whether Lynn can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Lynn","Kendra","Rebecca"],"index":57696,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987427592,"difficulty":0.0012572408}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Letha can now know whether Billy can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Billy","Letha","Robert"],"index":14487,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9778705835,"difficulty":0.0221294165}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ruth can now know whether Phillip can know whether Jessica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Jessica","James","Phillip"],"index":22381,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994083643,"difficulty":0.0005916357}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ira knows whether Paula's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ira can now know that Ira's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ira","Paula","Deborah","Teresa"],"index":27036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955132604,"difficulty":0.0044867396}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dave does not know whether Gerald is thirsty. It is publicly announced that Gerald does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gerald can now know that Gerald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gerald","Mary","Dave"],"index":3676,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9751726985,"difficulty":0.0248273015}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know whether Christopher can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Lindsay","Emily","Mark"],"index":41542,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994038343,"difficulty":0.0005961657}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. Clayton's card is shown to Betty. Betty's card is shown to Clayton. Barbara's card is shown to Clayton. William's card is shown to Clayton. Barbara's card is shown to Barbara. William's card is shown to Barbara. Betty's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that Barbara knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3,4 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Barbara can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Clayton","Barbara","William"],"index":29996,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942071438,"difficulty":0.0057928562}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether or not nobody's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Teresa can now know that Robert can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kristie","Christopher","Teresa","Robert"],"index":62886,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993021488,"difficulty":0.0006978512}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia knows whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robyn can now know that Jonathan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robyn","Jonathan","Patricia","James"],"index":24099,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974996448,"difficulty":0.0025003552}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather does not know whether Roberto is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Heather can now know whether Jason can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rachel","Jason","Roberto","Heather"],"index":7285,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993036985,"difficulty":0.0006963015}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Jeffrey. Christina's card is shown to Jeffrey. Doris's card is shown to Mary. Mary's card is shown to Mary. Mary's card is shown to Christina. Christina's card is shown to Christina. It is publicly announced that someone picked a red card. It is publicly announced that Doris does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Doris can now know that Jeffrey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeffrey","Doris","Mary","Christina"],"index":18999,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9912840128,"difficulty":0.0087159872}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Dorathy can now know that Anita can know whether Ashley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anita","Ashley","Dorathy"],"index":35361,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9790109992,"difficulty":0.0209890008}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ryan can now know that Ryan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shelley","Larry","Ryan","George"],"index":39982,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9490451217,"difficulty":0.0509548783}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Jean. Jean's card is shown to Joey. Jean's card is shown to Robert. Joey's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Jean knows whether Jean picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jean can now know whether Jean picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jean","Joey","Robert"],"index":63017,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.973906219,"difficulty":0.026093781}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Angela. Lacie's card is shown to Angela. Cheryl's card is shown to Angela. Chassidy's card is shown to Cheryl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Angela can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chassidy","Angela","Lacie","Cheryl"],"index":18921,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989129305,"difficulty":0.0010870695}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael is thirsty. It is publicly announced that Ralph does not know whether or not everyone is thirsty. It is publicly announced that Ralph does not know whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Daniel can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Christopher","Michael","Ralph"],"index":15198,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994729161,"difficulty":0.0005270839}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joel is not thirsty. It is publicly announced that Theodore does not know whether Louis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Theodore can now know whether Joel can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Angela","Joel","Theodore"],"index":39788,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999494791,"difficulty":0.000505209}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Walter's card is shown to Walter. It is publicly announced that someone picked a red card. It is publicly announced that Walter knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Walter can now know that Donald can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donald","Walter"],"index":55877,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9061483741,"difficulty":1.9061483741}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew does not know whether Maryalice is thirsty. It is publicly announced that Tyson does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Maryalice can now know that Maryalice is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matthew","Maryalice","Rosemary","Tyson"],"index":27208,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7724627852,"difficulty":0.2275372148}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tonia does not know whether Charles is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"Tonia can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Ada","Tonia","Kenneth"],"index":6039,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993846416,"difficulty":0.0006153584}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Ervin knows whether or not nobody's forehead is muddy. It is publicly announced that Herbert knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Ervin can now know whether Herbert can know whether Ervin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Ervin","James","Herbert"],"index":561,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992665648,"difficulty":0.0007334352}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Karen can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Heather","Melinda","David"],"index":13163,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981586337,"difficulty":0.0018413663}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Theresa can now know whether Theresa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Kenneth","Jody","Theresa"],"index":49714,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9765500426,"difficulty":0.0234499574}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kendra's card is shown to Philip. Sidney's card is shown to Philip. Micheal's card is shown to Kendra. Philip's card is shown to Sidney. Sidney's card is shown to Micheal. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Micheal can now know whether Sidney can know that Philip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Philip","Kendra","Sidney","Micheal"],"index":14262,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9315169454,"difficulty":1.9315169454}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisca's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Lynda can now know whether Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lynda","Francisca","James","Edward"],"index":43737,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999443233,"difficulty":0.000556767}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Patricia. Patricia's card is shown to Nicole. Adam's card is shown to Adam. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Nicole can know whether Adam picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Nicole","Adam","Shawn"],"index":27157,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7636412978,"difficulty":1.7636412978}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juan knows whether or not nobody is thirsty. It is publicly announced that Juan does not know whether Sheldon is thirsty. It is publicly announced that Sheldon knows whether Juan is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sheldon can now know whether Juan can know whether Sheldon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sheldon","Juan"],"index":5743,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989135265,"difficulty":0.0010864735}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Cassandra. Cassandra's card is shown to Cassandra. Jose's card is shown to Cassandra. Ronald's card is shown to Jose. Cassandra's card is shown to Jose. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cassandra can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","Cassandra","Jose"],"index":53936,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989439845,"difficulty":0.0010560155}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Zina knows whether or not everyone's forehead is muddy. It is publicly announced that Alyssa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentd knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Alyssa can now know that Daniel can know that Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Teresa","Daniel","Zina","Alyssa"],"index":36253,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9913713932,"difficulty":0.0086286068}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Magdalena does not know whether Ida is thirsty. It is publicly announced that Wayne does not know whether Magdalena is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Patrick can now know whether Ida is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wayne","Patrick","Magdalena","Ida"],"index":1729,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9968783855,"difficulty":0.0031216145}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell does not know whether or not everyone's forehead is muddy. It is publicly announced that Russell does not know whether Russell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Pearlie can now know that Russell's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","John","Pearlie","Russell"],"index":25514,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7058917284,"difficulty":0.2941082716}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. Kerry's card is shown to Kimberly. It is publicly announced that someone picked a red card. It is publicly announced that Jessica picked a black card. It is publicly announced that Jessica does not know whether Kimberly picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jessica can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kerry","Jessica","Kimberly"],"index":21723,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994630218,"difficulty":0.0005369782}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. Clifford's card is shown to Clifford. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clifford can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Curtis","Clifford","Michael","Martha"],"index":734,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9929305315,"difficulty":0.0070694685}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edward's card is shown to Minerva. Minerva's card is shown to Edward. Minerva's card is shown to Anna. Edward's card is shown to Anna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anna can now know whether Edward can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Minerva","Edward","Anna"],"index":37061,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994034767,"difficulty":0.0005965233}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Margaret can now know whether Sarah can know that Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sarah","Margaret","John"],"index":14712,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9376046062,"difficulty":1.9376046062}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Ashley's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ashley can now know whether John can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ashley","Annabelle","John"],"index":777,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999358952,"difficulty":0.000641048}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Jeffery can now know that Daniel can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeffery","Daniel"],"index":48962,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982370138,"difficulty":0.0017629862}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to James. James's card is shown to John. John's card is shown to John. Ida's card is shown to John. James's card is shown to Alan. Ida's card is shown to Alan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether John can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","John","Ida","Alan"],"index":34943,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999309659,"difficulty":0.000690341}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Virginia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Charles can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wayne","Virginia","Doreen","Charles"],"index":31583,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990110397,"difficulty":0.0009889603}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Judy can now know whether Donna can know that Judy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Judy","Donna"],"index":10952,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993872643,"difficulty":0.0006127357}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Corrine's card is shown to Robert. Tammy's card is shown to Robert. Robert's card is shown to Corrine. Robert's card is shown to Tammy. It is publicly announced that someone picked a red card. It is publicly announced that Tammy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Corrine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Corrine","Tammy"],"index":33789,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990447164,"difficulty":0.0009552836}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Oscar's forehead is muddy. It is publicly announced that Audrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Audrey can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Oscar","Kenneth","Audrey","Robert"],"index":18295,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992893934,"difficulty":0.0007106066}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy's forehead is not muddy. It is publicly announced that Dorothy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! ~(2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Stephanie can now know whether Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Stephanie","Dorothy"],"index":13214,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991926551,"difficulty":0.0008073449}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Ryan can now know that Ryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Ryan","Mark","Michael"],"index":44722,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981848598,"difficulty":0.0018151402}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amber's card is shown to James. James's card is shown to Amber. Amber's card is shown to Amber. Nichol's card is shown to Amber. Amber's card is shown to Nichol. Joaquin's card is shown to Joaquin. It is publicly announced that someone picked a red card. It is publicly announced that Joaquin picked a red card. It is publicly announced that James picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"James can now know that Amber picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Amber","Nichol","Joaquin"],"index":38963,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6930367351,"difficulty":0.3069632649}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"John can now know that Lynne can know that Roberto's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Lynne","Roberto"],"index":43736,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997612834,"difficulty":0.002387166}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty. It is publicly announced that Dawn knows whether David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Kathleen can now know that James can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","James","David","Dawn"],"index":8445,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984177351,"difficulty":0.0015822649}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Rachel can now know whether Christopher can know whether Rachel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christopher","Rachel"],"index":35619,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994384646,"difficulty":0.0005615354}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Barbara's card is shown to Lola. Lola's card is shown to Lola. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Barbara can now know that Lola can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barbara","Lola"],"index":26597,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7723222971,"difficulty":0.2276777029}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Armanda does not know whether Lance is thirsty. It is publicly announced that Franklin does not know whether Armanda is thirsty. It is publicly announced that Lance does not know whether Franklin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Armanda can now know that Armanda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susana","Franklin","Lance","Armanda"],"index":48935,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9747602344,"difficulty":0.0252397656}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lydia can now know whether Richard can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Lydia","Delilah"],"index":57601,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993911982,"difficulty":0.0006088018}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Trula knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Glenn can now know that Blanche can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Blanche","Trula","Glenn"],"index":45684,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989614487,"difficulty":0.0010385513}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Jim's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Robert can now know that Jim can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jim","Robert"],"index":22346,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989487529,"difficulty":0.0010512471}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Lori knows whether someone is thirsty. It is publicly announced that Jonathan does not know whether Lori is thirsty. It is publicly announced that Jonathan knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jonathan can now know whether Brenda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brenda","Jonathan","Lori"],"index":77,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984480143,"difficulty":0.0015519857}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Stephanie is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Marvis can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Stephanie","Marvis"],"index":53850,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989797473,"difficulty":0.0010202527}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathaniel knows whether Nathaniel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Nathaniel can now know whether Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nathaniel","Michelle"],"index":14372,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994131327,"difficulty":0.0005868673}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Eric can now know whether Gilbert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Ronald","Lise","Gilbert"],"index":64578,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9927661419,"difficulty":0.0072338581}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roland's card is shown to Joseph. Mable's card is shown to Mable. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Mable","Roland"],"index":46344,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951620698,"difficulty":0.0048379302}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bobby does not know whether William is thirsty. It is publicly announced that Bobby is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(1) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Bobby can now know that William can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bobby","Janet","William"],"index":31172,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989369512,"difficulty":0.0010630488}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cassandra's card is shown to Cassandra. Cassandra's card is shown to Sarah. Sarah's card is shown to Sarah. Matthew's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Cassandra does not know whether Robert picked a red card. It is publicly announced that Matthew picked a red card. It is publicly announced that Sarah does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Sarah can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cassandra","Sarah","Robert","Matthew"],"index":34968,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8818668127,"difficulty":0.1181331873}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Carrie. Carrie's card is shown to Mark. Mark's card is shown to Marquis. Robert's card is shown to Marquis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know whether Robert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carrie","Mark","Robert","Marquis"],"index":30120,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993483424,"difficulty":0.0006516576}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gerald can now know that Gary can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcy","Geoffrey","Gerald","Gary"],"index":19213,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992739558,"difficulty":0.0007260442}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Diane can now know that Jose can know whether Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Diane","Allen","Jose"],"index":25706,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6503702402,"difficulty":0.3496297598}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy. It is publicly announced that Carl does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Justin can now know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carl","Justin","Donald","Gerald"],"index":4124,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9964912534,"difficulty":0.0035087466}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Jody can now know whether Anna can know that Sheila's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jody","Sheila","Anna"],"index":37791,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9858797193,"difficulty":0.0141202807}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jared does not know whether Kylie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Patricia can now know that Jared can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jared","Patricia","Kylie","Harold"],"index":33647,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9950829744,"difficulty":0.0049170256}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Kenneth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Billy","Kenneth"],"index":45592,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988049269,"difficulty":0.0011950731}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amber is not thirsty. It is publicly announced that Holly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] Agenta knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"John can now know that Holly can know that Amber is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Bryan","Amber","Holly"],"index":42467,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955507517,"difficulty":0.0044492483}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Christopher can now know whether Arlene can know whether Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Arlene","Christopher"],"index":6128,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993388057,"difficulty":0.0006611943}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susie does not know whether Derek is thirsty. It is publicly announced that Susie does not know whether Jill is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Susie can now know that Derek can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Derek","Don","Jill","Susie"],"index":24060,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997304678,"difficulty":0.002695322}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Travis does not know whether Jason is thirsty. It is publicly announced that Travis does not know whether Sam is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jason can now know whether Travis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Travis","Sam"],"index":3529,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9727503657,"difficulty":0.0272496343}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Dominic can now know that Lori can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dominic","Lori","Nicole","Jan"],"index":29902,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989727736,"difficulty":0.0010272264}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ernest does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Sergio can now know whether Ernest can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sergio","Ernest"],"index":14435,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994420409,"difficulty":0.0005579591}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha does not know whether Glen is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"Glen can now know whether Martha is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Glen","Juana","Martha","Albert"],"index":21631,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9906650782,"difficulty":0.0093349218}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Alana can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chantelle","Amy","Silva","Alana"],"index":16228,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990064502,"difficulty":0.0009935498}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Gloria can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jesus","Israel","Maria","Gloria"],"index":25862,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992676377,"difficulty":0.0007323623}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to John. Larry's card is shown to Larry. Patricia's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Linda can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","John","Larry","Patricia"],"index":36599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9915508032,"difficulty":0.0084491968}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether Jarrett's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Jarrett can now know that Kelly can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Jarrett","Barbara","Evelyn"],"index":839,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989451766,"difficulty":0.0010548234}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kendra knows whether Kendra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Rodney can now know that James can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","James","Kendra","Rodney"],"index":12116,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9578652978,"difficulty":1.9578652978}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marion's forehead is not muddy. It is publicly announced that Pearl does not know whether Pearl's forehead is muddy. It is publicly announced that Pearl knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Randy can now know that Pearl can know whether Pearl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Randy","Marion","Pearl"],"index":36650,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8090915084,"difficulty":0.1909084916}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diana does not know whether Dennis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Diana can now know that Josephine can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Diana","Josephine","Dennis"],"index":28234,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989861846,"difficulty":0.0010138154}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether Nicholas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Linda can now know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Linda","Larry","Nicholas"],"index":38295,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981125593,"difficulty":0.0018874407}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mariana knows whether or not everyone's forehead is muddy. It is publicly announced that Kristi does not know whether Kristi's forehead is muddy. It is publicly announced that Mariana does not know whether Mariana's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Barry can now know that Kristi can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Isaiah","Kristi","Barry","Mariana"],"index":46859,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8036678433,"difficulty":0.1963321567}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adam does not know whether or not everyone is thirsty. It is publicly announced that Beulah knows whether Adam is thirsty. It is publicly announced that Beulah is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Adam can now know whether Beulah can know whether Beulah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Beulah","Adam"],"index":65893,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984939098,"difficulty":0.0015060902}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Margaret does not know whether Bernardo is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Margaret can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bernardo","Margaret","Thomas","Judith"],"index":35558,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994577765,"difficulty":0.0005422235}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Arnulfo can now know whether Charles can know that Arnulfo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Linda","Arnulfo"],"index":27708,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9705817699,"difficulty":0.0294182301}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Margart's card is shown to Jennifer. Jennifer's card is shown to Margart. Matthew's card is shown to Margart. Jennifer's card is shown to Barbara. Margart's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether Margart can know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Matthew","Margart","Barbara"],"index":30681,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998747468,"difficulty":0.001252532}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Van does not know whether Robin is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Robin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Van can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kevin","Van","Robin"],"index":49207,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954633117,"difficulty":0.0045366883}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Philip can now know that Mario can know that Mario's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mario","Philip"],"index":48763,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9956362844,"difficulty":0.0043637156}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana's forehead is muddy. It is publicly announced that Anthony knows whether Dana's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"David can now know that Dana can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Christine","Dana","Anthony"],"index":433,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990301132,"difficulty":0.0009698868}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know that Shaina can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","James","Shaina"],"index":61892,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992932081,"difficulty":0.0007067919}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Eileen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Eileen can now know that Kenneth can know that Eileen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Eileen","Kenneth"],"index":12154,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936161041,"difficulty":0.0063838959}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Rebecca can now know that Keith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebecca","Joan","Keith","Evan"],"index":13499,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.992379427,"difficulty":0.007620573}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francine's card is shown to Francine. Francine's card is shown to Amanda. Amanda's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that Francine does not know whether Amanda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Francine can now know whether Amanda can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Francine","Amanda"],"index":66146,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.98171103,"difficulty":1.98171103}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jack does not know whether Dorothy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Katherine can now know that Bruce can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katherine","Jack","Bruce","Dorothy"],"index":57137,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993861914,"difficulty":0.0006138086}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether or not everyone is thirsty. It is publicly announced that Evelyn does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jennifer can now know that Evelyn can know that Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","George","Evelyn"],"index":36171,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9632091522,"difficulty":0.0367908478}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Odell. David's card is shown to David. Odell's card is shown to James. Odell's card is shown to Randall. David's card is shown to Randall. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Odell can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Odell","David","James","Randall"],"index":11628,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9918640852,"difficulty":0.0081359148}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sylvia is thirsty. It is publicly announced that Sylvia knows whether Sylvia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"John can now know whether Sylvia can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Ernest","Sylvia"],"index":26414,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994906187,"difficulty":0.0005093813}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether Margaret's forehead is muddy. It is publicly announced that Margaret knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Clay can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Margaret","Clay"],"index":65233,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989150763,"difficulty":0.0010849237}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gayle is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Nancy can now know that Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Mary","Gayle","Ruth"],"index":63228,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975373745,"difficulty":0.0024626255}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether or not everyone's forehead is muddy. It is publicly announced that Gary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Dean can now know whether Gary can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dean","Gary"],"index":274,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9947631955,"difficulty":0.0052368045}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacqueline's card is shown to Tamara. Jacqueline's card is shown to Jacqueline. Tamara's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jacqueline can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tamara","Jacqueline","Robert"],"index":30148,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967239499,"difficulty":0.0032760501}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Manuel can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gayle","Barbara","Manuel"],"index":18462,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9920286536,"difficulty":0.0079713464}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mildred knows whether Lynelle's forehead is muddy. It is publicly announced that Mildred's forehead is not muddy. It is publicly announced that James knows whether Mildred's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Lynelle can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mildred","Lynelle","James"],"index":45031,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998886764,"difficulty":0.001113236}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathryn knows whether Kathryn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"William can now know whether Camille can know whether Carrie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Carrie","Camille","Kathryn"],"index":59622,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999147296,"difficulty":0.000852704}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Betty can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Robert","Betty"],"index":32909,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988718629,"difficulty":0.0011281371}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Kevin's forehead is muddy. It is publicly announced that Keith's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Keith can now know whether Teresita can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Teresita","Kevin","Keith"],"index":16209,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994429946,"difficulty":0.0005570054}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly knows whether Sherry is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Kimberly can now know that Sherry can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kimberly","Sherry"],"index":19369,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.982236743,"difficulty":1.982236743}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Matthew. Anne's card is shown to Anne. Anne's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"John can now know that Matthew can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Matthew","Anne","John"],"index":62714,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981665611,"difficulty":0.0018334389}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brad knows whether or not nobody's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Brad can now know whether John can know that Brad's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brad","John"],"index":24616,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5932915211,"difficulty":0.4067084789}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Lisa is not thirsty. It is publicly announced that Lisa knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Lisa can now know that Robert can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Lisa"],"index":44723,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976871014,"difficulty":0.0023128986}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Elizabeth. Mary's card is shown to William. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","William","Mary"],"index":10730,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998599112,"difficulty":0.001400888}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Kevin can now know whether Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Adrienne","Kevin"],"index":127,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9923920035,"difficulty":0.0076079965}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"John can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amy","John","Milton"],"index":31582,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992158413,"difficulty":0.0007841587}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy. It is publicly announced that Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] 0","hypothesis":"Michael can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Kelly","Christopher"],"index":53737,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969137907,"difficulty":0.0030862093}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Matthew can now know that Brenda can know that Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Timothy","Matthew","Robert"],"index":20758,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9592518806,"difficulty":0.0407481194}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mercedes does not know whether Jeffrey is thirsty. It is publicly announced that Mercedes does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mercedes can now know that Mercedes is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mercedes","Michael","Jeffrey"],"index":56078,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6902409196,"difficulty":1.6902409196}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Delbert's card is shown to Stephen. Delbert's card is shown to Delbert. Amanda's card is shown to Delbert. Stephen's card is shown to Amanda. Delbert's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that Amanda knows whether Delbert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Delbert can now know that Amanda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephen","Delbert","Amanda"],"index":62405,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9872186184,"difficulty":0.0127813816}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Georgeanna does not know whether Elsie is thirsty. It is publicly announced that Ricky does not know whether Elsie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Georgeanna can now know whether Elsie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Georgeanna","Ricky","Elsie"],"index":67412,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9105522037,"difficulty":0.0894477963}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Coral's card is shown to Andrea. Andrea's card is shown to Coral. It is publicly announced that someone picked a red card. It is publicly announced that Coral knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Andrea can now know that Coral can know whether Andrea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrea","Coral"],"index":13883,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8634062409,"difficulty":0.1365937591}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cindy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Paul can now know whether Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cindy","Paul","Frederick","Victor"],"index":15322,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9673060775,"difficulty":0.0326939225}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Calvin's card is shown to Calvin. Joseph's card is shown to Calvin. Randall's card is shown to Calvin. Joseph's card is shown to Joseph. Randall's card is shown to Randall. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Calvin can now know that Randall picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Calvin","Joseph","Randall"],"index":14300,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973276854,"difficulty":0.0026723146}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kimberly can now know that Rosa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Garland","Rosa","Charlotte","Kimberly"],"index":26393,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9914064407,"difficulty":0.0085935593}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Lynn can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anne","Robert","Lynn"],"index":24612,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993788004,"difficulty":0.0006211996}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Tamika can now know that Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tamika","Michelle","Charles"],"index":32938,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9708653688,"difficulty":0.0291346312}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel does not know whether or not everyone's forehead is muddy. It is publicly announced that Amanda knows whether or not nobody's forehead is muddy. It is publicly announced that Manuel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Amanda can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rebecca","Manuel","Amanda"],"index":46374,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999486804,"difficulty":0.000513196}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert is not thirsty. It is publicly announced that Robert does not know whether Alisa is thirsty. It is publicly announced that Sue does not know whether John is thirsty. It is publicly announced that Sue does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Alisa can now know whether Robert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sue","Alisa","Robert","John"],"index":39747,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994750619,"difficulty":0.0005249381}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katherine","Leslie","Rita","Jerry"],"index":49691,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994117022,"difficulty":0.0005882978}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cynthia does not know whether Brandy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Edward can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brandy","Edward","Cynthia","Dorthy"],"index":29851,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993383288,"difficulty":0.0006616712}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edith does not know whether Richard is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Madaline can now know that Richard can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Madaline","Edith"],"index":26819,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994792342,"difficulty":0.0005207658}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Richard can now know that Gidget can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Gidget","Irene","John"],"index":605,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9938743711,"difficulty":0.0061256289}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joesph knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Lasandra can now know whether John can know whether Joyce's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lasandra","Joyce","Joesph","John"],"index":20524,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993450046,"difficulty":0.0006549954}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Robert can now know that Danielle can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Danielle","Patricia"],"index":23153,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988507032,"difficulty":0.0011492968}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"John can now know that Delma can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Delma","Joseph","David","John"],"index":61563,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976114035,"difficulty":0.0023885965}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","William","Jerry","Juan"],"index":32898,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993257523,"difficulty":0.0006742477}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Teresa can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betty","Teresa","Karen"],"index":18930,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990084767,"difficulty":0.0009915233}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hope knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Hope can now know that Hope's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Todd","Hope","Laura"],"index":40426,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.984431982,"difficulty":0.015568018}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Tanya can now know that Tasha can know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Tanya","Tasha","Robert"],"index":44505,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9912488461,"difficulty":0.0087511539}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Shannon. Harold's card is shown to Harold. Harold's card is shown to Christine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harold can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shannon","Harold","Christine","Delores"],"index":28332,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989810586,"difficulty":0.0010189414}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy. It is publicly announced that William knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rod does not know whether Rod's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rod can now know that Lewis can know that Lewis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rod","William","Lewis"],"index":34326,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9980521202,"difficulty":1.9980521202}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Larry. Daniel's card is shown to Herman. Herman's card is shown to Herman. It is publicly announced that someone picked a red card. It is publicly announced that Larry does not know whether Larry picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","James","Daniel","Herman"],"index":13076,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8677440286,"difficulty":0.1322559714}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jeffrey can now know whether Constance can know that Corazon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeffrey","Constance","Corazon"],"index":1697,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.960775435,"difficulty":0.039224565}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tim's card is shown to Julia. Fred's card is shown to Tim. It is publicly announced that someone picked a red card. It is publicly announced that Earl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Earl can now know that Julia can know that Julia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julia","Earl","Tim","Fred"],"index":48520,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9830649495,"difficulty":0.0169350505}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dillon's card is shown to Marva. Marva's card is shown to Ruthie. Katie's card is shown to Dillon. Marva's card is shown to Katie. Ruthie's card is shown to Katie. It is publicly announced that someone picked a red card. It is publicly announced that Ruthie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Marva can now know that Katie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marva","Ruthie","Dillon","Katie"],"index":33329,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989821315,"difficulty":0.0010178685}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara does not know whether Steven is thirsty. It is publicly announced that Donald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] Agentd knows that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 2 ] 0","hypothesis":"Steven can now know that Barbara can know that Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chelsea","Donald","Barbara","Steven"],"index":61038,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9594336748,"difficulty":0.0405663252}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know that Nancy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Margaret","Nancy","Bobby"],"index":12274,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992741942,"difficulty":0.0007258058}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Marion. Marjorie's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Marion knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Marion can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marion","Marjorie"],"index":55800,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994231462,"difficulty":0.0005768538}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. John's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher does not know whether Christopher picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that John knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Christopher can now know whether John can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Christopher"],"index":3566,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9947240949,"difficulty":0.0052759051}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nettie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Nettie can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Trisha","Nettie","Jesse"],"index":33887,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977545142,"difficulty":0.0022454858}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loretta's forehead is not muddy. It is publicly announced that Marvin knows whether Loretta's forehead is muddy. It is publicly announced that Loretta knows whether Marvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Marvin can now know that Bonnie can know that Marvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marvin","Bonnie","Loretta"],"index":24785,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974412918,"difficulty":0.0025587082}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Judy can now know that Ashley can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ashley","Judy"],"index":22399,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989540577,"difficulty":0.0010459423}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Willie can now know that Julia can know whether Julia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julia","Sarah","Willie","Elvira"],"index":50649,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994082451,"difficulty":0.0005917549}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Bobby does not know whether or not everyone is thirsty. It is publicly announced that Bobby does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Leo can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Leo","Bobby"],"index":18014,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994472861,"difficulty":0.0005527139}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Laverne's forehead is muddy. It is publicly announced that Laverne knows whether Robert's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agentc knows that (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Richard can now know that Laverne can know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Laverne","Richard"],"index":65112,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.992980063,"difficulty":0.007019937}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debra's card is shown to Debra. Michael's card is shown to Debra. Debra's card is shown to Robert. Robert's card is shown to Robert. Michael's card is shown to Robert. Debra's card is shown to Michael. Robert's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Debra can now know that Michael can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debra","Robert","Michael"],"index":6310,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958561063,"difficulty":0.0041438937}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tina's card is shown to Joseph. Joseph's card is shown to Lois. Lois's card is shown to Lois. Tina's card is shown to Lois. Lois's card is shown to Tina. Tina's card is shown to Tina. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lois can now know whether Tina can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Lois","Tina"],"index":32100,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9842748046,"difficulty":0.0157251954}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether James is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"James can now know whether Mary can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","James"],"index":4532,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994495511,"difficulty":0.0005504489}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Penny does not know whether Penny's forehead is muddy. It is publicly announced that Jennifer knows whether Penny's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Penny can now know whether Glenn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Penny","Jennifer","Trinidad","Glenn"],"index":25490,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991722107,"difficulty":0.0008277893}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Al knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Al can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Al","Robert"],"index":64016,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9915739894,"difficulty":0.0084260106}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Sara. Allen's card is shown to Sara. Sara's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Timothy does not know whether Timothy picked a red card. It is publicly announced that Sara knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Timothy can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sara","Timothy","Allen"],"index":16400,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993927479,"difficulty":0.0006072521}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank does not know whether Scott is thirsty. It is publicly announced that Hal knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Frank can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Hal","Richard","Scott"],"index":29361,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988051653,"difficulty":0.0011948347}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alan does not know whether Barbara is thirsty. It is publicly announced that Barbara knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Nicole can now know that Linda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicole","Linda","Barbara","Alan"],"index":8439,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984439015,"difficulty":0.0015560985}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Louise. Louise's card is shown to Alma. Alma's card is shown to Alma. Steven's card is shown to Alma. Steven's card is shown to Steven. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know whether Alma can know that Alma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Louise","Alma","Steven"],"index":32532,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6458678842,"difficulty":1.6458678842}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lasonya's card is shown to Lasonya. Lori's card is shown to Lasonya. Richard's card is shown to Lasonya. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lori can now know that Lori picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lasonya","Lori","Richard"],"index":21947,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9827210307,"difficulty":0.0172789693}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristy knows whether Kristy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Angel can now know that Kristy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kristy","Angel","Harold","Jeanne"],"index":50346,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9316931367,"difficulty":0.0683068633}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Evette's card is shown to Evette. Wanda's card is shown to Wanda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Evette","Wanda"],"index":5018,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993625283,"difficulty":0.0006374717}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lee's card is shown to Robert. Larry's card is shown to Larry. Robert's card is shown to Lee. It is publicly announced that someone picked a red card. It is publicly announced that Lee does not know whether Lee picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Larry can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Larry","Lee"],"index":6525,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9863305092,"difficulty":0.0136694908}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Leticia can now know whether Kathy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathy","Jessica","Leticia"],"index":29994,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99948138,"difficulty":0.00051862}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ralph knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ralph can now know that Ralph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Hubert","Jim"],"index":55770,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9484904408,"difficulty":0.0515095592}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pam does not know whether Michael is thirsty. It is publicly announced that Pam is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Jose can now know that Michael can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Jose","Pam"],"index":52485,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9967477322,"difficulty":0.0032522678}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Sarah knows whether Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"John can now know whether Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sarah","Mabel","John","Ralph"],"index":27561,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994516969,"difficulty":0.0005483031}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bobby knows whether or not nobody is thirsty. It is publicly announced that Donna does not know whether Bobby is thirsty. It is publicly announced that Lorrie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Lorrie can now know that Bobby can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donna","Bobby","Lorrie"],"index":23821,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994606376,"difficulty":0.0005393624}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Quinn can know that Karla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Karla","Quinn","Michael"],"index":6139,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975245595,"difficulty":0.0024754405}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Luke can now know that Verna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Luke","Scott","Verna","Penny"],"index":12293,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954136014,"difficulty":0.0045863986}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Debra can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Kathleen","Debra"],"index":64403,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7606953979,"difficulty":0.2393046021}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether someone's forehead is muddy. It is publicly announced that Gary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"Gary can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Norman","Gary","Sharon","Matthew"],"index":6160,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994650483,"difficulty":0.0005349517}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Sonya can now know that Kellie can know that Kellie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sonya","Susan","Kellie"],"index":23195,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9899920821,"difficulty":0.0100079179}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yan's card is shown to Yan. Yan's card is shown to Patti. Patti's card is shown to Patti. It is publicly announced that someone picked a red card. It is publicly announced that Patti knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Yan does not know whether Patti picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Yan can now know that Patti can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Yan","Patti"],"index":37965,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6851365566,"difficulty":0.3148634434}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sally does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Sally can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stanley","Patricia","Adam","Sally"],"index":41094,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994108677,"difficulty":0.0005891323}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Gretchen can now know that Melinda can know that Melinda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Mistie","Melinda","Gretchen"],"index":31869,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982341528,"difficulty":0.0017658472}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas does not know whether Nicholas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jacob can now know that Bernadette can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jacob","Bernadette","Nicholas","William"],"index":51133,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993069172,"difficulty":0.0006930828}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josephine knows whether Josephine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agenta knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Lawrence can now know whether Josephine can know that Jamie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Patrick","Jamie","Josephine"],"index":12462,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994451404,"difficulty":0.0005548596}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sonia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Sonia can now know that Catherine can know whether Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sonia","Catherine","Kenneth"],"index":13978,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5651639104,"difficulty":1.5651639104}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Era knows whether Lisa's forehead is muddy. It is publicly announced that Era knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Era can now know that Era's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Louise","Pat","Lisa","Era"],"index":2190,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974871874,"difficulty":0.0025128126}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Libby's forehead is not muddy. It is publicly announced that Christina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ashley can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christina","Libby","Ashley"],"index":51474,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989408851,"difficulty":0.0010591149}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Melvin can now know whether Christopher can know whether Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Melvin","Christopher"],"index":36687,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993861914,"difficulty":0.0006138086}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clifton does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Ollie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clifton","Ollie","Chad"],"index":13244,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9892732501,"difficulty":0.0107267499}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Brian can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Robert","Brian","Joseph"],"index":19859,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989991784,"difficulty":0.0010008216}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"June can now know that David can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["David","June"],"index":4495,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998914361,"difficulty":0.001085639}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Arturo can now know whether Betty can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Martin","Arturo"],"index":18727,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999327302,"difficulty":0.000672698}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annette's card is shown to Debbie. Julie's card is shown to Debbie. Annette's card is shown to Annette. Debbie's card is shown to Julie. Annette's card is shown to Julie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debbie","Annette","Julie"],"index":7104,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998967886,"difficulty":0.001032114}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonnie's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jacquelyn knows whether Bonnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Bonnie can now know that Jacquelyn can know whether Bonnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jacquelyn","Joseph","Bonnie"],"index":34625,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999380827,"difficulty":0.000619173}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Catherine can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dora","Monica","Claude","Catherine"],"index":34785,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993415475,"difficulty":0.0006584525}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heather can now know that Dorothy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lester","Dorothy","Heather","Manuel"],"index":15334,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988170862,"difficulty":0.0011829138}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erik knows whether Charlene's forehead is muddy. It is publicly announced that Erik's forehead is not muddy. It is publicly announced that Lashanda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Lashanda can now know whether Charlene can know whether Erik's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lashanda","Charlene","Joel","Erik"],"index":13729,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991108775,"difficulty":0.0008891225}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rick's card is shown to Carol. Jaime's card is shown to Jaime. Rick's card is shown to Jaime. Cindy's card is shown to Jaime. Cindy's card is shown to Rick. Rick's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Rick does not know whether Rick picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Cindy can now know whether Rick can know that Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Jaime","Rick","Cindy"],"index":53839,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.84882164,"difficulty":0.15117836}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnnie's card is shown to Johnnie. Maria's card is shown to Johnnie. Johnnie's card is shown to Tina. Tina's card is shown to Maria. Maria's card is shown to Maria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tina can now know that Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Johnnie","Tina","Maria"],"index":16076,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948764443,"difficulty":0.0051235557}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Melissa can now know whether Christine can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Melissa","Christine"],"index":67611,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993335605,"difficulty":0.0006664395}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Julia's forehead is muddy. It is publicly announced that Julia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Julia can now know that Kimberly can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kimberly","Julia"],"index":43619,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959158301,"difficulty":0.0040841699}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Oliver can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Oliver","Bethany","Harry","Linda"],"index":59441,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987904429,"difficulty":0.0012095571}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Wayne. Leana's card is shown to Leana. Wayne's card is shown to Norman. Leana's card is shown to Robin. It is publicly announced that someone picked a red card. It is publicly announced that Wayne does not know whether Leana picked a red card. It is publicly announced that Robin knows whether Leana picked a red card. It is publicly announced that Wayne does not know whether Norman picked a red card. It is publicly announced that Leana knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Norman can now know whether Wayne can know whether Robin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","Leana","Norman","Robin"],"index":10236,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986352324,"difficulty":0.0013647676}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jennifer knows whether Doris's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Doris can now know whether Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Doris","Jennifer","Debbie"],"index":27616,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999360621,"difficulty":0.000639379}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Tonya can now know that James can know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Kevin","Jordan","Tonya"],"index":30052,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977468848,"difficulty":0.0022531152}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nan knows whether Nan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Nan can now know that Martha can know that Nan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bettina","Nicholas","Martha","Nan"],"index":29828,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967104197,"difficulty":0.0032895803}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mckenzie knows whether someone is thirsty. It is publicly announced that Everette does not know whether Andre is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Everette can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mckenzie","Everette","Jared","Andre"],"index":19750,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993675351,"difficulty":0.0006324649}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles knows whether Charles is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Charles can now know whether June can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","June","Eric"],"index":56402,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994787574,"difficulty":0.0005212426}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leona's card is shown to Leona. Anthony's card is shown to Leona. Leona's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shirley can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leona","Shirley","Anthony"],"index":8882,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993002415,"difficulty":0.0006997585}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gloria can now know whether Daniel can know whether Gloria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shamika","Daniel","Gloria"],"index":26001,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958031774,"difficulty":0.0041968226}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wanda knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Gloria can now know whether Carolyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wanda","Larry","Carolyn","Gloria"],"index":4102,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966781139,"difficulty":0.0033218861}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether Larry's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Hector can now know whether Larry can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hector","Larry"],"index":18115,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994462132,"difficulty":0.0005537868}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Milton's card is shown to Milton. Pedro's card is shown to Pedro. Milton's card is shown to Shirley. Pedro's card is shown to Josh. It is publicly announced that someone picked a red card. It is publicly announced that Milton does not know whether Pedro picked a red card. It is publicly announced that Josh knows whether Pedro picked a red card. It is publicly announced that Milton does not know whether Shirley picked a red card. It is publicly announced that Pedro knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Milton can now know that Shirley can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Milton","Pedro","Shirley","Josh"],"index":7134,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9856851101,"difficulty":0.0143148899}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Abigail does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Abigail can now know that Jeffrey is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Abigail","Jeffrey"],"index":25348,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9912899733,"difficulty":0.0087100267}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Saul's card is shown to Angela. Marcela's card is shown to Angela. Saul's card is shown to Josephine. Josephine's card is shown to Marcela. Marcela's card is shown to Marcela. It is publicly announced that someone picked a red card. It is publicly announced that Marcela picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Saul can now know that Josephine can know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Saul","Josephine","Marcela"],"index":18998,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9849328399,"difficulty":0.0150671601}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cindy knows whether Alma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Adrienne can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alma","Cindy","Peggy","Adrienne"],"index":59734,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994421601,"difficulty":0.0005578399}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marco does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Barbara can now know whether Marco can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marco","Barbara"],"index":55080,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999338448,"difficulty":0.000661552}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Maria. Maria's card is shown to Christopher. Christopher's card is shown to Christopher. Maria's card is shown to Richard. Christopher's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know that Darla picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Christopher","Darla","Richard"],"index":64448,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985697269,"difficulty":0.0014302731}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Lucile. Louise's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Daniel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Daniel can now know whether Lucile can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucile","Daniel","Louise"],"index":52553,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8700281382,"difficulty":0.1299718618}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lindsay knows whether or not everyone is thirsty. It is publicly announced that Miguel knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lindsay can now know whether Miguel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Delia","Miguel","Lindsay"],"index":60756,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9089178443,"difficulty":0.0910821557}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. Laura's card is shown to Jessica. Barbara's card is shown to Laura. Laura's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessica","Laura","Barbara"],"index":58907,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949352145,"difficulty":0.0050647855}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Catherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] 0","hypothesis":"Sherri can now know whether Sherri's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Catherine","Sherri","Misty"],"index":21464,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999301672,"difficulty":0.000698328}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Lino is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Lino can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lino","Ronald"],"index":28889,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988732934,"difficulty":0.0011267066}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Elsa's forehead is muddy. It is publicly announced that Elsa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Estella can now know whether John can know that Estella's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Estella","John","Elsa"],"index":29774,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993790388,"difficulty":0.0006209612}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] 0","hypothesis":"John can now know that David can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","John"],"index":750,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999355495,"difficulty":0.000644505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lindsey does not know whether Rita is thirsty. It is publicly announced that Jerry is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] 0","hypothesis":"Thelma can now know whether Rita can know whether Rita is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Thelma","Rita","Lindsey"],"index":56163,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988273978,"difficulty":0.0011726022}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Roy. Brandon's card is shown to Brandon. Roy's card is shown to Lawrence. Brandon's card is shown to Annetta. It is publicly announced that someone picked a red card. It is publicly announced that Roy does not know whether Brandon picked a red card. It is publicly announced that Annetta knows whether Brandon picked a red card. It is publicly announced that Roy does not know whether Lawrence picked a red card. It is publicly announced that Brandon knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Roy can now know that Lawrence can know whether Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roy","Brandon","Lawrence","Annetta"],"index":2311,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8034885526,"difficulty":0.1965114474}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harold's card is shown to Harold. Jennifer's card is shown to Harold. Harold's card is shown to Jennifer. Ray's card is shown to Jennifer. Jennifer's card is shown to Ray. Harold's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer picked a black card. It is publicly announced that Harold does not know whether Teresa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Harold can now know whether Teresa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Jennifer","Ray","Teresa"],"index":2721,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999302268,"difficulty":0.000697732}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Bonnie can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Juan","Gerald","Bonnie"],"index":12251,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994674325,"difficulty":0.0005325675}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to John. John's card is shown to Lisa. Tracy's card is shown to Lisa. John's card is shown to Tracy. Tracy's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Tracy can now know that Lisa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Lisa","Tracy"],"index":26671,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993652701,"difficulty":0.0006347299}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maureen knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Nancy can now know whether Maureen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Maureen","John","Nancy"],"index":26018,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9749914408,"difficulty":0.0250085592}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether or not nobody's forehead is muddy. It is publicly announced that Carolyn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Pamela can now know whether Andrea's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andrea","Carolyn","Pamela"],"index":31043,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993994236,"difficulty":0.0006005764}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Esmeralda can now know whether Brianna can know that Brianna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brianna","Esmeralda","Carmen","Mark"],"index":22355,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968730807,"difficulty":0.0031269193}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Richard's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know that Melissa can know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melissa","David","Richard"],"index":10895,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976854324,"difficulty":0.0023145676}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Tim. James's card is shown to Jeannie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tim can now know whether Lee can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tim","Lee","Jeannie","James"],"index":20690,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.980581522,"difficulty":0.019418478}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Diane can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Diane","Anton"],"index":60434,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9893501401,"difficulty":0.0106498599}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Carolyn. Carolyn's card is shown to Alexis. Alexis's card is shown to Alexis. Alexis's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether Alexis can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Alexis","Richard"],"index":28452,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993938208,"difficulty":0.0006061792}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elton's card is shown to Clarence. Clarence's card is shown to Grover. Grover's card is shown to Grover. Clarence's card is shown to Elton. Grover's card is shown to Elton. It is publicly announced that someone picked a red card. It is publicly announced that Grover knows whether Grover picked a red card. It is publicly announced that Clarence does not know whether Grover picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Clarence can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clarence","Grover","Elton"],"index":9371,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994459748,"difficulty":0.0005540252}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fredrick knows whether Terry's forehead is muddy. It is publicly announced that Terry's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Fredrick can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Fredrick","Terry"],"index":45895,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993597865,"difficulty":0.0006402135}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erica knows whether or not nobody's forehead is muddy. It is publicly announced that Erica knows whether Erica's forehead is muddy. It is publicly announced that Veronica's forehead is muddy. It is publicly announced that Jacqueline knows whether Veronica's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jacqueline can now know whether Philip can know that Erica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Veronica","Erica","Jacqueline","Philip"],"index":55763,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994723201,"difficulty":0.0005276799}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emanuel's card is shown to Juanita. Erica's card is shown to Juanita. Ruth's card is shown to Juanita. Juanita's card is shown to Erica. Erica's card is shown to Erica. Erica's card is shown to Ruth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emanuel can now know whether Juanita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Emanuel","Erica","Ruth"],"index":19470,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7010813951,"difficulty":1.7010813951}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Christina can now know that Darla can know whether Darla's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirlee","John","Darla","Christina"],"index":24556,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959706664,"difficulty":0.0040293336}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Edward can now know whether Carolyn can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Edward","Carolyn"],"index":42691,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991045594,"difficulty":0.0008954406}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether or not everyone's forehead is muddy. It is publicly announced that Roy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Karen can now know whether Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Sandra","Roy","Jeffrey"],"index":30301,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999445498,"difficulty":0.000554502}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Christopher","John","Phillip"],"index":9231,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8934299946,"difficulty":0.1065700054}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hattie's forehead is not muddy. It is publicly announced that Juan knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Juan can now know that Hattie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juan","Thomas","Hattie","Kathleen"],"index":43708,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994837046,"difficulty":0.0005162954}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether Daniel can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Clark","Daniel","Frederick"],"index":41361,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9883660078,"difficulty":0.0116339922}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ophelia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Dave can now know that Ophelia can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachel","Dave","Ophelia","Connie"],"index":41855,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8762412667,"difficulty":1.8762412667}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alfred's card is shown to Alfred. Lela's card is shown to Alfred. Georgianna's card is shown to Alfred. Alfred's card is shown to Kathleen. Lela's card is shown to Kathleen. Georgianna's card is shown to Lela. Alfred's card is shown to Georgianna. Lela's card is shown to Georgianna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kathleen can now know whether Alfred can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfred","Kathleen","Lela","Georgianna"],"index":9428,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848874807,"difficulty":0.0151125193}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradford does not know whether Bradford's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Lawrence can now know that Elizabeth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lawrence","Elizabeth","Jacqueline","Bradford"],"index":44038,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9883602858,"difficulty":0.0116397142}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Gary can now know whether Dorothy can know that Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Rachel","Gary","Bonnie"],"index":56626,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.723357141,"difficulty":1.723357141}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Barbara can now know whether Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Margaret","Evelyn"],"index":44327,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9868645072,"difficulty":0.0131354928}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Julia can now know that Joe can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Larry","Joe","Julia"],"index":44935,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991810918,"difficulty":0.0008189082}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristi's card is shown to Kyong. Kyong's card is shown to Kristi. It is publicly announced that someone picked a red card. It is publicly announced that Kyong knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Kristi can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kyong","Kristi"],"index":6868,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7173641324,"difficulty":0.2826358676}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to Cassie. Cassie's card is shown to Linda. Janice's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that Janice does not know whether Linda picked a red card. It is publicly announced that Cassie does not know whether Cassie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Janice can now know that Cassie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cassie","Linda","Janice"],"index":38896,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994165897,"difficulty":0.0005834103}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Melissa can now know that Clifford can know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Clifford","Courtney","Melissa"],"index":52706,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980925918,"difficulty":0.0019074082}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Nicholas. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Nicholas picked a red card. It is publicly announced that David does not know whether Nicholas picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Nicholas can now know whether David can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nicholas","David"],"index":65208,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9741520882,"difficulty":0.0258479118}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karon knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jennifer can now know that Karon can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Karon","Jennifer"],"index":48480,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986849427,"difficulty":0.0013150573}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mona is thirsty. It is publicly announced that Betty does not know whether Cynthia is thirsty. It is publicly announced that Dina knows whether or not nobody is thirsty. It is publicly announced that Dina is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Betty can now know whether Dina can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Betty","Dina","Mona"],"index":38874,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995055199,"difficulty":0.0004944801}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christine knows whether Jerry is thirsty. It is publicly announced that Christine knows whether Jerry is thirsty. It is publicly announced that Jerry knows whether Christine is thirsty. It is publicly announced that Christine knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Christine can now know that Jerry can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christine","Jerry"],"index":13933,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9242162108,"difficulty":1.9242162108}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Prudence's card is shown to Prudence. Helen's card is shown to Prudence. Darrell's card is shown to Prudence. Helen's card is shown to Helen. Darrell's card is shown to Helen. Prudence's card is shown to Darrell. Helen's card is shown to Darrell. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Helen can now know that Darrell can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Prudence","Helen","Darrell"],"index":19447,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992732406,"difficulty":0.0007267594}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Mildred is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Mildred can now know that Maria can know that Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mildred","Maria","Rose"],"index":51445,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.990737021,"difficulty":0.009262979}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Christopher's card is shown to Barbara. Barbara's card is shown to Christopher. Christopher's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Barbara knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Barbara can now know that Christopher can know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barbara","Christopher"],"index":3837,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9747530818,"difficulty":0.0252469182}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Michelle can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dawn","Angela","Michelle","Maple"],"index":26586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998908639,"difficulty":0.001091361}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jeffrey can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Darcy","Jeffrey"],"index":20645,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988294244,"difficulty":0.0011705756}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth does not know whether Charles is thirsty. It is publicly announced that Mary is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Mary","Charles"],"index":5641,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986463189,"difficulty":0.0013536811}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Arthur. Jared's card is shown to Nora. Nora's card is shown to Jared. It is publicly announced that someone picked a red card. It is publicly announced that Nora does not know whether Arthur picked a red card. It is publicly announced that Nora picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Arthur can now know that Nora can know whether Jared picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Arthur","Nora","Jared"],"index":65246,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9203265309,"difficulty":0.0796734691}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marietta is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Marietta can now know whether Mary can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marietta","Mary","Russell"],"index":10203,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9967355132,"difficulty":0.0032644868}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Gladys. James's card is shown to James. Janet's card is shown to James. Gladys's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Gladys does not know whether Gladys picked a red card. It is publicly announced that James picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Janet can now know that Gladys can know that Janet picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gladys","James","Janet"],"index":3218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9719681144,"difficulty":0.0280318856}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Billy does not know whether Duane is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Duane can now know that Billy can know whether Martha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Duane","Karen","Billy","Martha"],"index":63542,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979435802,"difficulty":0.0020564198}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maryjane's card is shown to Maryjane. Kristy's card is shown to Maryjane. Charles's card is shown to Maryjane. Charles's card is shown to Bradley. Maryjane's card is shown to Kristy. Bradley's card is shown to Charles. Kristy's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Kristy picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Kristy can now know that Charles can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maryjane","Bradley","Kristy","Charles"],"index":47170,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985528588,"difficulty":0.0014471412}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Emma. Emma's card is shown to Janice. Arthur's card is shown to Janice. Janice's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Emma does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Emma can now know that Janice can know whether Emma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emma","Janice","Arthur"],"index":34981,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.892663002,"difficulty":0.107336998}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Emily can now know whether Judy can know that Judy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vanessa","Emily","Judy","Brian"],"index":47415,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991663694,"difficulty":0.0008336306}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Janice can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Janice","James"],"index":62015,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990383387,"difficulty":0.0009616613}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ada does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Ada can now know whether Sally is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Ada","Sally","Suzanne"],"index":4230,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941763878,"difficulty":0.0058236122}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tabetha's card is shown to Tabetha. Tabetha's card is shown to George. George's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Tabetha knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Denise can now know whether George can know whether Tabetha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tabetha","George","Denise","Mary"],"index":35312,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990556836,"difficulty":0.0009443164}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Glen's card is shown to Janice. Margaret's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that Glen knows whether Margaret picked a red card. It is publicly announced that Glen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! 1 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! 1 ] 0","hypothesis":"Glen can now know whether Glen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Glen","Janice","Margaret"],"index":65021,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9609564543,"difficulty":0.0390435457}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Andrew can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deborah","Mary","Annette","Andrew"],"index":59330,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983224273,"difficulty":0.0016775727}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald knows whether or not nobody is thirsty. It is publicly announced that Donald does not know whether Heather is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Heather can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Heather","Christy"],"index":67539,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955932498,"difficulty":0.0044067502}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terrence knows whether or not everyone's forehead is muddy. It is publicly announced that Sandra knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Sandra can now know that Terrence can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clifton","Terrence","Abbie","Sandra"],"index":34276,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990280867,"difficulty":0.0009719133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dusty does not know whether Darin is thirsty. It is publicly announced that Darin does not know whether Homer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"David can now know whether Darin can know whether Homer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Homer","David","Darin","Dusty"],"index":51924,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991656542,"difficulty":0.0008343458}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Marilyn can know that Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marilyn","Kevin","Robert"],"index":61616,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975450635,"difficulty":0.0024549365}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra does not know whether Sandra's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Sandra can now know whether Jennifer can know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sandra","Jennifer"],"index":44242,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9628126025,"difficulty":1.9628126025}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Valerie can now know whether Edward can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Edward","Valerie","Eleanor"],"index":4579,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991320968,"difficulty":0.0008679032}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Charles can now know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Lloyd"],"index":45641,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.951230526,"difficulty":0.048769474}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Paul can now know whether Barbara can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","James","Barbara","Ralph"],"index":63565,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991482496,"difficulty":0.0008517504}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know whether Paul can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","George","Charles","Paul"],"index":19448,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.984320879,"difficulty":0.015679121}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Wendy can now know that Jennifer can know whether Wendy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Wendy","Brian","Christopher"],"index":6698,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9875939488,"difficulty":0.0124060512}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Merle does not know whether or not everyone is thirsty. It is publicly announced that Calvin does not know whether Sharon is thirsty. It is publicly announced that Sharon knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Calvin can now know that Sharon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Merle","Sharon","Calvin"],"index":27770,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9151220322,"difficulty":0.0848779678}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jayme does not know whether Jayme's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Teresa can now know that Goldie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jayme","Teresa","Goldie","Eric"],"index":32097,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994196892,"difficulty":0.0005803108}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Camille's forehead is not muddy. It is publicly announced that Khalilah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Camille can now know that Khalilah can know that Camille's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melania","Khalilah","Camille","Jason"],"index":32748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9752750397,"difficulty":0.0247249603}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Debra can now know that Jason can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jason","Albert","Christina","Debra"],"index":66254,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989756346,"difficulty":0.0010243654}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cassandra does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Michael can now know that Virginia can know whether Virginia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cassandra","Michael","Virginia","Sarah"],"index":66960,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.979493916,"difficulty":1.979493916}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Brian's card is shown to Brian. Brian's card is shown to Andrew. Linda's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Brian","Andrew","William"],"index":7756,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7796804309,"difficulty":0.2203195691}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allison does not know whether or not everyone's forehead is muddy. It is publicly announced that Allison does not know whether Allison's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Allison can now know that Ruby can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Allison","Ruby"],"index":4203,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990175962,"difficulty":0.0009824038}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentd knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know whether Ronald can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Abel","Ronald","Randy","David"],"index":55388,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9981939197,"difficulty":0.0018060803}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Toni is not thirsty. It is publicly announced that James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"James can now know whether Gene can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gene","Mary","Toni","James"],"index":51740,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993727803,"difficulty":0.0006272197}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jo's card is shown to Jo. Jo's card is shown to Norine. Norine's card is shown to Julio. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julio can now know that Norine can know that Julio picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jo","Norine","Julio"],"index":64920,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980314374,"difficulty":0.0019685626}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Gabrielle can now know whether Amy can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Gabrielle","Amy"],"index":62761,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990068078,"difficulty":0.0009931922}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harriet's card is shown to Harriet. Taylor's card is shown to Harriet. Harriet's card is shown to Taylor. Taylor's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Harriet does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Linda can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harriet","Taylor","Linda"],"index":67170,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984745383,"difficulty":0.0015254617}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diana does not know whether or not everyone is thirsty. It is publicly announced that Henry does not know whether Maritza is thirsty. It is publicly announced that Diana does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Maritza can now know whether Diana can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diana","Maritza","Henry"],"index":64622,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994809031,"difficulty":0.0005190969}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katie knows whether Chasity's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Katie can now know whether Chasity can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Desiree","Chasity","Katie"],"index":37714,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993216991,"difficulty":0.0006783009}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dale. Laura's card is shown to Dana. Dorothy's card is shown to Dana. Dale's card is shown to Laura. Dale's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Laura knows whether or not everyone picked a red card. It is publicly announced that Dana knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Dale can now know that Dana can know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dale","Dana","Laura","Dorothy"],"index":35455,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9537006617,"difficulty":0.0462993383}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michael can now know that Lauren's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","Michael","Ronald","Lauren"],"index":11824,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977439642,"difficulty":0.0022560358}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robin's card is shown to Joe. Carolyn's card is shown to Joe. Carolyn's card is shown to Robin. Carolyn's card is shown to Carolyn. It is publicly announced that someone picked a red card. It is publicly announced that Robin does not know whether or not everyone picked a red card. It is publicly announced that Carolyn does not know whether Robin picked a red card. It is publicly announced that Carolyn does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Joe can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joe","Robin","Carolyn"],"index":8852,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994490743,"difficulty":0.0005509257}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty does not know whether Betty's forehead is muddy. It is publicly announced that Anibal knows whether Anibal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Anibal can now know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anibal","Karen","Betty"],"index":26663,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9902950525,"difficulty":0.0097049475}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Santo's card is shown to Santo. Santo's card is shown to Marsha. It is publicly announced that someone picked a red card. It is publicly announced that Marsha does not know whether Marsha picked a red card. It is publicly announced that Santo does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Santo can now know whether Marsha can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Santo","Marsha"],"index":63940,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990946054,"difficulty":0.0009053946}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie's forehead is not muddy. It is publicly announced that Bobby knows whether Bobby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Melanie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Melanie","Rachael","Bobby","Christopher"],"index":15150,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994766116,"difficulty":0.0005233884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annie knows whether Annie's forehead is muddy. It is publicly announced that Stormy's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kenneth can now know whether Annie can know that Annie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Stormy","Annie"],"index":50317,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9795976281,"difficulty":0.0204023719}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachael knows whether Ida's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Masako can now know that Masako's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rafael","Ida","Masako","Rachael"],"index":7330,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980710149,"difficulty":0.0019289851}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Michael can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Walter","Kenneth","Michael"],"index":11386,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9847970009,"difficulty":0.0152029991}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arturo knows whether Arturo is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Arturo can now know that Paul is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Arturo","Beatrice","Paul","George"],"index":47572,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9968630075,"difficulty":0.0031369925}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey is thirsty. It is publicly announced that Jeffrey knows whether Jeffrey is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jeffrey can now know whether Rose can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raymond","Rose","Jeffrey"],"index":54439,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9955904484,"difficulty":0.0044095516}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Eva. Margaret's card is shown to Eva. Kenneth's card is shown to Kenneth. Carol's card is shown to Margaret. Eva's card is shown to Margaret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know that Eva picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Eva","Kenneth","Margaret"],"index":64218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969991446,"difficulty":0.0030008554}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether Beatrice's forehead is muddy. It is publicly announced that Kenny does not know whether Kenny's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kenny can now know that Robin can know whether Kenny's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenny","Beatrice","Robin"],"index":35112,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9477405548,"difficulty":0.0522594452}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erica does not know whether Bryan is thirsty. It is publicly announced that Sheldon does not know whether Erica is thirsty. It is publicly announced that Erica does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Bryan can now know whether Erica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sheldon","Erica","Bryan","Mathew"],"index":41142,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8757396936,"difficulty":0.1242603064}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Sandra can now know that Cheryl can know that Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Cheryl","Kelly","Amanda"],"index":41904,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947169423,"difficulty":0.0052830577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bonnie knows whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether Mary can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bonnie","Inez","Mary","Charles"],"index":21068,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.992638588,"difficulty":0.007361412}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Mark is thirsty. It is publicly announced that James knows whether or not everyone is thirsty. It is publicly announced that James does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mark can now know that Richard can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Richard","James"],"index":65524,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7032881975,"difficulty":1.7032881975}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Katelyn knows whether Deanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Deanne can now know whether Deangelo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deangelo","Deanne","Katelyn","Stella"],"index":50639,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994526505,"difficulty":0.0005473495}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lawrence does not know whether Gary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Richard can now know whether Lawrence is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Lawrence","Gary"],"index":58998,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9804340005,"difficulty":0.0195659995}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yvonne's card is shown to Yvonne. Elsie's card is shown to Nicholas. Nicholas's card is shown to Elsie. Elsie's card is shown to Elsie. Yvonne's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Donna knows whether Yvonne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Yvonne can now know whether Donna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Yvonne","Nicholas","Elsie","Donna"],"index":3517,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971334934,"difficulty":0.0028665066}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Virgina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Allan can now know whether Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Virgina","Elizabeth","Donald","Allan"],"index":47555,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994264841,"difficulty":0.0005735159}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Justina's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"Justina can now know that Justina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Justina","Mark","James"],"index":26729,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9666437507,"difficulty":0.0333562493}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Madeline can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Madeline","Robert","William","Kevin"],"index":29927,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988456964,"difficulty":0.0011543036}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Elois can now know whether Megan can know that Betty is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elois","Megan","John","Betty"],"index":64036,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9898542762,"difficulty":0.0101457238}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jacob's card is shown to Virginia. Virginia's card is shown to Mary. Jacob's card is shown to Vicki. Vicki's card is shown to Vicki. It is publicly announced that someone picked a red card. It is publicly announced that Virginia does not know whether Virginia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that Jacob can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Virginia","Jacob","Mary","Vicki"],"index":33365,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981513619,"difficulty":0.0018486381}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steve's card is shown to Martin. Martin's card is shown to Deborah. Martin's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Steve does not know whether Steve picked a red card. It is publicly announced that Deborah knows whether or not everyone picked a red card. It is publicly announced that Deborah picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 2 ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Deborah can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Martin","Deborah","Steve"],"index":33965,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964398742,"difficulty":0.0035601258}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wayne knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Clayton can now know whether Wayne can know whether Wayne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clayton","Wayne","James","Jessica"],"index":23696,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986634254,"difficulty":0.0013365746}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Catarina's card is shown to Catarina. Dan's card is shown to Dan. It is publicly announced that someone picked a red card. It is publicly announced that Bonnie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Dan can now know that Dan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Catarina","Dan","Bonnie"],"index":26306,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8082428575,"difficulty":0.1917571425}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Adam's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] 0","hypothesis":"Adam can now know that Mary can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Adam"],"index":60022,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999392271,"difficulty":0.000607729}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Guadalupe. Kellie's card is shown to Guadalupe. Guadalupe's card is shown to Kellie. Kellie's card is shown to Kellie. Linda's card is shown to Kellie. Kellie's card is shown to Linda. Linda's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Guadalupe can now know that Kellie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Guadalupe","Kellie","Linda","Jennifer"],"index":36729,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.994002521,"difficulty":0.005997479}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Rocky. Malcolm's card is shown to Erna. Paul's card is shown to Erna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Malcolm can now know that Malcolm picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Malcolm","Rocky","Erna","Paul"],"index":38041,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940328002,"difficulty":0.0059671998}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ramon is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Ramon can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ramon","Dale","Don"],"index":59879,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995068312,"difficulty":0.0004931688}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Douglas can now know that Jean can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Jean","Douglas"],"index":7854,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983149767,"difficulty":0.0016850233}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Geneva can now know that Laurie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Laurie","Arlene","Geneva","Christine"],"index":39179,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9166053534,"difficulty":0.0833946466}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Billie. Billie's card is shown to Juanita. Juanita's card is shown to Juanita. It is publicly announced that someone picked a red card. It is publicly announced that Billie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Juanita can now know that Juanita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Billie","Juanita"],"index":10324,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.696727097,"difficulty":0.303272903}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Eloise's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Linda can now know that Eloise can know whether Eloise's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melissia","Eloise","Linda"],"index":27056,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.874684751,"difficulty":0.125315249}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darlene knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Paul can now know whether Robert can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Robert","Paul","Darlene"],"index":39700,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993466735,"difficulty":0.0006533265}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Melvin. Jesse's card is shown to Melvin. Melvin's card is shown to Jesse. Jesse's card is shown to Jesse. Yvonne's card is shown to Jesse. Jesse's card is shown to Yvonne. Yvonne's card is shown to Brandi. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melvin can now know whether Yvonne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melvin","Jesse","Yvonne","Brandi"],"index":29936,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7295969725,"difficulty":1.7295969725}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Mary. Andre's card is shown to James. Mary's card is shown to Alvin. Andre's card is shown to Alvin. James's card is shown to Andre. Andre's card is shown to Andre. It is publicly announced that someone picked a red card. It is publicly announced that Andre picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Alvin can now know that Andre can know that Alvin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","James","Alvin","Andre"],"index":41463,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6174641252,"difficulty":0.3825358748}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wesley knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Peter can now know that Juliana can know that Juliana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hazel","Juliana","Peter","Wesley"],"index":51166,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977533221,"difficulty":0.0022466779}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Frances can now know that Emeline can know whether Danielle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frances","Danielle","Emeline"],"index":21973,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993033409,"difficulty":0.0006966591}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that Darrell can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Michael","Darrell","Corey"],"index":66309,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9915269017,"difficulty":0.0084730983}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Kenneth can now know that Leanna can know whether Leanna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Robert","Leanna"],"index":56521,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993775487,"difficulty":0.0006224513}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Courtney knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Sean can now know whether Courtney can know whether Courtney's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Courtney","Sean"],"index":38619,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8782017827,"difficulty":0.1217982173}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adrianne does not know whether Guillermo is thirsty. It is publicly announced that Melvin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] Agentc knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] 0","hypothesis":"Melvin can now know that Adrianne can know whether Melvin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Guillermo","Adrianne","Melvin","Lucille"],"index":324,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9610414505,"difficulty":0.0389585495}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Art knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Art can now know that James can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Art","James"],"index":12518,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989919066,"difficulty":0.0010080934}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Barbara can now know whether Thelma can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thelma","Byron","Barbara"],"index":3063,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993313551,"difficulty":0.0006686449}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marjorie can now know that William can know whether Kathy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Donna","Kathy","Marjorie"],"index":52975,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993558526,"difficulty":0.0006441474}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oscar knows whether Lettie's forehead is muddy. It is publicly announced that Lettie knows whether Lettie's forehead is muddy. It is publicly announced that Oscar knows whether Oscar's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lettie can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Oscar","Lettie"],"index":64334,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992357492,"difficulty":0.0007642508}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew does not know whether Robert is thirsty. It is publicly announced that Andrew does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jamie can now know that Robert can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nanci","Andrew","Jamie","Robert"],"index":504,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994671941,"difficulty":0.0005328059}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randall is not thirsty. It is publicly announced that Vannesa does not know whether Homer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Randall can now know that Vannesa can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Homer","Vannesa","Randall"],"index":50985,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9880119562,"difficulty":1.9880119562}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Ronald. Ronald's card is shown to Jennifer. Ronald's card is shown to Jon. Jennifer's card is shown to Jon. It is publicly announced that someone picked a red card. It is publicly announced that Ronald knows whether Ronald picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jon can now know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ronald","Jennifer","Jon"],"index":63454,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9173111916,"difficulty":0.0826888084}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Roberta can now know that Maria can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maria","Roberta"],"index":15737,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993750453,"difficulty":0.0006249547}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathryn does not know whether Kathryn's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Ronald can now know whether Kathryn can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathryn","Ronald"],"index":66877,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993784428,"difficulty":0.0006215572}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rodney does not know whether or not everyone is thirsty. It is publicly announced that Michele does not know whether Terrance is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Terrance can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michele","Rodney","Terrance"],"index":2217,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994972944,"difficulty":0.0005027056}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmy does not know whether Hubert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jimmy can now know that Hubert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmy","Hubert","Michael"],"index":8281,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994043112,"difficulty":0.0005956888}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Vincent can now know whether Amanda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Billy","Amanda","Vincent"],"index":19528,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9971593618,"difficulty":0.0028406382}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know that Brian can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Brian","Florence","Luis"],"index":60007,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988491535,"difficulty":0.0011508465}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is not muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"John can now know that Ana can know that Ana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ana","Mary","John"],"index":22607,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976543784,"difficulty":0.0023456216}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cynthia's card is shown to Josephine. Josephine's card is shown to Everett. It is publicly announced that someone picked a red card. It is publicly announced that Everett knows whether Josephine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Josephine can now know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Josephine","Everett","Cynthia"],"index":33299,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9856984019,"difficulty":1.9856984019}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret knows whether Margaret is thirsty. It is publicly announced that Barbara does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Margaret can now know whether Barbara can know whether Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bill","Barbara","Margaret"],"index":28131,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999158144,"difficulty":0.000841856}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ty does not know whether Heidi is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ty can now know whether Cynthia can know whether Heidi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Heidi","Ty","Cynthia"],"index":32180,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991618395,"difficulty":0.0008381605}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alison knows whether someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Michael can now know whether Alison can know whether Alison's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Alison"],"index":45182,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7818009853,"difficulty":0.2181990147}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Cindy can now know that Cindy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joshua","Lena","Cindy"],"index":29162,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9955859184,"difficulty":0.0044140816}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lana knows whether or not nobody's forehead is muddy. It is publicly announced that Colleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Geneva can now know that Colleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronald","Geneva","Lana","Colleen"],"index":48997,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.6824795604,"difficulty":1.6824795604}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michele does not know whether Blake is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Michele can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Blake","Collin","Michele","John"],"index":49767,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999420166,"difficulty":0.000579834}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Jennifer. Jennifer's card is shown to Jose. Jose's card is shown to Jeanine. It is publicly announced that someone picked a red card. It is publicly announced that Jeanine knows whether Jose picked a red card. It is publicly announced that Jose does not know whether Jeanine picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jennifer can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Jose","Jeanine"],"index":58982,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9710308313,"difficulty":0.0289691687}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Margaret knows whether Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Margaret can now know whether Lonnie can know that Stephen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Lonnie","Stephen"],"index":3943,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994020462,"difficulty":0.0005979538}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Andrea can now know that Bret can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bret","Andrea","Frank"],"index":18704,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998932302,"difficulty":0.001067698}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clara is thirsty. It is publicly announced that Willian knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Willian can now know whether Adam can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willian","Jeanne","Clara","Adam"],"index":39015,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995063543,"difficulty":0.0004936457}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allison's forehead is not muddy. It is publicly announced that Allison's forehead is not muddy. It is publicly announced that Norman knows whether Allison's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Vickie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Norman","Vickie","Allison"],"index":18144,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999486208,"difficulty":0.000513792}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bonita's card is shown to Bonita. Bonita's card is shown to Susan. Susan's card is shown to Susan. Susan's card is shown to Brenda. Bonita's card is shown to Lee. It is publicly announced that someone picked a red card. It is publicly announced that Bonita does not know whether Lee picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Susan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bonita","Susan","Brenda","Lee"],"index":11905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990246296,"difficulty":0.0009753704}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Donna can now know whether Justin can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Nancy","Ruth","Donna"],"index":14629,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991214871,"difficulty":0.0008785129}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Paul's forehead is muddy. It is publicly announced that Paul's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Carter can now know that Paul can know that Duane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Duane","Carter","Richard"],"index":15857,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9926914573,"difficulty":0.0073085427}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Salvador can now know that Stephanie can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Salvador","Jacquelyn","Elizabeth","Stephanie"],"index":37260,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991297126,"difficulty":0.0008702874}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kellie knows whether someone's forehead is muddy. It is publicly announced that Rachel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kellie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kellie","Rachel","Timothy","Charles"],"index":65885,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973196387,"difficulty":0.0026803613}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Ann. Ann's card is shown to Cathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ann can now know that Cathy can know whether Cathy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ann","Cathy","Angela"],"index":42006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9733980298,"difficulty":0.0266019702}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Lina does not know whether Lina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jon can now know that Daniel can know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Jon","Lina"],"index":52922,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9928042293,"difficulty":1.9928042293}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Crystal. Crystal's card is shown to Rebecca. Francis's card is shown to Rebecca. Crystal's card is shown to Francis. Francis's card is shown to Francis. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Crystal can now know that Rebecca can know whether Rebecca picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Crystal","Rebecca","Francis"],"index":62296,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7894194126,"difficulty":1.7894194126}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Sarah. Lemuel's card is shown to Lemuel. Shannon's card is shown to Lemuel. Sarah's card is shown to Shannon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sarah can now know that Lemuel can know whether Lemuel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Lemuel","Shannon"],"index":32984,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7970950603,"difficulty":1.7970950603}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shayne's card is shown to Lottie. David's card is shown to Shayne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shayne can now know that Lottie can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lottie","Shayne","David"],"index":6559,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980533123,"difficulty":0.0019466877}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Lauren can now know that Jeanne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","Jeanne","Diane","Lauren"],"index":65704,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975038171,"difficulty":0.0024961829}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Gary can now know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Wm","Jane","Gary"],"index":43498,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998408258,"difficulty":0.001591742}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hal's card is shown to Hal. Hal's card is shown to Tanya. Tanya's card is shown to Tanya. Hal's card is shown to Ann. Tanya's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Tanya does not know whether Ann picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Larry can now know that Tanya can know whether Hal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hal","Tanya","Larry","Ann"],"index":19285,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7277581096,"difficulty":1.7277581096}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mamie does not know whether Mamie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Angela can now know that Mamie can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Angela","Mamie"],"index":23500,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993456006,"difficulty":0.0006543994}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy knows whether Dorothy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Bradley can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Betty","Bradley","Erin"],"index":63895,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998940289,"difficulty":0.001059711}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sang can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","Nestor","John","Sang"],"index":8377,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9916166663,"difficulty":0.0083833337}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yolanda knows whether someone is thirsty. It is publicly announced that Joleen does not know whether Eugenia is thirsty. It is publicly announced that Mario is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Mario can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mario","Yolanda","Joleen","Eugenia"],"index":50316,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985973239,"difficulty":0.0014026761}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elenor can now know whether Jerry can know that Jerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosie","Jerry","Elenor"],"index":65552,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992893934,"difficulty":0.0007106066}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracy's card is shown to Josie. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Josie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Josie","Trish","Tracy"],"index":44515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953733087,"difficulty":0.0046266913}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Mariano can now know whether Mariano's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jackie","Mark","Robert","Mariano"],"index":21821,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993914366,"difficulty":0.0006085634}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Patricia does not know whether Brenda is thirsty. It is publicly announced that Patricia does not know whether Brenda is thirsty. It is publicly announced that Patricia does not know whether Brenda is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Brenda can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Patricia","Brenda"],"index":29470,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989570379,"difficulty":0.0010429621}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael is not thirsty. It is publicly announced that Michael does not know whether Jacqueline is thirsty. It is publicly announced that Robert does not know whether Richard is thirsty. It is publicly announced that Robert does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Jacqueline can now know that Michael can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Jacqueline","Michael","Richard"],"index":42793,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9931530952,"difficulty":0.0068469048}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lonnie knows whether someone's forehead is muddy. It is publicly announced that Lonnie knows whether Lonnie's forehead is muddy. It is publicly announced that Marvin knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Lori can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lonnie","Lori","Marvin"],"index":51824,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988308549,"difficulty":0.0011691451}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Rhea can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Catherine","Rhea","Joshua"],"index":6547,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994418025,"difficulty":0.0005581975}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know whether Brittany can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Heather","Brittany","James"],"index":5433,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994859695,"difficulty":0.0005140305}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathryn does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Bessie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Celia","Bessie","Kathryn","Richard"],"index":6132,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988823533,"difficulty":0.0011176467}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melinda does not know whether Melinda's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Melinda can now know whether Pamula can know that Pamula's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melinda","Pamula"],"index":11627,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9918869138,"difficulty":1.9918869138}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rose knows whether Rose is thirsty. It is publicly announced that Eric does not know whether Rose is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Eric can now know that Eric is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rose","Alexis","Eric"],"index":37150,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9340416193,"difficulty":0.0659583807}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Leslie can now know that Leonard can know that Leslie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Leonard","Leslie"],"index":14483,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9946618676,"difficulty":0.0053381324}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy is thirsty. It is publicly announced that Nancy does not know whether Shirley is thirsty. It is publicly announced that Chantel does not know whether Shirley is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Chantel can now know whether Susan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chantel","Susan","Shirley","Nancy"],"index":46197,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976075888,"difficulty":0.0023924112}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Dennis. Xuan's card is shown to Dennis. Dennis's card is shown to Charles. Charles's card is shown to Xuan. Xuan's card is shown to Xuan. It is publicly announced that someone picked a red card. It is publicly announced that Xuan picked a red card. It is publicly announced that Dennis does not know whether or not everyone picked a red card. It is publicly announced that Dennis knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Dennis can now know that Xuan can know that Dennis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Charles","Xuan"],"index":1665,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5129795671,"difficulty":0.4870204329}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Grady is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jose can now know that Joseph can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Linda","Jose","Grady"],"index":16381,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966380596,"difficulty":0.0033619404}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy. It is publicly announced that Gary knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentc knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jane can now know that William can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Gary","Jane","William"],"index":37474,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9930766821,"difficulty":0.0069233179}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isaac knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jeff can now know that Isaac can know that Rafael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Isaac","Rafael","Donald","Jeff"],"index":31435,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9885679483,"difficulty":0.0114320517}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Christina does not know whether Arthur is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Christina can now know whether Arthur can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arthur","Christina"],"index":11335,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993113279,"difficulty":0.0006886721}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Marie can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Agnes","Ronnie","Clayton"],"index":57348,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989851117,"difficulty":0.0010148883}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cindy knows whether Cindy is thirsty. It is publicly announced that Cindy does not know whether Carla is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Cindy can now know whether Lynn can know that Carla is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Carla","Cindy","Lynn"],"index":4210,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9667963982,"difficulty":0.0332036018}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Walter does not know whether Patsy is thirsty. It is publicly announced that Edmond does not know whether Walter is thirsty. It is publicly announced that Walter does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Edmond can now know that Edmond is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edmond","Walter","Patsy","Delia"],"index":10739,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7406820655,"difficulty":0.2593179345}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles knows whether or not everyone is thirsty. It is publicly announced that Lance is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Lance can now know that Lance is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Charles","Lance"],"index":34373,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7503621578,"difficulty":0.2496378422}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenn knows whether Heather's forehead is muddy. It is publicly announced that Heather knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Heather can now know that Glenn can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Heather","Glenn"],"index":7427,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981331229,"difficulty":0.0018668771}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bianca knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Nicholas can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bianca","Dean","Nicholas"],"index":19275,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986743927,"difficulty":0.0013256073}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charla does not know whether Dennis is thirsty. It is publicly announced that Charla does not know whether or not everyone is thirsty. It is publicly announced that Charla does not know whether Kenneth is thirsty. It is publicly announced that Dennis does not know whether Kenneth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"John can now know whether Kenneth can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","John","Dennis","Charla"],"index":45092,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987871051,"difficulty":0.0012128949}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debbie's card is shown to Rosemary. Rosemary's card is shown to Debbie. It is publicly announced that someone picked a red card. It is publicly announced that Rosemary does not know whether Rosemary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rosemary can now know that Debbie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rosemary","Debbie"],"index":10938,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988945127,"difficulty":0.0011054873}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Linda can now know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Linda","Francisco"],"index":51895,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9938003421,"difficulty":0.0061996579}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco knows whether or not everyone's forehead is muddy. It is publicly announced that Waylon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Waylon can now know whether Christopher can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Charles","Francisco","Waylon"],"index":11178,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993574023,"difficulty":0.0006425977}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Cheryl. Tom's card is shown to Cheryl. Dawn's card is shown to Dawn. Tom's card is shown to Tom. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tom can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cheryl","Dawn","Tom"],"index":5623,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990008473,"difficulty":0.0009991527}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas does not know whether Jarrett is thirsty. It is publicly announced that Douglas does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Douglas can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Jarrett","Douglas"],"index":37263,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994258881,"difficulty":0.0005741119}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracey's card is shown to Tracey. Susan's card is shown to Susan. Tracey's card is shown to Jose. Susan's card is shown to Jose. Jose's card is shown to Jose. It is publicly announced that someone picked a red card. It is publicly announced that Tracey does not know whether or not everyone picked a red card. It is publicly announced that Susan knows whether Susan picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jose can now know whether Tracey can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracey","Susan","Jose"],"index":50680,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994322658,"difficulty":0.0005677342}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"William can now know that Freda can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Freda","Robert"],"index":35998,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9922352433,"difficulty":0.0077647567}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacy knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Mai can now know whether Stacy can know whether Mai is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mai","Stacy"],"index":54795,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990021586,"difficulty":0.0009978414}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amanda can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Gary","Dave","Amanda"],"index":4862,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989488721,"difficulty":0.0010511279}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Howard knows whether Anthony's forehead is muddy. It is publicly announced that Howard's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Donald can now know that Howard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Anthony","Howard"],"index":13959,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.992401123,"difficulty":0.007598877}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy. It is publicly announced that George knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Ray can now know whether Stacy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stacy","Donna","Ray","George"],"index":11970,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994051456,"difficulty":0.0005948544}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Daniel's forehead is not muddy. It is publicly announced that Martin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agenta knows that (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Martin can now know that Daniel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Martin","Daniel"],"index":22085,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937822223,"difficulty":0.0062177777}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy. It is publicly announced that Lisha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] 0","hypothesis":"Lisha can now know that Lisha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Ashley","Lisha"],"index":24245,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8791567087,"difficulty":0.1208432913}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steven's card is shown to David. Claude's card is shown to Steven. David's card is shown to Claude. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Claude can now know that Claude picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Steven","Claude"],"index":40930,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952457547,"difficulty":0.0047542453}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Derek knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Dorothy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Derek","Steven"],"index":52792,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987787604,"difficulty":0.0012212396}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Fletcher knows whether or not nobody's forehead is muddy. It is publicly announced that Kasey knows whether Derek's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Richard can now know that Fletcher can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Fletcher","Derek","Kasey"],"index":17667,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9878236055,"difficulty":0.0121763945}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlotte's card is shown to Charlotte. Charlotte's card is shown to Kristin. Charlotte's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Charlotte knows whether Charlotte picked a red card. It is publicly announced that Charlotte knows whether Charlotte picked a red card. It is publicly announced that Charlotte does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Christopher can now know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charlotte","Kristin","Christopher"],"index":31080,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5079874992,"difficulty":0.4920125008}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhonda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Genevieve can now know whether David can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rhonda","Delores","David","Genevieve"],"index":37828,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993028641,"difficulty":0.0006971359}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chester's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Barbara can now know that Karen can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Emily","Karen","Chester"],"index":11502,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989775419,"difficulty":0.0010224581}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy. It is publicly announced that Frieda knows whether Gerald's forehead is muddy. It is publicly announced that Gerald does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know that Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Gerald","Susan","Frieda"],"index":19375,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.818981111,"difficulty":0.181018889}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet does not know whether Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Janet can now know whether Michael can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosetta","Michael","Janet"],"index":63335,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994438291,"difficulty":0.0005561709}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether John's forehead is muddy. It is publicly announced that John knows whether Mary's forehead is muddy. It is publicly announced that Sarah does not know whether Sarah's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mary can now know whether John can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Mary","John"],"index":14279,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994465709,"difficulty":0.0005534291}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Amy's card is shown to Paul. Paul's card is shown to Paul. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Amy can now know that Paul can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Amy","Paul"],"index":4967,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9767599702,"difficulty":0.0232400298}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Thomas can now know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thomas","Malinda"],"index":13757,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.965547502,"difficulty":0.034452498}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether Patsy is thirsty. It is publicly announced that Daniel knows whether someone is thirsty. It is publicly announced that Trudy does not know whether Patsy is thirsty. It is publicly announced that Patsy does not know whether Daniel is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Trudy can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","Patsy","Trudy"],"index":16315,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989855886,"difficulty":0.0010144114}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Clarence can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dorothy","Deanna","Heather","Clarence"],"index":12683,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8723496199,"difficulty":0.1276503801}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Krystal does not know whether Clyde is thirsty. It is publicly announced that Clyde does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Krystal can now know that Maryetta can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Krystal","Clyde","Maryetta","Christina"],"index":58387,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990303516,"difficulty":0.0009696484}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Terry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Don can now know that Victor can know whether Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terry","Victor","Don","Jose"],"index":57302,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992621541,"difficulty":0.0007378459}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Ryan can now know that Carol can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louis","Carol","Ryan"],"index":61182,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999150753,"difficulty":0.000849247}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether Courtney's forehead is muddy. It is publicly announced that Damion's forehead is not muddy. It is publicly announced that Damion knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Courtney can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Damion","Courtney"],"index":33741,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989814162,"difficulty":0.0010185838}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gina's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Shery can now know that Gillian can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shery","Mabel","Gillian","Gina"],"index":35920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994493127,"difficulty":0.0005506873}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joanne does not know whether Ronald is thirsty. It is publicly announced that Arthur does not know whether Ronald is thirsty. It is publicly announced that Arthur knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Ronald can now know that Joanne can know that Joanne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Joanne","Arthur"],"index":45628,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957916737,"difficulty":0.0042083263}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy's forehead is muddy. It is publicly announced that Judy knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kimberley can now know whether Judy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberley","Karin","Judy"],"index":63223,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994401336,"difficulty":0.0005598664}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christine does not know whether Susan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Susan can now know whether Alma can know that Christine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Christine","Celia","Alma"],"index":58651,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9857442975,"difficulty":0.0142557025}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jim's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Lola can now know that Jim's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Lola","Jim"],"index":33130,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9909732938,"difficulty":0.0090267062}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Adam can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Adam","Robert","Miriam"],"index":18238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99892658,"difficulty":0.00107342}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill knows whether someone's forehead is muddy. It is publicly announced that Kerri's forehead is muddy. It is publicly announced that Mindy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Mindy can now know whether Bill can know whether Bill's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bill","Mindy","Kerri"],"index":8319,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9370028377,"difficulty":1.9370028377}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brett does not know whether or not everyone's forehead is muddy. It is publicly announced that Rosalyn's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Brett can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brett","Rosalyn"],"index":12795,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990116358,"difficulty":0.0009883642}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kurt knows whether someone's forehead is muddy. It is publicly announced that Kurt's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] 0","hypothesis":"Patrick can now know that Carolyn can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kurt","Carolyn","Patrick"],"index":27532,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994767308,"difficulty":0.0005232692}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gary can now know that Vera's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vera","Gary","Andrew","Joan"],"index":37638,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965803027,"difficulty":0.0034196973}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Linda. Linda's card is shown to Linda. Patricia's card is shown to Linda. Arnold's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Arnold does not know whether Linda picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] 0","hypothesis":"Arnold can now know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Arnold","Linda","Patricia"],"index":3108,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9898563623,"difficulty":0.0101436377}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heidi knows whether someone is thirsty. It is publicly announced that Virginia does not know whether Kelly is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kelly can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virginia","Heidi","Kelly"],"index":60744,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990064502,"difficulty":0.0009935498}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether Douglas's forehead is muddy. It is publicly announced that Brian's forehead is not muddy. It is publicly announced that Nancy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Douglas can now know that Nancy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Douglas","Rickie","Brian"],"index":63349,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998817265,"difficulty":0.001182735}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. Florence's card is shown to Jessica. Jessica's card is shown to Olga. Jessica's card is shown to Florence. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Florence can now know whether Olga can know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Olga","Florence"],"index":27296,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989138842,"difficulty":0.0010861158}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ivette's card is shown to Howard. Jeanne's card is shown to Howard. Howard's card is shown to Ivette. Ivette's card is shown to Ivette. Steven's card is shown to Jeanne. It is publicly announced that someone picked a red card. It is publicly announced that Ivette does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ivette can now know whether Ivette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Howard","Steven","Ivette","Jeanne"],"index":52908,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9356247187,"difficulty":1.9356247187}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Juanita. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Timothy can now know whether Juanita can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Juanita","Timothy"],"index":41895,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9952511787,"difficulty":0.0047488213}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juana's card is shown to Linda. Linda's card is shown to Juana. Juana's card is shown to Juana. Juana's card is shown to Beatrice. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Beatrice picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Beatrice knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Beatrice can now know whether Juana can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Juana","Beatrice"],"index":35332,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9939838052,"difficulty":0.0060161948}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martin knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Martin can now know that Kenneth can know that Martin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Martin","Kenneth"],"index":26159,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9919670224,"difficulty":0.0080329776}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irving knows whether Irving is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Harry can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harry","Irving"],"index":5980,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994803071,"difficulty":0.0005196929}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cammie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jane can now know whether Ashley can know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jane","Kimberly","Cammie","Ashley"],"index":41347,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993264675,"difficulty":0.0006735325}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mildred does not know whether Deborah is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Christopher can now know whether Deborah can know that Deborah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Deborah","Mildred","Christopher"],"index":30924,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9465329051,"difficulty":1.9465329051}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"John can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Kevin","Leslie","Katherine"],"index":66122,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994493127,"difficulty":0.0005506873}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jason can now know that Jason's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alice","Victoria","Jason"],"index":36886,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9700398445,"difficulty":0.0299601555}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carrol's card is shown to Carly. Carly's card is shown to Carrol. Carrol's card is shown to Carrol. Glenn's card is shown to Carrol. Glenn's card is shown to Glenn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Glenn can now know whether Carly can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carly","Carrol","Glenn"],"index":60533,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991280437,"difficulty":0.0008719563}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy. It is publicly announced that Melissa does not know whether or not everyone's forehead is muddy. It is publicly announced that Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Melissa can now know that John can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Melissa"],"index":66274,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9191597104,"difficulty":0.0808402896}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Enrique's card is shown to Enrique. Alexandra's card is shown to Enrique. Enrique's card is shown to Alexandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stewart can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stewart","Enrique","Alexandra","Chris"],"index":39892,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989953637,"difficulty":0.0010046363}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Evelyn can now know whether Mary can know that Evelyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Mary","Evelyn"],"index":13737,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9550065994,"difficulty":0.0449934006}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlene's card is shown to Bernie. Stacie's card is shown to Stacie. Bernie's card is shown to Craig. Marlene's card is shown to Marlene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stacie can now know that Stacie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernie","Stacie","Craig","Marlene"],"index":13048,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9936742783,"difficulty":0.0063257217}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Gary. Gary's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Thomas knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Gary can now know whether Thomas can know that Gary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gary","Thomas"],"index":23567,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9369220734,"difficulty":0.0630779266}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Violet's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Joyce can now know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joyce","Richard","Violet"],"index":43929,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9960253239,"difficulty":0.0039746761}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Rodney. Rodney's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rodney","Richard","Kevin"],"index":63070,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983855486,"difficulty":0.0016144514}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kevin. Kenneth's card is shown to Meredith. Meredith's card is shown to Meredith. Dolores's card is shown to Meredith. Dolores's card is shown to Dolores. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kevin can now know whether Meredith can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Kenneth","Meredith","Dolores"],"index":20369,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993815422,"difficulty":0.0006184578}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva knows whether Beulah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Beulah can now know whether Michael can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Beulah","Eva"],"index":31349,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999381423,"difficulty":0.000618577}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sonya's card is shown to Frank. Frank's card is shown to Sonya. Timothy's card is shown to Sonya. Patricia's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Patricia does not know whether Frank picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Frank can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Sonya","Patricia","Timothy"],"index":11816,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989940524,"difficulty":0.0010059476}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Teresa can now know whether Krista's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Teresa","Richard","Krista"],"index":16190,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994757771,"difficulty":0.0005242229}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leroy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Denise can now know that Leroy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Denise","John","Leroy"],"index":41734,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9936724901,"difficulty":0.0063275099}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Frank can now know that Thomas can know that Frank's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eula","Thomas","Frank","Juan"],"index":24246,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980072379,"difficulty":0.0019927621}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Sara knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Virginia can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sara","Virginia"],"index":630,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994243383,"difficulty":0.0005756617}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Gerald can now know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Gerald","Pauline","Terrell"],"index":47643,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969363213,"difficulty":0.0030636787}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shante's card is shown to Oscar. Oscar's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Oscar can now know that Earlene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earlene","Oscar","Janice","Shante"],"index":55809,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980683923,"difficulty":0.0019316077}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mildred knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Julie can now know that Mildred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maxine","Mildred","Julie","John"],"index":40206,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980814457,"difficulty":0.0019185543}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alfredo is thirsty. It is publicly announced that Edna does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Toni can now know whether Ruth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edna","Alfredo","Toni","Ruth"],"index":13913,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9876403213,"difficulty":0.0123596787}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Rose. Rose's card is shown to Roy. Francis's card is shown to Francis. It is publicly announced that someone picked a red card. It is publicly announced that Francis picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Roy can now know that Rose can know whether Roy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Michael","Roy","Francis"],"index":22860,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7935570478,"difficulty":1.7935570478}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lacey's card is shown to Joseph. Lacey's card is shown to Roseanne. Keith's card is shown to Roseanne. Keith's card is shown to Lacey. Roseanne's card is shown to Keith. Keith's card is shown to Keith. It is publicly announced that someone picked a red card. It is publicly announced that Keith does not know whether Lacey picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Lacey can now know whether Roseanne can know that Lacey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Roseanne","Lacey","Keith"],"index":64845,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8055714965,"difficulty":1.8055714965}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lloyd is thirsty. It is publicly announced that Edwin knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Russell can now know that Raymond can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edwin","Raymond","Lloyd","Russell"],"index":12176,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994096756,"difficulty":0.0005903244}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Norine can now know whether Lisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Norine","Lisa"],"index":57032,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994447827,"difficulty":0.0005552173}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lynda can now know that Lester can know that Jay's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lester","Jay","Lynda"],"index":59739,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974386692,"difficulty":0.0025613308}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Crystal's card is shown to Erica. Aleida's card is shown to Crystal. Linda's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Aleida can now know that Crystal can know whether Crystal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Erica","Crystal","Aleida","Linda"],"index":21745,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5479358435,"difficulty":0.4520641565}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corinne does not know whether Corinne's forehead is muddy. It is publicly announced that Corinne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jennifer can now know whether Corinne can know whether Corinne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Gretchen","Corinne"],"index":66128,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9727588296,"difficulty":0.0272411704}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Christina can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christina","Mary","Andra"],"index":61549,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5284424424,"difficulty":0.4715575576}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hassan is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Hassan can now know that Cory is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cory","John","Hassan"],"index":3489,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958497286,"difficulty":0.0041502714}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tabitha's card is shown to Robert. Tabitha's card is shown to Tabitha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Tabitha can now know whether Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Tabitha"],"index":43368,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994130135,"difficulty":0.0005869865}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracey does not know whether or not everyone's forehead is muddy. It is publicly announced that Jeremy knows whether Tracey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Tracey can now know that Maria can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracey","Jeremy","Karen","Maria"],"index":1466,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6393005848,"difficulty":0.3606994152}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jon does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Sharon can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jon","Ashley","Sharon"],"index":53252,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994814992,"difficulty":0.0005185008}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Bernard can now know that Pearlie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pearlie","Malcolm","Bernard","Robert"],"index":4069,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993792772,"difficulty":0.0006207228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynette does not know whether Alicia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lynette can now know that Ronald can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lynette","Alicia","Ronald","James"],"index":5519,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983593822,"difficulty":0.0016406178}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose does not know whether Rose's forehead is muddy. It is publicly announced that Rose does not know whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rose can now know that Nick can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rose","Nick"],"index":11810,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9657897353,"difficulty":1.9657897353}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Carrie does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Martin can now know whether Carrie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carrie","Martin"],"index":14710,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994378686,"difficulty":0.0005621314}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elaine knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Elaine can now know that Judith can know whether Judith is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elaine","Florence","Silvana","Judith"],"index":32234,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9506759644,"difficulty":0.0493240356}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lizette's forehead is not muddy. It is publicly announced that Lee knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Lee can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sofia","David","Lizette","Lee"],"index":28494,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994949102,"difficulty":0.0005050898}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Edward can know that Brunilda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","William","Brunilda","Edward"],"index":5583,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956788421,"difficulty":0.0043211579}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lyda's card is shown to Craig. Lyda's card is shown to Lyda. Richard's card is shown to Lyda. Craig's card is shown to Bruce. Bruce's card is shown to Bruce. Craig's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bruce can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Craig","Lyda","Bruce","Richard"],"index":55539,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9019395709,"difficulty":0.0980604291}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilmer can now know that Jacob can know whether Wilmer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clark","Wilmer","Jacob","Melissa"],"index":29343,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8823232651,"difficulty":0.1176767349}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ron can now know whether Rita can know whether Gerard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ron","Gerard","Rita"],"index":65746,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992102385,"difficulty":0.0007897615}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Rebecca. Rebecca's card is shown to Thomas. Thomas's card is shown to Thomas. Casey's card is shown to Thomas. Thomas's card is shown to Casey. Thomas's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Thomas can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Thomas","Casey","James"],"index":18237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8463199139,"difficulty":0.1536800861}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Lettie. George's card is shown to Louis. Lettie's card is shown to George. Louis's card is shown to George. George's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louis can now know that Lettie can know whether George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Lettie","Louis","George"],"index":56976,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9211332798,"difficulty":0.0788667202}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Stephen can now know that Michael can know that Rosa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosa","Michael","Stephen"],"index":9470,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9965232611,"difficulty":0.0034767389}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lakeisha's card is shown to Lakeisha. Betty's card is shown to Lakeisha. Frances's card is shown to Lakeisha. Lakeisha's card is shown to Betty. Betty's card is shown to Frances. Frances's card is shown to Debi. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether Betty picked a red card. It is publicly announced that Betty does not know whether Betty picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Betty can now know whether Frances can know whether Debi picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lakeisha","Betty","Frances","Debi"],"index":9865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985972047,"difficulty":0.0014027953}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacqueline does not know whether Lindsey is thirsty. It is publicly announced that Jacqueline does not know whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Lindsey can now know whether Barbara can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lindsey","James","Barbara","Jacqueline"],"index":50960,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9948230982,"difficulty":0.0051769018}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Roger. Roger's card is shown to Roger. Melanie's card is shown to Roger. Mary's card is shown to Melanie. Roger's card is shown to Melanie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Roger can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Roger","Melanie"],"index":25593,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993178844,"difficulty":0.0006821156}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Michael's card is shown to Eugene. Louis's card is shown to Eugene. Michael's card is shown to Michael. Louis's card is shown to Louis. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Louis picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Louis can now know whether Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eugene","Michael","Louis"],"index":20557,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8739506006,"difficulty":1.8739506006}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith does not know whether or not everyone's forehead is muddy. It is publicly announced that Ebony knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Tom can now know that Ebony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Judith","Tom","Ebony"],"index":46186,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8648713827,"difficulty":0.1351286173}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"David can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","David","Joshua"],"index":10277,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.999004066,"difficulty":0.000995934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew does not know whether Rick is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Patricia can now know that Lorie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rick","Lorie","Patricia","Matthew"],"index":46240,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982607961,"difficulty":0.0017392039}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margery knows whether or not everyone's forehead is muddy. It is publicly announced that Michelle's forehead is muddy. It is publicly announced that Max's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Margery can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michelle","Margery","Max"],"index":63592,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994494319,"difficulty":0.0005505681}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerry's card is shown to Jerry. Darlene's card is shown to Darlene. It is publicly announced that someone picked a red card. It is publicly announced that Jerry does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Darlene can now know that Jerry can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Darlene","Frank"],"index":12340,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989357591,"difficulty":0.0010642409}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether Morton is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Steven can now know whether Morton can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Morton","Steven","Crystal"],"index":42243,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992578626,"difficulty":0.0007421374}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diana's card is shown to Deborah. Scott's card is shown to Scott. Deborah's card is shown to Diana. Scott's card is shown to Diana. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Bryan can now know that Bryan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deborah","Bryan","Scott","Diana"],"index":25242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8466079235,"difficulty":0.1533920765}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Herbert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Leslie can now know that Leslie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julio","Dallas","Herbert","Leslie"],"index":25638,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.602435112,"difficulty":0.397564888}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elizabeth","Opal","Michael"],"index":39088,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993938208,"difficulty":0.0006061792}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Booker knows whether someone is thirsty. It is publicly announced that Willard does not know whether Booker is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Booker can now know whether Willard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Booker","Willard","Matthew"],"index":50182,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954336286,"difficulty":0.0045663714}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Anthony can now know that James can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Anthony"],"index":5803,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993662238,"difficulty":0.0006337762}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sherri can now know whether Ronald can know whether Ronald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Sherri","Gordon","Lula"],"index":26984,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9942445159,"difficulty":0.0057554841}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Suzanne's card is shown to Danielle. Danielle's card is shown to Suzanne. Suzanne's card is shown to Suzanne. Suzanne's card is shown to Karin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Danielle can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Danielle","Suzanne","Karin"],"index":40933,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994204044,"difficulty":0.0005795956}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"John can now know that Audrey can know that Gloria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Audrey","John"],"index":42798,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969325066,"difficulty":0.0030674934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Suk does not know whether Delois is thirsty. It is publicly announced that Crystal does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Keesha can now know that Keesha is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Suk","Delois","Keesha","Crystal"],"index":48315,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.869263649,"difficulty":0.130736351}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew does not know whether Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Andrew can now know that Lloyd can know whether Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clarence","Andrew","Lloyd"],"index":24458,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9944785833,"difficulty":0.0055214167}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather's forehead is not muddy. It is publicly announced that James knows whether Heather's forehead is muddy. It is publicly announced that Heather knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"James can now know that Heather can know that Heather's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Leticia","Heather"],"index":65772,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9707245231,"difficulty":0.0292754769}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether Tracy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Bob can now know that Tracy can know whether Tracy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Bob","Tracy","Vada"],"index":17428,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9877588153,"difficulty":0.0122411847}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margaret knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Karen can now know whether Shelia can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Karen","Shelia","James"],"index":67610,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8336336613,"difficulty":0.1663663387}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary knows whether Mary is thirsty. It is publicly announced that Harry does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Harry can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Harry","Mary"],"index":21746,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985320568,"difficulty":0.0014679432}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leanne knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Leanne can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Leanne","Shane"],"index":45907,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986724854,"difficulty":0.0013275146}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephen's card is shown to Stephen. Stephen's card is shown to Will. Bertha's card is shown to Will. Will's card is shown to Bertha. Adam's card is shown to Bertha. Will's card is shown to Adam. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Stephen knows whether Stephen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2,4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Will can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephen","Will","Bertha","Adam"],"index":56349,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994210005,"difficulty":0.0005789995}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elsie does not know whether Jenna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Elsie can now know that Jenna can know that Elsie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tracey","Elsie","Lakisha","Jenna"],"index":10806,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954724908,"difficulty":0.0045275092}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Mary can now know that David can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Mary","William","Ana"],"index":56097,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9912836552,"difficulty":0.0087163448}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that April knows whether April's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"April can now know whether Eric can know that April's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["April","Eric"],"index":54753,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993109703,"difficulty":0.0006890297}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annie knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Joseph can now know whether Annie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Annie","Joseph"],"index":32416,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9348027706,"difficulty":0.0651972294}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mathilda knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ronald can now know that John can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mathilda","John","Ronald","Bobby"],"index":41350,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991137385,"difficulty":0.0008862615}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Walter","Christopher","Robert"],"index":62093,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980617166,"difficulty":0.0019382834}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Dwayne can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dwayne","Clara","Robert"],"index":59860,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989199638,"difficulty":0.0010800362}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carline's forehead is not muddy. It is publicly announced that Carline knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Nicholas can now know that Carline's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nicholas","Carline","Steven"],"index":54471,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940641522,"difficulty":0.0059358478}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Alta is thirsty. It is publicly announced that Duane knows whether someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that Joseph does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Duane can know whether Alta is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Duane","James","Alta","Joseph"],"index":66006,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9932224751,"difficulty":0.0067775249}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether or not everyone is thirsty. It is publicly announced that Paul knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Paul can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Paul"],"index":44367,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9658123851,"difficulty":0.0341876149}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrea does not know whether Andrea's forehead is muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Andrea can now know that Jennifer can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Andrea","Jennifer","Mae"],"index":67634,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9772891402,"difficulty":0.0227108598}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David does not know whether Mitchell is thirsty. It is publicly announced that Mitchell does not know whether David is thirsty. It is publicly announced that David is thirsty. It is publicly announced that Theodore does not know whether Mitchell is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] [ ! ~(Agentc knows whether 2) ] (Agentc knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Theodore can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Mitchell","Theodore","James"],"index":60935,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987892509,"difficulty":0.0012107491}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Samuel can now know that Robin can know that Lisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robin","Cassandra","Samuel","Lisa"],"index":22995,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978742599,"difficulty":0.0021257401}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gloria does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Juan can now know whether Kenneth can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Gloria","Kenneth","Juan"],"index":37568,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992704988,"difficulty":0.0007295012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phyllis knows whether or not everyone's forehead is muddy. It is publicly announced that Phyllis knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Kelly can now know whether Phyllis can know whether Phyllis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shirley","Phyllis","Kelly"],"index":49110,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.732637763,"difficulty":1.732637763}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Darrell can now know whether Charles can know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrell","Kay","Richard","Charles"],"index":46018,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994456172,"difficulty":0.0005543828}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gail does not know whether Mayme is thirsty. It is publicly announced that Gail does not know whether Kathrine is thirsty. It is publicly announced that Mayme knows whether Mayme is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gail can now know that Mayme can know whether Gail is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathrine","Gail","Mayme"],"index":38401,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6656938791,"difficulty":1.6656938791}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Kimberly. Mallory's card is shown to Kimberly. Mallory's card is shown to Mallory. It is publicly announced that someone picked a red card. It is publicly announced that Mallory knows whether or not nobody picked a red card. It is publicly announced that Mallory does not know whether Kimberly picked a red card. It is publicly announced that Kimberly picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Kimberly can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kimberly","Mallory"],"index":36648,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9086900949,"difficulty":0.0913099051}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie knows whether or not nobody is thirsty. It is publicly announced that Willie does not know whether Julia is thirsty. It is publicly announced that Julia knows whether Willie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Julia can now know whether Willie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Julia","Willie"],"index":53366,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9905390739,"difficulty":0.0094609261}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"James can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Judith","James"],"index":58545,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986038804,"difficulty":0.0013961196}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hannah knows whether or not nobody's forehead is muddy. It is publicly announced that Andrea's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Andrea can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Linda","Hannah","Andrea"],"index":12114,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988724589,"difficulty":0.0011275411}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Annie can now know whether Richard can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Annie"],"index":50702,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994729161,"difficulty":0.0005270839}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie does not know whether or not everyone is thirsty. It is publicly announced that Willie does not know whether Joel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Willie can now know that Joel can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Joel","David","Willie"],"index":48792,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994959831,"difficulty":0.0005040169}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Antoinette can now know that Antoinette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Antoinette","Michael","Kenneth"],"index":55479,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9956348538,"difficulty":0.0043651462}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellen does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Stephanie can now know that George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Brian","Ellen","George"],"index":17898,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9178130031,"difficulty":0.0821869969}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kyle does not know whether Viola is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Kyle can now know whether Danny is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danny","Kyle","Viola"],"index":13899,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998051405,"difficulty":0.001948595}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Sabrina can now know that Joy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Freda","Sylvia","Joy","Sabrina"],"index":25760,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988743663,"difficulty":0.0011256337}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Jennifer is thirsty. It is publicly announced that Kristy does not know whether Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"James can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Betty","Kristy","Jennifer"],"index":53156,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9901928902,"difficulty":0.0098071098}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashlee's card is shown to Edward. Julie's card is shown to Edward. Ashlee's card is shown to Reuben. Reuben's card is shown to Reuben. Reuben's card is shown to Julie. Julie's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Ashlee does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Ashlee can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","Ashlee","Reuben","Julie"],"index":14916,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994120598,"difficulty":0.0005879402}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Harry's card is shown to Patricia. Edna's card is shown to Harry. Edna's card is shown to Edna. Jack's card is shown to Jack. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jack can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Harry","Edna","Jack"],"index":1087,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.994664669,"difficulty":0.005335331}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marion's card is shown to Stacy. Susan's card is shown to Susan. Susan's card is shown to Marion. It is publicly announced that someone picked a red card. It is publicly announced that Stacy picked a red card. It is publicly announced that Stacy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Marion can now know whether Susan can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stacy","Susan","Marion"],"index":31672,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9804852009,"difficulty":0.0195147991}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Leon. Mary's card is shown to Mary. Leon's card is shown to Justin. Mary's card is shown to Justin. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether Justin picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Leon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leon","Mary","Justin"],"index":60575,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999435246,"difficulty":0.000564754}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie does not know whether Julie's forehead is muddy. It is publicly announced that Julie knows whether Susan's forehead is muddy. It is publicly announced that Susan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Susan can now know whether Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Julie","Susan"],"index":22043,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9137208462,"difficulty":0.0862791538}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Margie's card is shown to Helen. Helen's card is shown to Jeffery. Bryan's card is shown to Margie. Helen's card is shown to Bryan. Jeffery's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Jeffery does not know whether Jeffery picked a red card. It is publicly announced that Jeffery does not know whether Margie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jeffery can now know whether Bryan can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Jeffery","Margie","Bryan"],"index":30051,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989688396,"difficulty":0.0010311604}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victor's card is shown to Genevieve. Victor's card is shown to Victor. Mike's card is shown to Victor. Victor's card is shown to Mike. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Genevieve can now know whether Mike can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Genevieve","Victor","Mike"],"index":47510,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9929959178,"difficulty":0.0070040822}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas knows whether Nicholas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Catherine can now know that Nicholas can know that Ilana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicholas","Ilana","Catherine"],"index":41655,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963382483,"difficulty":0.0036617517}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Ida's card is shown to John. Ida's card is shown to Ida. Richard's card is shown to Ida. Mark's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ida can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","John","Ida","Richard"],"index":2006,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994081259,"difficulty":0.0005918741}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carl's card is shown to Carl. Velva's card is shown to Carl. Deborah's card is shown to Carl. Carl's card is shown to Donald. Donald's card is shown to Deborah. Deborah's card is shown to Deborah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know whether Velva can know whether Carl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Donald","Velva","Deborah"],"index":21845,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9968339801,"difficulty":0.0031660199}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenifer's card is shown to Michael. Jonathan's card is shown to Jenifer. Michael's card is shown to Jonathan. Jenifer's card is shown to Jonathan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jonathan can now know that Michael can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Jenifer","Jonathan"],"index":19046,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993702769,"difficulty":0.0006297231}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Alice. Alice's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Alice can now know whether Joan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alice","Jay","Joan"],"index":61144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6297245026,"difficulty":0.3702754974}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Jean can now know that Florentino can know whether Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Florentino","Russell","Jean"],"index":37713,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986519217,"difficulty":0.0013480783}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly does not know whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Geraldine can now know whether Kimberly can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","Geraldine","Michael"],"index":16040,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9634833336,"difficulty":0.0365166664}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugene's card is shown to Eugene. Eugene's card is shown to David. Eugene's card is shown to Faye. David's card is shown to Faye. Faye's card is shown to Faye. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eugene can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eugene","David","Faye"],"index":34534,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5232340097,"difficulty":0.4767659903}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessie's forehead is muddy. It is publicly announced that Jose does not know whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Ryan can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessie","John","Ryan","Jose"],"index":59796,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6838151813,"difficulty":0.3161848187}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mavis can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Curtis","Jennifer","Dale","Mavis"],"index":62589,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993727803,"difficulty":0.0006272197}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Lawrence"],"index":41731,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976482987,"difficulty":0.0023517013}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to Rhonda. Brenda's card is shown to Gregory. Rhonda's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Rhonda's card is shown to Brenda. Brenda's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Gregory does not know whether Elizabeth picked a red card. It is publicly announced that Brenda picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] 0","hypothesis":"Elizabeth can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rhonda","Gregory","Elizabeth","Brenda"],"index":60703,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990419745,"difficulty":0.0009580255}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether Lacie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Sandra can now know whether Lacie can know that Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ron","Sandra","Lacie"],"index":27446,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994451404,"difficulty":0.0005548596}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Helen's card is shown to Dennis. Dennis's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Helen knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Dennis can now know that Helen can know that Dennis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Helen","Dennis"],"index":39333,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925463796,"difficulty":0.0074536204}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Vita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Vita can now know that Mary can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vita","Victoria","Mary"],"index":23774,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993683696,"difficulty":0.0006316304}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Mike. Christopher's card is shown to Anthony. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mike","Anthony","Christopher"],"index":35082,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7131146789,"difficulty":1.7131146789}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Sandra. Christina's card is shown to Christina. Carole's card is shown to Christina. Carole's card is shown to Clyde. Clyde's card is shown to Carole. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christina can now know that Christina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Christina","Clyde","Carole"],"index":57825,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942713976,"difficulty":0.0057286024}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marc's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Richard can now know that Dale can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elaine","Dale","Richard","Marc"],"index":2270,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9977818131,"difficulty":0.0022181869}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillian does not know whether Lillian's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lillian can now know whether Billy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lillian","Billy","Genevieve"],"index":50534,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993558526,"difficulty":0.0006441474}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Toi knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Eric can now know that Toi can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Agustin","Toi","Eric","Karen"],"index":65151,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9643188715,"difficulty":0.0356811285}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nina knows whether Nina is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Corey can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nina","Helen","Corey","Joan"],"index":21701,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999489665,"difficulty":0.000510335}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel does not know whether Rachel's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"William can now know that Rachel can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","William","Rachel","Jennifer"],"index":4786,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9920759201,"difficulty":0.0079240799}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dee's card is shown to Phillip. Gordon's card is shown to Gordon. Phillip's card is shown to Dee. It is publicly announced that someone picked a red card. It is publicly announced that Dee does not know whether Gordon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Phillip can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Phillip","Gordon","Dee"],"index":2319,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993517995,"difficulty":0.0006482005}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"James can now know whether Andrea can know that Andrea is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Robert","Andrea","Pamela"],"index":54461,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9901260138,"difficulty":0.0098739862}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jodi's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Jodi can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Norma","Mary","Jodi"],"index":34342,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9951213002,"difficulty":0.0048786998}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ann","Dustin","Robert"],"index":48550,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9849218726,"difficulty":0.0150781274}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irene does not know whether Gladys is thirsty. It is publicly announced that Nancy is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Irene can now know that Irene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gladys","Irene","Nancy"],"index":2946,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9913293123,"difficulty":0.0086706877}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janet does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Janet can now know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Sue","Janet"],"index":34248,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967509508,"difficulty":0.0032490492}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Jennifer. Jennifer's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ashley can now know whether Jennifer can know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Ashley"],"index":5683,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973716736,"difficulty":0.0026283264}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mabel can now know whether Jacqueline can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Jacqueline","Yvonne","Mabel"],"index":8136,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9861183167,"difficulty":0.0138816833}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether Catherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Keith can now know that David can know that Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Ruth","Catherine","David"],"index":6578,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983692765,"difficulty":0.0016307235}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Richard. Craig's card is shown to Richard. Robert's card is shown to Craig. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether Robert can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Robert","Craig"],"index":11434,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9778644443,"difficulty":0.0221355557}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aubrey does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Carly can now know that Aubrey can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hollis","Alice","Carly","Aubrey"],"index":192,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989155531,"difficulty":0.0010844469}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffany's card is shown to Tiffany. Jean's card is shown to Tiffany. David's card is shown to David. Harriett's card is shown to David. David's card is shown to Jean. Jean's card is shown to Harriett. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tiffany can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tiffany","David","Jean","Harriett"],"index":38571,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993050098,"difficulty":0.0006949902}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Noemi's card is shown to Josephine. Ivan's card is shown to Noemi. Jacqueline's card is shown to Ivan. Ivan's card is shown to Jacqueline. It is publicly announced that someone picked a red card. It is publicly announced that Ivan does not know whether or not everyone picked a red card. It is publicly announced that Josephine does not know whether Josephine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jacqueline can now know that Ivan can know whether Noemi picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Josephine","Noemi","Ivan","Jacqueline"],"index":32206,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7213336229,"difficulty":0.2786663771}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Mabel can now know whether Rachel can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mabel","Rachel"],"index":51517,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994187355,"difficulty":0.0005812645}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dolores does not know whether Annie is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dolores can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clarence","Dolores","Jeanette","Annie"],"index":4535,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987552166,"difficulty":0.0012447834}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Robert. Jeremy's card is shown to Jeremy. Marcus's card is shown to Jeremy. Marcus's card is shown to Kathleen. Robert's card is shown to Marcus. Jeremy's card is shown to Marcus. Kathleen's card is shown to Marcus. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Jeremy can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Jeremy","Kathleen","Marcus"],"index":12409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.600885272,"difficulty":0.399114728}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sadie's card is shown to Sadie. Sadie's card is shown to Jacob. Jacob's card is shown to Jacob. It is publicly announced that someone picked a red card. It is publicly announced that Sadie knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jacob can now know whether Sadie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sadie","Jacob"],"index":61715,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993324876,"difficulty":0.0006675124}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Briana can now know whether June can know whether Harold is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harold","June","Briana"],"index":43176,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990279675,"difficulty":0.0009720325}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittney's card is shown to Brittney. Nicolas's card is shown to Kimberly. Kimberly's card is shown to Naomi. Brittney's card is shown to Nicolas. Kimberly's card is shown to Nicolas. It is publicly announced that someone picked a red card. It is publicly announced that Naomi knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Brittney can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brittney","Kimberly","Naomi","Nicolas"],"index":30309,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994584918,"difficulty":0.0005415082}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Janet can now know that Eileen can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Janet","Eileen"],"index":589,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.995644927,"difficulty":0.004355073}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wade's card is shown to Wade. Carl's card is shown to Wade. Carl's card is shown to Carl. It is publicly announced that someone picked a red card. It is publicly announced that Carl does not know whether or not everyone picked a red card. It is publicly announced that Carl does not know whether Wade picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Wade can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wade","Carl"],"index":64901,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977872372,"difficulty":0.0022127628}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy. It is publicly announced that Harry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Harry can now know whether Eleanore can know whether Eleanore's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eleanore","Charlotte","Elizabeth","Harry"],"index":59462,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993895292,"difficulty":0.0006104708}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Desiree's card is shown to Desiree. Desiree's card is shown to Angie. Julio's card is shown to Angie. Julio's card is shown to Julio. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Julio can now know that Angie can know whether Angie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Desiree","Angie","Julio"],"index":52043,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9421415329,"difficulty":0.0578584671}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brent does not know whether Leopoldo is thirsty. It is publicly announced that Leopoldo does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Leopoldo can now know whether Brent can know that Brent is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leopoldo","Brent","Mary"],"index":51942,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7910176516,"difficulty":1.7910176516}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valerie's card is shown to Heidi. Heidi's card is shown to Valerie. It is publicly announced that someone picked a red card. It is publicly announced that Heidi does not know whether Heidi picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Heidi can now know whether Valerie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Heidi","Valerie"],"index":31594,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9990724325,"difficulty":0.0009275675}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary knows whether or not everyone is thirsty. It is publicly announced that Laticia knows whether Gary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jeffery can now know whether Laticia can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laticia","Gary","Jeffery"],"index":21357,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994940758,"difficulty":0.0005059242}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ralph can now know that Lisa can know whether Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ralph","Lisa"],"index":29500,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7980246544,"difficulty":1.7980246544}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Tony. Tony's card is shown to Brian. Jeremy's card is shown to Brian. Tony's card is shown to Jeremy. Brian's card is shown to Jeremy. Jeremy's card is shown to Boyd. It is publicly announced that someone picked a red card. It is publicly announced that Boyd knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentb knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Brian can now know that Jeremy can know whether Boyd picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tony","Brian","Jeremy","Boyd"],"index":41319,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9864826202,"difficulty":0.0135173798}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dianne knows whether or not everyone is thirsty. It is publicly announced that Dianne knows whether Jaclyn is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Dianne can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jaclyn","Dianne"],"index":37880,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994695783,"difficulty":0.0005304217}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joann's card is shown to Helen. Linda's card is shown to Anita. Helen's card is shown to Joann. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Anita can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Linda","Anita","Joann"],"index":41497,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9912921786,"difficulty":0.0087078214}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Josh's card is shown to Dominick. Dominick's card is shown to Josh. It is publicly announced that someone picked a red card. It is publicly announced that Josh does not know whether Josh picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Josh can now know that Josh picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dominick","Josh"],"index":2912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9593834281,"difficulty":0.0406165719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lonnie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Fredrick can now know whether Fredrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lonnie","Vicki","Guadalupe","Fredrick"],"index":14836,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8384720087,"difficulty":0.1615279913}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Randall's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"George can now know that Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Randall","George","Gary"],"index":58989,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981831908,"difficulty":0.0018168092}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Shella. Mark's card is shown to Mark. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Lori picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Lori can now know whether Shella can know that Maria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lori","Shella","Mark","Maria"],"index":4014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9528834224,"difficulty":0.0471165776}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Michael. Hazel's card is shown to Eileen. Tyree's card is shown to Hazel. Eileen's card is shown to Tyree. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Hazel can now know that Tyree can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Eileen","Hazel","Tyree"],"index":19923,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990015626,"difficulty":0.0009984374}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelly's card is shown to Kelly. Joseph's card is shown to Kelly. Isidro's card is shown to Kelly. Isidro's card is shown to Joseph. Kelly's card is shown to Isidro. Isidro's card is shown to Isidro. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kelly can now know whether Isidro can know whether Isidro picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kelly","Joseph","Isidro"],"index":29313,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980303645,"difficulty":0.0019696355}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Rita knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Susan can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Susan","Rita","Gene"],"index":21031,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999437511,"difficulty":0.000562489}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean knows whether or not everyone's forehead is muddy. It is publicly announced that Alfred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Alfred can now know whether Alfred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alfred","Arthur","Jean","Paul"],"index":18678,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994577765,"difficulty":0.0005422235}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew does not know whether Sondra is thirsty. It is publicly announced that Harold knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"William can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Harold","William","Sondra"],"index":61574,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953183532,"difficulty":0.0046816468}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sonja's card is shown to Jack. Chris's card is shown to Donald. Jack's card is shown to Sonja. Jack's card is shown to Chris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Chris can now know that Donald can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jack","Donald","Sonja","Chris"],"index":65374,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953269958,"difficulty":0.0046730042}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rachael does not know whether or not everyone is thirsty. It is publicly announced that Michael does not know whether Jorge is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Rachael can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Rachael","Jorge"],"index":3347,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994889498,"difficulty":0.0005110502}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Stephen can now know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephen","John","Mark"],"index":8626,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994440675,"difficulty":0.0005559325}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lois does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lois can now know that Jerry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lois","Jerry","Viola"],"index":13735,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9736953974,"difficulty":0.0263046026}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marie is not thirsty. It is publicly announced that David does not know whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Marie can now know whether Elaine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elaine","David","Barbara","Marie"],"index":33793,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983144999,"difficulty":0.0016855001}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bob knows whether Sandy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Cecilia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bob","Sandy","Cecilia"],"index":27343,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990038276,"difficulty":0.0009961724}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry's forehead is muddy. It is publicly announced that Jennie's forehead is not muddy. It is publicly announced that Henry knows whether Jennie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jennie can now know whether Henry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennie","Henry","Elliot"],"index":24061,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991470575,"difficulty":0.0008529425}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Diane can now know that Julie can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julie","Gretchen","Diane"],"index":42026,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992973804,"difficulty":0.0007026196}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lloyd does not know whether or not everyone is thirsty. It is publicly announced that Oscar knows whether Oscar is thirsty. It is publicly announced that Lloyd does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Angelo can now know whether Lloyd can know that Oscar is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Oscar","Lloyd","Angelo"],"index":4794,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9887136221,"difficulty":0.0112863779}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry does not know whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Sara","Henry"],"index":30274,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9896444082,"difficulty":0.0103555918}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joann knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tammy can now know that Joann can know that Amy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tammy","Amy","Marcus","Joann"],"index":8856,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981172085,"difficulty":0.0018827915}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vivian's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Vivian can now know whether Ronnie can know that Ronnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronnie","Vivian"],"index":8809,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999104917,"difficulty":0.000895083}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William knows whether Tamara is thirsty. It is publicly announced that William knows whether Tamara is thirsty. It is publicly announced that Tamara knows whether William is thirsty. It is publicly announced that William knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Tamara can now know that William can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Tamara"],"index":63800,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8946742415,"difficulty":0.1053257585}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melvin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Yvonne can now know that Shameka can know that Melvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melvin","Shameka","Yvonne"],"index":6882,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9799126387,"difficulty":0.0200873613}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Louise. Rosie's card is shown to Louise. Louise's card is shown to Rosie. Rosie's card is shown to Rosie. Imogene's card is shown to Rosie. Rosie's card is shown to Imogene. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Louise can now know whether Imogene can know whether Louise picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louise","Rosie","Imogene"],"index":20939,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997831881,"difficulty":0.002168119}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roger's card is shown to Lana. Carolyn's card is shown to Lana. Gerry's card is shown to Lana. Lana's card is shown to Carolyn. Carolyn's card is shown to Carolyn. Carolyn's card is shown to Gerry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lana","Roger","Carolyn","Gerry"],"index":19797,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989808202,"difficulty":0.0010191798}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nellie's card is shown to Nellie. Armand's card is shown to Nellie. Antonio's card is shown to Nellie. Antonio's card is shown to Armand. Nellie's card is shown to Antonio. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Antonio can now know that Armand can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nellie","Armand","Antonio"],"index":14382,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990310669,"difficulty":0.0009689331}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sonia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Debbie can now know whether Jeffrey can know that Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Sonia","Debbie","Rosemary"],"index":17450,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5227000117,"difficulty":0.4772999883}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Larry can now know that Nancy can know that Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Larry","Teresa"],"index":21862,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953428507,"difficulty":0.0046571493}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Art does not know whether David is thirsty. It is publicly announced that Santiago knows whether Santiago is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Santiago","Art","Mercedes"],"index":937,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.990236938,"difficulty":0.009763062}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ricardo knows whether Tim's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Tim can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tim","Ricardo","Ronald"],"index":60636,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986955523,"difficulty":0.0013044477}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edgar knows whether Manuel's forehead is muddy. It is publicly announced that Edgar knows whether Manuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentd knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Stephen can now know that Thomas can know that Edgar's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edgar","Manuel","Thomas","Stephen"],"index":45239,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984180927,"difficulty":0.0015819073}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ira does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Ira can now know whether Mary can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melanie","Mary","Ira"],"index":4093,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992510676,"difficulty":0.0007489324}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David knows whether David is thirsty. It is publicly announced that Robert does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Eddie can now know that Robert can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eddie","Robert","David"],"index":5187,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994056225,"difficulty":0.0005943775}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joan. Betty's card is shown to Robert. Joseph's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card. It is publicly announced that Joseph knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Joan can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joan","Joseph","Robert","Betty"],"index":52386,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987447262,"difficulty":0.0012552738}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristi's card is shown to Kristi. Donna's card is shown to Kristi. Kristi's card is shown to Donna. Donna's card is shown to Donna. Zachary's card is shown to Donna. Kristi's card is shown to Zachary. Zachary's card is shown to Zachary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donna can now know whether Kristi can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kristi","Donna","Zachary"],"index":57481,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992622733,"difficulty":0.0007377267}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Stacey. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Margaret can now know whether Stacey can know that Stacey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stacey","Margaret"],"index":25429,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9065496922,"difficulty":1.9065496922}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Angela. Maria's card is shown to Angela. Angela's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Angela does not know whether or not everyone picked a red card. It is publicly announced that Angela knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Angela can now know that Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Angela","Linda","Maria"],"index":63474,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9362954497,"difficulty":1.9362954497}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Horace knows whether Horace's forehead is muddy. It is publicly announced that Horace's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Horace can now know that Mark can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Horace","Mark"],"index":27621,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990252256,"difficulty":0.0009747744}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marlon does not know whether William is thirsty. It is publicly announced that William knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"William can now know that Marlon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marlon","Frank","William","James"],"index":54539,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974808097,"difficulty":0.0025191903}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond does not know whether or not everyone is thirsty. It is publicly announced that Dayna knows whether Raymond is thirsty. It is publicly announced that Cecil does not know whether Dayna is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Raymond can now know that Dayna can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dayna","Raymond","Cecil"],"index":30693,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989957213,"difficulty":0.0010042787}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erma knows whether James's forehead is muddy. It is publicly announced that James knows whether Erma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"James can now know whether Erma can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ellen","Erma","James","Kayla"],"index":4363,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994452596,"difficulty":0.0005547404}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to Victoria. Lourdes's card is shown to Barbara. Victoria's card is shown to Jenny. Jenny's card is shown to Jenny. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Victoria can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Barbara","Jenny","Lourdes"],"index":13093,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995496273,"difficulty":0.004503727}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clarence is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Clarence can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tomeka","Warren","Clarence","Julian"],"index":30664,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995033741,"difficulty":0.0004966259}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teddy's card is shown to Ronald. John's card is shown to Evelyn. Ronald's card is shown to John. Evelyn's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Teddy can now know that Evelyn can know that Teddy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Teddy","Ronald","Evelyn","John"],"index":58491,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982984662,"difficulty":0.0017015338}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy. It is publicly announced that Phyllis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Kenneth can now know that Annette's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annette","Phyllis","Kenneth"],"index":65890,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9781011343,"difficulty":0.0218988657}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Robert can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sharon","Robert"],"index":49091,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993682504,"difficulty":0.0006317496}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irvin knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Adam can now know that Irvin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Geri","Leonard","Adam","Irvin"],"index":56753,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9907169938,"difficulty":0.0092830062}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Teresa. Donna's card is shown to Donna. Betty's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Betty knows whether Betty picked a red card. It is publicly announced that Donna picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 2 ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 2 ] 0","hypothesis":"Donna can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Teresa","Donna","Betty"],"index":12297,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990451932,"difficulty":0.0009548068}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cedric does not know whether Cedric's forehead is muddy. It is publicly announced that Karen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Eric can now know whether Cedric can know whether Cedric's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Joshua","Karen","Cedric"],"index":54197,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8637580276,"difficulty":0.1362419724}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vito knows whether Gwendolyn's forehead is muddy. It is publicly announced that Vito knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jason can now know that Gwendolyn can know that Vito's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gwendolyn","Vito","Jason"],"index":35818,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981846213,"difficulty":0.0018153787}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronnie knows whether or not nobody is thirsty. It is publicly announced that Helen does not know whether Ronnie is thirsty. It is publicly announced that Ronnie is thirsty. It is publicly announced that Jake does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ronnie can now know that Helen can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Lee","Jake","Ronnie"],"index":30813,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995042086,"difficulty":0.0004957914}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ada knows whether Ada's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ada can now know that Jonathan can know that Sherry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ada","Jonathan","Sherry"],"index":35116,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980071187,"difficulty":0.0019928813}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether Lorene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Jonathan can now know that Christina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorene","Jonathan","Christina","George"],"index":24256,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980503321,"difficulty":0.0019496679}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether Alfredo can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfredo","John","Charles","Cassandra"],"index":49520,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993896484,"difficulty":0.0006103516}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Paula's card is shown to Barbara. Barbara's card is shown to Tameka. Paula's card is shown to Tameka. Barbara's card is shown to Paula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Tameka","Paula"],"index":24918,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989877343,"difficulty":0.0010122657}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janet knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Raymond can now know that Raymond is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janet","Earl","Raymond"],"index":18623,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9825226068,"difficulty":0.0174773932}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether or not everyone's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ivory can now know whether Ruth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Ivory","Scott","Ruth"],"index":66801,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9521650076,"difficulty":0.0478349924}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alice's card is shown to Alice. Kim's card is shown to Alice. Ashley's card is shown to Alice. Alice's card is shown to Kim. Ashley's card is shown to Ashley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Alice can now know that Ashley can know whether Kim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alice","Kim","Ashley"],"index":33682,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9920648932,"difficulty":0.0079351068}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daren does not know whether Timothy is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Shanell knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows whether (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Daren can now know whether Timothy can know that Shanell is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Daren","Shanell"],"index":51996,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9801928401,"difficulty":0.0198071599}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emerson does not know whether Emerson's forehead is muddy. It is publicly announced that Ryan knows whether Ryan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Emerson can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ryan","Emerson"],"index":40242,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989934564,"difficulty":0.0010065436}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether Darla is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Robert can now know whether Darla is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darla","Leonard","Robert","Dorothy"],"index":29730,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958221912,"difficulty":0.0041778088}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Karen can now know whether Ernest can know whether Ernest's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ernest","Mark","Nancy","Karen"],"index":41509,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993909597,"difficulty":0.0006090403}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that James knows whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"James can now know whether Christopher can know that Christopher is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Thomas","James"],"index":20773,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9764302373,"difficulty":0.0235697627}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carol's card is shown to Calvin. Mary's card is shown to Charles. Carol's card is shown to Mary. Mary's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether Carol can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Calvin","Charles","Mary","Carol"],"index":31374,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993652701,"difficulty":0.0006347299}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gerald knows whether or not nobody's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! 2 ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! 2 ] 0","hypothesis":"Ruth can now know that Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gerald","Mary","Ruth"],"index":32001,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931771755,"difficulty":0.0068228245}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ian's card is shown to Ian. Gloria's card is shown to Ian. Gloria's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Gloria does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Gloria can now know that Ian can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ian","Gloria"],"index":35003,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989087582,"difficulty":0.0010912418}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly knows whether Ada's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentd knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Richard can now know that Kelly can know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Ada","Kelly","Richard"],"index":65327,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981984496,"difficulty":0.0018015504}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Robert. Robert's card is shown to Elijah. Paul's card is shown to Marian. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a red card. It is publicly announced that Robert does not know whether Elijah picked a red card. It is publicly announced that Elijah does not know whether Marian picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Elijah can now know that Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Robert","Elijah","Marian"],"index":15353,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994556308,"difficulty":0.0005443692}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Autumn can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Autumn","George","Kristen","Mary"],"index":52,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994320273,"difficulty":0.0005679727}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Daniel can now know that Vernon can know that Vernon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Susan","Vernon"],"index":17432,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952161312,"difficulty":0.0047838688}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy. It is publicly announced that Mary knows whether Betty's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Mary can now know that Betty can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Betty"],"index":62046,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994400144,"difficulty":0.0005599856}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Jose can now know that Jose is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Melissa","Jose","Mary"],"index":11210,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.878739655,"difficulty":0.121260345}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know that Sara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Trina","Douglas","Sara"],"index":40263,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973105192,"difficulty":0.0026894808}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua's forehead is muddy. It is publicly announced that Germaine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Joshua can now know that Germaine can know that Germaine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Germaine","Joshua"],"index":36281,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9909193516,"difficulty":0.0090806484}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Carmen. Andrea's card is shown to Andrea. Melanie's card is shown to Andrea. John's card is shown to Andrea. Andrea's card is shown to Melanie. It is publicly announced that someone picked a red card. It is publicly announced that Carmen does not know whether Melanie picked a red card. It is publicly announced that Andrea picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Carmen can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carmen","Andrea","Melanie","John"],"index":3274,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8698601127,"difficulty":0.1301398873}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Danny can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Cindy","Danny","Jeffrey"],"index":40740,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988437891,"difficulty":0.0011562109}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Cheryl can now know that Cheryl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tara","Cheryl"],"index":48760,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966474175,"difficulty":0.0033525825}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valerie knows whether Valerie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Candy can now know that Valerie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Valerie","Candy"],"index":16134,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9956931472,"difficulty":0.0043068528}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Joshua can now know that Debra can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debra","Joshua","Melissa"],"index":50247,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989665747,"difficulty":0.0010334253}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos knows whether or not nobody's forehead is muddy. It is publicly announced that Carlos knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Carlos can now know that Tony can know that Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tony","Jill","Carlos"],"index":32332,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9841273427,"difficulty":0.0158726573}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chad is not thirsty. It is publicly announced that Ernesto knows whether Chad is thirsty. It is publicly announced that Chad does not know whether Eric is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Chad can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ernesto","Mark","Eric","Chad"],"index":29140,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995273352,"difficulty":0.0004726648}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ron's card is shown to Ron. Edgar's card is shown to Ron. Edgar's card is shown to Edgar. Ron's card is shown to Brenda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Edgar can now know that Ron can know that Edgar picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ron","Edgar","Brenda"],"index":28642,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970858693,"difficulty":0.0029141307}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacob knows whether Susan's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy. It is publicly announced that Teresa knows whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Susan can now know whether Jacob can know whether Jacob's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","Teresa","Jacob","Patricia"],"index":25726,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.864223361,"difficulty":1.864223361}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cecil does not know whether Marion is thirsty. It is publicly announced that Marion does not know whether or not everyone is thirsty. It is publicly announced that Marion does not know whether Shannon is thirsty. It is publicly announced that Marion does not know whether Shannon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Shannon can now know whether Marion can know that Cecil is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cecil","Marion","Shannon"],"index":7638,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.977979362,"difficulty":0.022020638}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rodney is thirsty. It is publicly announced that Martha does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Barbara can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rodney","Martha","Jill","Barbara"],"index":17230,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994803071,"difficulty":0.0005196929}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randy's card is shown to Marie. Danita's card is shown to Marie. Randy's card is shown to Randy. Randy's card is shown to Danita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Randy can now know whether Marie can know that Danita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marie","Randy","Danita"],"index":64164,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9456144571,"difficulty":1.9456144571}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether or not nobody's forehead is muddy. It is publicly announced that Monika's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] 0","hypothesis":"Monika can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Violet","Dorothy","Monika"],"index":21993,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984382987,"difficulty":0.0015617013}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Nicholas is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Brenda is not thirsty. It is publicly announced that Nicholas knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Brenda","Nicholas","Helen"],"index":2637,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990338087,"difficulty":0.0009661913}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deanna does not know whether or not everyone's forehead is muddy. It is publicly announced that Deanna knows whether Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentc knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Nathan can now know whether Matthew can know that Nathan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deanna","Johnnie","Nathan","Matthew"],"index":28512,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6326598525,"difficulty":0.3673401475}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to Lou. Lou's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Lou can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lou","William"],"index":17508,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990487695,"difficulty":0.0009512305}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Sarah. Sarah's card is shown to Karen. Roy's card is shown to Karen. Karen's card is shown to Roy. Roy's card is shown to Roy. It is publicly announced that someone picked a red card. It is publicly announced that Sarah does not know whether or not everyone picked a red card. It is publicly announced that Roy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] Agentc knows that (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Karen can now know that Sarah can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","Robert","Karen","Roy"],"index":45344,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7315065265,"difficulty":1.7315065265}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy. It is publicly announced that Leandra's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Leandra can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Carrie","Gary","Leandra"],"index":65404,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994441867,"difficulty":0.0005558133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lindsey knows whether Thelma's forehead is muddy. It is publicly announced that Edith's forehead is not muddy. It is publicly announced that Lindsey knows whether Lindsey's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Thelma can now know whether Lindsey can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lindsey","Brenda","Thelma","Edith"],"index":20246,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993442893,"difficulty":0.0006557107}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy. It is publicly announced that Elizabeth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Elizabeth can now know that Ruby can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","William","Ruby"],"index":21124,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994382262,"difficulty":0.0005617738}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle knows whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"John can now know that Mimi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mimi","John","Michelle"],"index":56321,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980119467,"difficulty":0.0019880533}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tabatha does not know whether or not everyone's forehead is muddy. It is publicly announced that Tabatha knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Tabatha can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Hector","Tabatha","Darren","Carlos"],"index":8356,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994603992,"difficulty":0.0005396008}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Lou. Thomas's card is shown to Thomas. Jennifer's card is shown to William. Lou's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Thomas can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lou","Thomas","William","Jennifer"],"index":13736,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993608594,"difficulty":0.0006391406}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamika does not know whether or not everyone's forehead is muddy. It is publicly announced that Christine knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Christine can now know that Tamika can know that Tamika's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tamika","Christine"],"index":65881,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5764622092,"difficulty":0.4235377908}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Enola is thirsty. It is publicly announced that Juan knows whether Juan is thirsty. It is publicly announced that Enola does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Enola can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Enola","Sean","Albert"],"index":21172,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995011091,"difficulty":0.0004988909}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Val does not know whether Val's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"David can now know that Rhonda can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rhonda","Val","David"],"index":49937,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993051291,"difficulty":0.0006948709}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luke's card is shown to Luke. Carolyn's card is shown to Luke. Gary's card is shown to Luke. Karen's card is shown to Karen. Carolyn's card is shown to Carolyn. Karen's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Gary picked a red card. It is publicly announced that Luke knows whether Carolyn picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Carolyn can now know whether Karen can know whether Carolyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Luke","Karen","Carolyn","Gary"],"index":28567,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985498786,"difficulty":0.0014501214}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen does not know whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kathleen can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathleen","Stephen","Olivia","Charles"],"index":31652,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993306398,"difficulty":0.0006693602}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is not muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Peter can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Becky","Patricia","Peter"],"index":25709,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vanessa knows whether or not nobody's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Vanessa can now know whether Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Vanessa","Tammy","Thomas"],"index":35515,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994624257,"difficulty":0.0005375743}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Karen can now know that Jeffrey can know whether Latisha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Thomas","Latisha","Karen"],"index":52202,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9964141846,"difficulty":0.0035858154}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether Jeff's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Vincent can now know whether Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vincent","Sarah","Jeff","Teresa"],"index":22961,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992159605,"difficulty":0.0007840395}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Cynthia can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dwayne","Cynthia","Robert","Thomas"],"index":42134,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989848733,"difficulty":0.0010151267}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel does not know whether Rachel's forehead is muddy. It is publicly announced that Aaron knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Rachel can now know that Aaron can know that Rachel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rachel","Aaron"],"index":37794,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.918343842,"difficulty":0.081656158}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Elizabeth. Samuel's card is shown to John. Elizabeth's card is shown to Robert. John's card is shown to Robert. Samuel's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Elizabeth can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","John","Samuel","Robert"],"index":2414,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930155277,"difficulty":0.0069844723}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Antonio can now know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Antonio","Michael","Anthony"],"index":63621,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999271214,"difficulty":0.000728786}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Sylvester can now know that Patricia can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sylvester","Patricia","Tamara"],"index":17150,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987665415,"difficulty":0.0012334585}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Iris knows whether Iris's forehead is muddy. It is publicly announced that Edward knows whether Carmelo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Edward can now know whether Iris can know that Carmelo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carmelo","Iris","Edward"],"index":6991,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994652867,"difficulty":0.0005347133}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen does not know whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kathleen can now know that Keisha can know that June's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Keisha","June","Della"],"index":21123,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976199269,"difficulty":0.0023800731}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Kathy does not know whether Daniel is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kathy can now know that Daniel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Anna","Daniel","Kathy"],"index":30100,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977218509,"difficulty":0.0022781491}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristin's card is shown to Suzanne. Ralph's card is shown to Isaac. Suzanne's card is shown to Isaac. Isaac's card is shown to Isaac. Kristin's card is shown to Isaac. Suzanne's card is shown to Kristin. Kristin's card is shown to Kristin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Suzanne can now know whether Isaac can know that Kristin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ralph","Suzanne","Isaac","Kristin"],"index":42507,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9169855118,"difficulty":0.0830144882}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sybil's card is shown to Sybil. Audrey's card is shown to Crystal. Crystal's card is shown to Audrey. It is publicly announced that someone picked a red card. It is publicly announced that Sybil does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Franklin can now know whether Sybil picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sybil","Crystal","Franklin","Audrey"],"index":60661,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9474049807,"difficulty":0.0525950193}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aimee knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"William can now know that Aimee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Elsa","Aimee"],"index":13871,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978041053,"difficulty":0.0021958947}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kendra can now know that Steven can know that Kendra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steven","Catherine","Kendra"],"index":12945,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9939011335,"difficulty":0.0060988665}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Jesus's forehead is muddy. It is publicly announced that Sandra knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sandra","Janette","Michael","Jesus"],"index":49574,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992657304,"difficulty":0.0007342696}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty knows whether Betty is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Doreen can now know whether Betty can know whether Doreen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Kerry","Doreen"],"index":64789,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986519217,"difficulty":0.0013480783}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Gwendolyn can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gwendolyn","John","Hazel","Donald"],"index":51507,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999412775,"difficulty":0.000587225}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anna's card is shown to Dallas. Robert's card is shown to Dallas. Dallas's card is shown to Anna. Dallas's card is shown to Robert. Anna's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Anna does not know whether Anna picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Anna can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dallas","Anna","Robert","Christopher"],"index":30250,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9915581942,"difficulty":0.0084418058}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Coleen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Coleen","Jonathan","Joseph","Wesley"],"index":17520,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998934567,"difficulty":0.001065433}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to George. Glen's card is shown to Glen. George's card is shown to Hilton. Glen's card is shown to Hilton. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Hilton can now know that Hilton picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Glen","Hilton"],"index":41197,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9938394427,"difficulty":0.0061605573}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether Henriette's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Henriette can now know whether Rebecca can know that Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Juan","Rebecca","Henriette"],"index":61638,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9876804352,"difficulty":0.0123195648}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Amy can now know whether Ronald can know whether Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronald","Gregory","Amy"],"index":44672,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985688925,"difficulty":0.0014311075}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy does not know whether or not everyone's forehead is muddy. It is publicly announced that Timothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Timothy can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Samuel","Timothy"],"index":51897,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985215068,"difficulty":0.0014784932}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Kevin can now know that Kevin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Sophie","Ann","Gregory"],"index":11443,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5357517004,"difficulty":0.4642482996}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erica does not know whether Stacy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Erica can now know whether Nicki can know that Brian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Erica","Nicki","Stacy","Brian"],"index":26391,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9962527752,"difficulty":0.0037472248}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mollie does not know whether Mollie's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Mollie can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elizabeth","Mollie","Caleb"],"index":20562,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994045496,"difficulty":0.0005954504}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Henry can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wm","John","Henry","Valda"],"index":36386,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993243217,"difficulty":0.0006756783}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Jason. Nancy's card is shown to Jason. Laura's card is shown to Laura. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Laura can now know whether Jason can know whether Laura picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Laura","Nancy"],"index":45888,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988299012,"difficulty":0.0011700988}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer knows whether Jennifer is thirsty. It is publicly announced that Wade knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jennifer can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wade","Donny","Jennifer"],"index":55231,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994834661,"difficulty":0.0005165339}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Christopher. Christopher's card is shown to Cheryl. Cheryl's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Cheryl","James"],"index":35390,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998403132,"difficulty":0.001596868}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mitchell knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mitchell can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherry","Mitchell","Lonnie"],"index":33169,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983855486,"difficulty":0.0016144514}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Grace. Thomas's card is shown to Grace. Grace's card is shown to Lisa. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know that Thomas can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Grace","Lisa","Thomas"],"index":48012,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7574623227,"difficulty":0.2425376773}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet knows whether Janet's forehead is muddy. It is publicly announced that Stephen knows whether Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Janet can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Janet","John","Stephen"],"index":30553,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987200499,"difficulty":0.0012799501}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"George can now know that Brittany can know whether Simone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Simone","Brittany","Luanne","George"],"index":32140,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993332028,"difficulty":0.0006667972}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Charles can now know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Charles","Cory","Raymond"],"index":20180,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984379411,"difficulty":0.0015620589}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy does not know whether Stanley is thirsty. It is publicly announced that Robbie is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] Agentb knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Robbie can now know whether John can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Robbie","Stanley","John"],"index":54680,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9243900776,"difficulty":0.0756099224}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Todd can now know that Jill can know that Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Jill","Scott","Todd"],"index":1578,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979113936,"difficulty":0.0020886064}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"George can now know whether Sarah can know whether Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sarah","Ann","George"],"index":11595,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989815354,"difficulty":0.0010184646}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynn's card is shown to Lynn. Ruby's card is shown to Ruby. Lynn's card is shown to Robert. Ruby's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Lynn can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lynn","Ruby","Robert"],"index":24319,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7443280816,"difficulty":1.7443280816}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Shirley can now know whether Jesse is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathryn","Philip","Shirley","Jesse"],"index":51356,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9568429589,"difficulty":0.0431570411}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie knows whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Julie can now know that Kathleen can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Julie","Kathleen"],"index":45940,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993591905,"difficulty":0.0006408095}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Louis can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Barbara","Louis"],"index":31928,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994592071,"difficulty":0.0005407929}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matthew knows whether someone is thirsty. It is publicly announced that James does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Matthew can now know that James can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Matthew","James"],"index":37288,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994594455,"difficulty":0.0005405545}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelby knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Sharon can now know that Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Erica","Shelby"],"index":44285,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982154369,"difficulty":0.0017845631}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly knows whether someone is thirsty. It is publicly announced that Jay does not know whether Gerald is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jay can now know whether Jay is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kelly","Jay","Gerald"],"index":4384,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9956696033,"difficulty":0.0043303967}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Sara. Joanne's card is shown to Tim. Latanya's card is shown to Tim. Tim's card is shown to Joanne. Tim's card is shown to Latanya. Joanne's card is shown to Latanya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Latanya can now know that Joanne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sara","Tim","Joanne","Latanya"],"index":45760,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953138828,"difficulty":0.0046861172}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Margaret can now know that William can know whether Claudio's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Claudio","William","Irene","Margaret"],"index":24440,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993169308,"difficulty":0.0006830692}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Daphne can now know that Christopher can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Daphne","Jesse"],"index":18246,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9773663282,"difficulty":0.0226336718}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ed can now know whether Zoe can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ed","Zoe","Stephen"],"index":64585,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999337256,"difficulty":0.000662744}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Michael knows whether Michael is thirsty. It is publicly announced that Michael knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Sherman can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Sherman","Michael"],"index":20013,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9886077046,"difficulty":0.0113922954}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Kayla can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gloria","Frank","Pearl","Kayla"],"index":46151,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985993505,"difficulty":0.0014006495}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Betty can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betty","Milagros","Jorge"],"index":17165,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988928437,"difficulty":0.0011071563}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stanley can now know whether Franklin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paz","Stanley","Franklin","Michael"],"index":49733,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964179993,"difficulty":0.0035820007}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sidney can now know that Sidney's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sidney","Dorothy","Derek","William"],"index":42965,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.992698729,"difficulty":0.007301271}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dolores is thirsty. It is publicly announced that Marilyn does not know whether Mark is thirsty. It is publicly announced that Nellie knows whether or not nobody is thirsty. It is publicly announced that Nellie is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentb knows that (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Marilyn can now know that Nellie can know that Nellie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Marilyn","Nellie","Dolores"],"index":21425,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9761663079,"difficulty":0.0238336921}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joann's card is shown to Rick. Howard's card is shown to Rick. Howard's card is shown to Joann. Rick's card is shown to Howard. Howard's card is shown to Howard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Howard can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rick","Joann","Howard"],"index":53522,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947058558,"difficulty":0.0052941442}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hazel does not know whether Adam is thirsty. It is publicly announced that Adam is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] 0","hypothesis":"Hazel can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Adam","Hazel"],"index":19893,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995120764,"difficulty":0.0004879236}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"James can now know that Irving can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elliott","James","Irving","William"],"index":66615,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994353652,"difficulty":0.0005646348}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Magda's card is shown to Magda. James's card is shown to Magda. Patrick's card is shown to Magda. Patrick's card is shown to Sharon. Magda's card is shown to Patrick. James's card is shown to Patrick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Magda can now know whether James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Magda","James","Sharon","Patrick"],"index":61570,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9853596091,"difficulty":0.0146403909}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy. It is publicly announced that Ronald knows whether someone's forehead is muddy. It is publicly announced that Ronald knows whether Carol's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Melissa can now know that Carol can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melissa","Ronald","Carol"],"index":18380,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989411235,"difficulty":0.0010588765}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Vanessa can now know that Vanessa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Aileen","Jeffrey","Vanessa"],"index":18536,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9935316443,"difficulty":0.0064683557}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Young's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Jennie can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jimmy","Jennie","Young"],"index":21198,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993839264,"difficulty":0.0006160736}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Melissa. Melissa's card is shown to Alberto. It is publicly announced that someone picked a red card. It is publicly announced that Alberto does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Alberto can now know whether Melissa can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melissa","Alberto"],"index":27206,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9748138785,"difficulty":0.0251861215}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jill does not know whether Timothy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"William can now know whether Jill can know whether Timothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Jill","Timothy","Mark"],"index":23389,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992019534,"difficulty":0.0007980466}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annette knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Richard can now know whether Janice can know whether Janice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Annette","Richard","Janice"],"index":64749,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.990042448,"difficulty":0.009957552}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gabrielle's forehead is muddy. It is publicly announced that Christian knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Mary can now know whether Gabrielle can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeanne","Mary","Gabrielle","Christian"],"index":38287,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994243383,"difficulty":0.0005756617}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Donald can now know whether Lawrence can know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laura","Lawrence","Donald"],"index":826,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9916144609,"difficulty":0.0083855391}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse is not thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Edward can now know that Thomas can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesse","Thomas","Edward"],"index":25978,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994037151,"difficulty":0.0005962849}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorene's forehead is not muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Donna can now know that Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Travis","Dorene","Richard"],"index":11789,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939925075,"difficulty":0.0060074925}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chrissy's card is shown to Chrissy. Sophie's card is shown to Chrissy. Sophie's card is shown to Sophie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Sophie can now know that Chrissy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Chrissy","Sophie"],"index":31187,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994004965,"difficulty":0.0005995035}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric does not know whether Eric's forehead is muddy. It is publicly announced that Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] 0","hypothesis":"Leo can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leo","Tamara","Betty","Eric"],"index":27982,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994997978,"difficulty":0.0005002022}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roberto knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Roberto can now know that Ronald can know that Ronald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Roberto","Matthew"],"index":31068,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.967910111,"difficulty":0.032089889}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ivan does not know whether Carole is thirsty. It is publicly announced that Kathryn does not know whether Joseph is thirsty. It is publicly announced that Ivan does not know whether Kathryn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Kathryn can now know that Carole can know that Carole is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathryn","Joseph","Carole","Ivan"],"index":61782,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9956328273,"difficulty":0.0043671727}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anna knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Lawrence can now know whether Justin can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lawrence","Anna","Justin"],"index":12663,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992449284,"difficulty":0.0007550716}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julienne does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Julienne can now know whether Jimmy can know that Wilbert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julienne","Jimmy","Wilbert"],"index":51875,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9660344124,"difficulty":0.0339655876}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Harlan's card is shown to William. Joyce's card is shown to Harlan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joyce","William","Dorothy","Harlan"],"index":58298,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993209839,"difficulty":0.0006790161}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Anthony can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karin","Drew","Anthony","David"],"index":4861,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998826921,"difficulty":0.001173079}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that James knows whether someone is thirsty. It is publicly announced that Pamela does not know whether James is thirsty. It is publicly announced that Pamela knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"William can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Pamela","James"],"index":59874,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993283749,"difficulty":0.0006716251}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Wayne. Richard's card is shown to Richard. Tom's card is shown to Richard. David's card is shown to Richard. Richard's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Wayne does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Tom can now know that Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wayne","Richard","Tom","David"],"index":37608,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9196255207,"difficulty":0.0803744793}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Amy can now know that Pete's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kendra","Pete","Amy","Troy"],"index":32680,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9945129156,"difficulty":0.0054870844}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"David can now know that Eli's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eli","David","Eugene"],"index":22232,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998103857,"difficulty":0.001896143}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Linda can now know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Janelle","Michael","Linda"],"index":51570,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9934351444,"difficulty":0.0065648556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Walter can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Willard","Rebecca","Frank"],"index":22389,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9925205708,"difficulty":0.0074794292}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janet knows whether someone is thirsty. It is publicly announced that Paula does not know whether or not everyone is thirsty. It is publicly announced that Paula does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Monica can now know whether Janet can know that Paula is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paula","Monica","Janet"],"index":6458,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9815581441,"difficulty":0.0184418559}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guadalupe's forehead is muddy. It is publicly announced that Guadalupe's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"William can now know that Tara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tara","William","Guadalupe","Madeline"],"index":52154,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9370167851,"difficulty":0.0629832149}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacob knows whether Tracey's forehead is muddy. It is publicly announced that Seth does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jacob can now know whether Tracey can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracey","Jacob","Seth"],"index":66168,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9384518266,"difficulty":0.0615481734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Teresa can now know that Nikki can know that Jamie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nikki","Teresa","Jamie","Eric"],"index":1189,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9961574674,"difficulty":0.0038425326}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phillip is not thirsty. It is publicly announced that John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] Agentb knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Catherine can now know whether Phillip can know that Catherine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Catherine","Susan","Phillip"],"index":56099,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.96925807,"difficulty":0.03074193}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois knows whether someone's forehead is muddy. It is publicly announced that Aida knows whether someone's forehead is muddy. It is publicly announced that Michael knows whether Aida's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Michael can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Micheal","Lois","Aida"],"index":46078,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989976287,"difficulty":0.0010023713}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"David can now know that Scott can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["David","Scott"],"index":63495,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982174039,"difficulty":0.0017825961}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"David can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Maria"],"index":33226,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9901638627,"difficulty":0.0098361373}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rocky knows whether Rocky's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Eddie can now know that Rocky can know whether Eddie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eddie","Frank","Rocky"],"index":32477,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993869066,"difficulty":0.0006130934}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doris does not know whether Merry is thirsty. It is publicly announced that Doris knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Doris can now know whether Merry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Merry","Doris"],"index":48439,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961037636,"difficulty":0.0038962364}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joanna can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joanna","George","Kristen","Brian"],"index":31109,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983509779,"difficulty":0.0016490221}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lena does not know whether or not everyone's forehead is muddy. It is publicly announced that Lena does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Jose can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jose","Lena"],"index":26769,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8980749249,"difficulty":0.1019250751}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen does not know whether or not everyone's forehead is muddy. It is publicly announced that Ellen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Matthew can now know that Ellen can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dwayne","Matthew","Ellen","Howard"],"index":7380,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9383232594,"difficulty":0.0616767406}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric does not know whether Frances is thirsty. It is publicly announced that Gloria does not know whether Eric is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Eric can now know whether Gloria can know that Eric is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frances","Gloria","Eric"],"index":1864,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9708245993,"difficulty":0.0291754007}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberly's card is shown to Karen. Karen's card is shown to Kimberly. Kimberly's card is shown to Kimberly. Karen's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Karen picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Karen can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Kimberly","Richard"],"index":14753,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9843103886,"difficulty":0.0156896114}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelvin's card is shown to Melissa. Melissa's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Kelvin knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Kelvin can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kelvin","Melissa"],"index":62091,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993828535,"difficulty":0.0006171465}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roberto does not know whether Beverly is thirsty. It is publicly announced that Mauricio does not know whether Ira is thirsty. It is publicly announced that Ira does not know whether Roberto is thirsty. It is publicly announced that Roberto knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Beverly can now know that Ira is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mauricio","Beverly","Roberto","Ira"],"index":30036,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949775338,"difficulty":0.0050224662}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Manuel does not know whether or not everyone is thirsty. It is publicly announced that Manuel does not know whether or not everyone is thirsty. It is publicly announced that Manuel does not know whether Colleen is thirsty. It is publicly announced that Manuel knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Colleen can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Colleen","Manuel"],"index":28253,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999070704,"difficulty":0.000929296}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Stanley can now know that Paul can know whether Roger's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverley","Stanley","Roger","Paul"],"index":64894,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994496703,"difficulty":0.0005503297}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brent's card is shown to Janie. Janie's card is shown to Barbara. Barbara's card is shown to Barbara. Barbara's card is shown to Brent. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janie can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janie","Barbara","Brent"],"index":522,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968115687,"difficulty":0.0031884313}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Monica does not know whether Monica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Candace can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Candace","Monica"],"index":57354,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9916843176,"difficulty":0.0083156824}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adrienne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donald","Robert","Adrienne","Karen"],"index":50037,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994378686,"difficulty":0.0005621314}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Renato can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jim","Kimberly","Renato","Brandon"],"index":55150,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995394945,"difficulty":0.0004605055}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darryl's card is shown to Darryl. Darryl's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Mary can now know whether Darryl can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Darryl","Mary"],"index":25032,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5494231582,"difficulty":1.5494231582}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gail can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gail","Robert","June"],"index":40898,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975931048,"difficulty":0.0024068952}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Bernice knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Bernice can now know whether Adrienne can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Adrienne","Bernice"],"index":21779,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9948635697,"difficulty":0.0051364303}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hilda's card is shown to Hilda. Ernestine's card is shown to Hilda. Margaret's card is shown to Ernestine. Marilyn's card is shown to Ernestine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Hilda can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Hilda","Ernestine","Margaret","Marilyn"],"index":33903,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994288087,"difficulty":0.0005711913}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luis does not know whether Luis's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dean can now know that Luis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Luis","Dean"],"index":59319,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.990737617,"difficulty":0.009262383}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miranda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jake can now know whether Jonathan can know whether Steve's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jake","Miranda","Steve","Jonathan"],"index":18274,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999150753,"difficulty":0.000849247}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jayne's card is shown to Jayne. Ruby's card is shown to Jayne. Jayne's card is shown to Christopher. Christopher's card is shown to Christopher. Ruby's card is shown to Christopher. Christopher's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Ruby knows whether someone picked a red card. It is publicly announced that Christopher picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] 0","hypothesis":"Christopher can now know whether Ruby can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jayne","Christopher","Ruby"],"index":54819,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993195534,"difficulty":0.0006804466}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caroline's card is shown to Caroline. Charles's card is shown to Caroline. Jay's card is shown to Caroline. Caroline's card is shown to Charles. Charles's card is shown to Charles. Caroline's card is shown to Jay. Charles's card is shown to Jay. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jay can now know whether Caroline can know whether Caroline picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Caroline","Charles","Jay"],"index":56697,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9974166155,"difficulty":0.0025833845}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Brent can now know whether Melissa can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eileen","George","Melissa","Brent"],"index":23270,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992012382,"difficulty":0.0007987618}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Hildegard. John's card is shown to John. Virginia's card is shown to John. Virginia's card is shown to Richard. Richard's card is shown to Virginia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Hildegard can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hildegard","John","Richard","Virginia"],"index":21772,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993869066,"difficulty":0.0006130934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theresa does not know whether Robert is thirsty. It is publicly announced that Kurt does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Thomas can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Theresa","Kurt","Robert"],"index":46768,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967157841,"difficulty":0.0032842159}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know whether Yvonne can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mildred","Joseph","Sarah","Yvonne"],"index":34749,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8503456712,"difficulty":0.1496543288}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michelle does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"James can now know that Carol can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Michelle","Mary","James"],"index":49932,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989495873,"difficulty":0.0010504127}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Miriam's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Miriam can now know that Thomas can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Miriam","Carolina"],"index":40404,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989686012,"difficulty":0.0010313988}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Claude does not know whether Claude's forehead is muddy. It is publicly announced that Dean does not know whether Dean's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kay can now know whether Claude can know whether Dean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dean","Kay","Claude"],"index":90,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991288781,"difficulty":0.0008711219}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario knows whether Alan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"James can now know that Michael can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alan","Michael","James","Mario"],"index":10880,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993879795,"difficulty":0.0006120205}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marjorie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Christine can now know that Chris can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Chris","Christine","Marjorie"],"index":51967,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994895458,"difficulty":0.0005104542}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte is thirsty. It is publicly announced that Scott is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(2) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(2) ] 0","hypothesis":"Scott can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charlotte","Scott"],"index":27816,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995071888,"difficulty":0.0004928112}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roy knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Susan can now know that Everett is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roy","Everett","Randall","Susan"],"index":65270,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980878234,"difficulty":0.0019121766}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brittani's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Jorge can now know whether Cory's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jorge","Cory","Brittani","Richard"],"index":56092,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993645549,"difficulty":0.0006354451}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Harold can now know that Maria can know whether Harold's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Harold","Maria"],"index":51455,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993661046,"difficulty":0.0006338954}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodney knows whether Cruz's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Silas can now know that George can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cruz","Silas","George","Rodney"],"index":47106,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998934567,"difficulty":0.001065433}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louie does not know whether Sandra is thirsty. It is publicly announced that Mario does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Brenda can now know whether Mario can know that Sandra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Brenda","Louie","Mario"],"index":20075,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9925048351,"difficulty":0.0074951649}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gary knows whether Heather's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Mary can now know that Heather can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Mary","Patricia","Heather"],"index":12659,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989793897,"difficulty":0.0010206103}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jamison knows whether or not nobody is thirsty. It is publicly announced that Jamison knows whether Jamison is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Maria can now know that Jamison can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Maria","Jamison"],"index":8973,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988540411,"difficulty":0.0011459589}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stella does not know whether or not everyone's forehead is muddy. It is publicly announced that Shannon knows whether Shannon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Stella can now know whether Shannon can know that Shannon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shannon","Dorothy","Stella"],"index":9812,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8426378369,"difficulty":0.1573621631}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to George. George's card is shown to Rita. Erin's card is shown to Erin. It is publicly announced that someone picked a red card. It is publicly announced that George picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Erin can now know that Rita can know that Rita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Rita","Erin"],"index":24188,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9903637767,"difficulty":0.0096362233}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Randy's card is shown to Donald. Adam's card is shown to Donald. Donald's card is shown to Adam. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know whether Adam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Randy","Adam"],"index":4658,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8318017721,"difficulty":1.8318017721}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhonda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Rhonda can now know that Felicia can know that Rhonda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Felicia","Gina","Rhonda"],"index":41030,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.8107855916,"difficulty":1.8107855916}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jasmine knows whether Anne's forehead is muddy. It is publicly announced that Anne does not know whether or not everyone's forehead is muddy. It is publicly announced that Jasmine knows whether Jesus's forehead is muddy. It is publicly announced that Jasmine knows whether Jeffery's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (Agentc knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jeffery can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jasmine","Jesus","Jeffery","Anne"],"index":17500,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994607568,"difficulty":0.0005392432}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcia does not know whether Christopher is thirsty. It is publicly announced that Christopher does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Christopher can now know that Joan can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcia","Christopher","Joan","Jessie"],"index":48282,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994965792,"difficulty":0.0005034208}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jean's card is shown to Jean. Harvey's card is shown to Harvey. Martha's card is shown to Harvey. Jean's card is shown to Perry. Perry's card is shown to Perry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Martha can now know that Harvey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jean","Harvey","Martha","Perry"],"index":22457,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981027246,"difficulty":0.0018972754}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Susan. Karen's card is shown to Susan. Ronald's card is shown to Brenda. Ronald's card is shown to Karen. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ronald can now know that Brenda can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Brenda","Karen","Ronald"],"index":32077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994125366,"difficulty":0.0005874634}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Rebecca can now know whether Victoria can know whether Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rebecca","Victoria"],"index":41219,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9857484698,"difficulty":0.0142515302}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmy knows whether or not nobody is thirsty. It is publicly announced that Debra does not know whether Jimmy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Debra can now know whether Carmen can know whether Debra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Debra","Jimmy","Carmen"],"index":55760,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998913765,"difficulty":0.001086235}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Christine's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy. It is publicly announced that Danny knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Danny can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kevin","Christine","Danny"],"index":43848,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.999019742,"difficulty":0.000980258}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen knows whether Karen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Willie can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michelle","Karen","Willie","Richard"],"index":27481,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994398952,"difficulty":0.0005601048}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Scott can now know whether Maria can know that Ernie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnny","Scott","Ernie","Maria"],"index":41141,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994263649,"difficulty":0.0005736351}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott does not know whether or not everyone's forehead is muddy. It is publicly announced that Sheri knows whether someone's forehead is muddy. It is publicly announced that Scott does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know that Mark can know that Sheri's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Scott","Sheri","Thomas"],"index":38754,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9828501344,"difficulty":1.9828501344}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to Joseph. James's card is shown to James. David's card is shown to James. Robert's card is shown to David. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"David can now know whether James can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","James","David","Robert"],"index":53290,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.981529355,"difficulty":0.018470645}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brittney knows whether John's forehead is muddy. It is publicly announced that John knows whether Brittney's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Nancy can now know that Barbara can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Brittney","John","Barbara"],"index":13680,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9454424381,"difficulty":0.0545575619}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deborah can now know that David can know that Wilma is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Wilma","Deborah"],"index":58502,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967267513,"difficulty":0.0032732487}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindy's card is shown to Candi. Luciano's card is shown to Candi. Candi's card is shown to Cindy. Cindy's card is shown to Cindy. Mary's card is shown to Luciano. It is publicly announced that someone picked a red card. It is publicly announced that Cindy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Cindy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Candi","Mary","Cindy","Luciano"],"index":60585,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985104203,"difficulty":0.0014895797}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elaine knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether or not nobody's forehead is muddy. It is publicly announced that Brenda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] 0","hypothesis":"Patricia can now know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brenda","Patricia","Elaine"],"index":50055,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9849190712,"difficulty":0.0150809288}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Farah knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Joseph can now know whether Alan can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","James","Alan","Farah"],"index":38162,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991334081,"difficulty":0.0008665919}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Dong can now know whether Dorothy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dong","Dorothy"],"index":62968,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9877551198,"difficulty":0.0122448802}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hector knows whether someone's forehead is muddy. It is publicly announced that Naomi's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Naomi can now know whether Naomi's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rosa","Gloria","Naomi","Hector"],"index":23532,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5655032396,"difficulty":0.4344967604}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Cynthia can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cynthia","Carol"],"index":8428,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989890456,"difficulty":0.0010109544}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Virginia can now know whether Virginia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Christopher","Travis","Virginia"],"index":18739,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9168277383,"difficulty":0.0831722617}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christian knows whether Jaime is thirsty. It is publicly announced that Christian knows whether Jaime is thirsty. It is publicly announced that Jaime knows whether Christian is thirsty. It is publicly announced that Christian knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jaime can now know that Christian can know whether Christian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christian","Jaime"],"index":4401,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9896309972,"difficulty":0.0103690028}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Edward can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Loraine","Robert","Dollie","Edward"],"index":19380,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992662072,"difficulty":0.0007337928}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know that Pasquale can know that Gloria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pasquale","Sharon","Mary","Gloria"],"index":14889,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9905738235,"difficulty":0.0094261765}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Steven can now know whether Alex is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amy","Patricia","Alex","Steven"],"index":60260,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974946976,"difficulty":0.0025053024}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jenifer knows whether Jenifer's forehead is muddy. It is publicly announced that Amy knows whether Vicky's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Maryann can now know that Amy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vicky","Jenifer","Maryann","Amy"],"index":52602,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979984164,"difficulty":0.0020015836}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Chad's card is shown to Charles. Robin's card is shown to Adrianne. It is publicly announced that someone picked a red card. It is publicly announced that Adrianne does not know whether Adrianne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Charles can now know whether Adrianne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Adrianne","Robin","Chad"],"index":38254,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7063955069,"difficulty":1.7063955069}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Eric can now know whether Esther can know that Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Eric","Esther","Sherwood"],"index":43408,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9927188158,"difficulty":0.0072811842}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Virginia. Jennifer's card is shown to Shellie. Christopher's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shellie can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virginia","Shellie","Christopher","Jennifer"],"index":36897,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971354008,"difficulty":0.0028645992}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jana knows whether or not everyone is thirsty. It is publicly announced that Martha knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Aaron can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Aaron","Martha","Jana"],"index":50387,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6637009978,"difficulty":1.6637009978}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Zelda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Richard can now know that Linda can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Zelda","Jacob","Richard"],"index":65859,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989541769,"difficulty":0.0010458231}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Andres is thirsty. It is publicly announced that Wilbur does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Andres does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Andres can now know that John can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wilbur","Andres","John"],"index":19811,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994537234,"difficulty":0.0005462766}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lou knows whether Barbara is thirsty. It is publicly announced that Barbara is thirsty. It is publicly announced that Barbara knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Lou can now know that Barbara can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lou","Barbara"],"index":18179,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994858503,"difficulty":0.0005141497}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Leonie can now know that Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gregory","Barbara","Leonie"],"index":66548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9906830788,"difficulty":0.0093169212}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juanita does not know whether Juanita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that Juanita can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juanita","Kevin","John"],"index":30110,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968729615,"difficulty":0.0031270385}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sylvia does not know whether Steven is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Steven can now know that Jennifer can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Steven","Sylvia"],"index":57467,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993065596,"difficulty":0.0006934404}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Irma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Lawrence can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Irma","Lawrence","Reba","Dan"],"index":52671,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993904829,"difficulty":0.0006095171}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Modesto knows whether Shirley's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Shirley can now know that Shirley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Modesto","Shirley"],"index":49855,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9891363382,"difficulty":0.0108636618}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon knows whether someone's forehead is muddy. It is publicly announced that Shannon's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] Agentc knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] 0","hypothesis":"Sharon can now know whether Daniel can know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shannon","Daniel","Sharon"],"index":58704,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9600672722,"difficulty":0.0399327278}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mike's card is shown to Noel. Noel's card is shown to Mike. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Mike can now know that Noel can know that Noel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Noel","Mike"],"index":11314,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9926405549,"difficulty":0.0073594451}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Luis can now know that Joyce can know whether Joyce's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","Katie","Emma","Luis"],"index":39286,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994753003,"difficulty":0.0005246997}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Sonia can now know whether Mary can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sonia","Mary"],"index":60761,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994574189,"difficulty":0.0005425811}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roxie's card is shown to Roxie. Tamela's card is shown to Roxie. Roxie's card is shown to Hung. Tamela's card is shown to Hung. Roxie's card is shown to Tamela. Hung's card is shown to Tamela. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Roxie picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Hung knows whether Tamela picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 1 ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Hung can now know whether Roxie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roxie","Hung","Tamela"],"index":20419,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9772597551,"difficulty":0.0227402449}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"David can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arthur","Sandy","David"],"index":987,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989820123,"difficulty":0.0010179877}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Clyde. Jonathan's card is shown to Joseph. Clyde's card is shown to Jonathan. Jason's card is shown to Jonathan. Clyde's card is shown to Jason. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clyde can now know that Jason can know that Jonathan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clyde","Joseph","Jonathan","Jason"],"index":27780,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982256293,"difficulty":0.0017743707}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty. It is publicly announced that Jerry is not thirsty. It is publicly announced that Jerry knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jerry can now know whether Robert can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Jerry"],"index":33554,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985295534,"difficulty":0.0014704466}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know whether Ruth can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Anthony","David","Bettie"],"index":3003,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999335587,"difficulty":0.000664413}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gloria does not know whether or not everyone is thirsty. It is publicly announced that Gloria does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Colin can now know that Gloria can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Michelle","Colin","Lyle"],"index":64054,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994822741,"difficulty":0.0005177259}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dominick knows whether Dominick's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Sara can now know that Ian can know that Ian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sara","Ian","Dominick"],"index":3279,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979746938,"difficulty":0.0020253062}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bessie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Bessie can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Bessie"],"index":37699,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9152849913,"difficulty":0.0847150087}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Agnes's card is shown to Joseph. Margaret's card is shown to Joseph. Agnes's card is shown to Agnes. Joseph's card is shown to Margaret. Margaret's card is shown to Margaret. Margaret's card is shown to Sharri. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Agnes","Margaret","Sharri"],"index":60724,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9929530025,"difficulty":0.0070469975}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon's forehead is muddy. It is publicly announced that Sharon knows whether Irene's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sharon can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sharon","Irene"],"index":51623,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994536042,"difficulty":0.0005463958}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy does not know whether Sergio is thirsty. It is publicly announced that Sergio does not know whether Glen is thirsty. It is publicly announced that Timothy does not know whether Sergio is thirsty. It is publicly announced that Timothy does not know whether Rachel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Timothy can now know that Glen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachel","Sergio","Glen","Timothy"],"index":6289,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989885688,"difficulty":0.0010114312}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandon's card is shown to Erica. Shannon's card is shown to Erica. Erica's card is shown to Brandon. Brandon's card is shown to Shannon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Shannon can now know whether Brandon can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erica","Brandon","Shannon"],"index":45099,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9806404114,"difficulty":0.0193595886}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy. It is publicly announced that Kenneth's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Kenneth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Pamela","Kenneth"],"index":25715,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9898357987,"difficulty":0.0101642013}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ben can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ben","Timothy","Amanda","Lloyd"],"index":2598,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982901216,"difficulty":0.0017098784}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raquel does not know whether Nicholas is thirsty. It is publicly announced that Kenneth does not know whether Nicholas is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] Agentd knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Nicholas can now know that Kenneth can know that Raquel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Raquel","Susan","Kenneth","Nicholas"],"index":65111,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977268577,"difficulty":0.0022731423}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sandra's card is shown to Sandra. Sandra's card is shown to Dale. Mathew's card is shown to Dale. Sandra's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Sandra does not know whether Mathew picked a red card. It is publicly announced that Jeffrey knows whether or not everyone picked a red card. It is publicly announced that Sandra does not know whether Dale picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Sandra can now know that Jeffrey can know that Mathew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Dale","Jeffrey","Mathew"],"index":49959,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9788634181,"difficulty":0.0211365819}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah does not know whether Marcus is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty. It is publicly announced that David does not know whether Marcus is thirsty. It is publicly announced that Marcus does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kelly can now know that Sarah can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kelly","Marcus","Sarah","David"],"index":34583,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9228290915,"difficulty":1.9228290915}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy. It is publicly announced that Julia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Scott can now know that Julia can know that Julia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Scott","Julia"],"index":14416,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5902116299,"difficulty":1.5902116299}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Christopher's card is shown to Ernest. Ernest's card is shown to Ernest. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Christopher can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christopher","Ernest"],"index":57114,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993664622,"difficulty":0.0006335378}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Carol can now know that John can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Amanda","Carol"],"index":24794,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9630798101,"difficulty":0.0369201899}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryn's card is shown to Kathryn. Charles's card is shown to Kathryn. Kathryn's card is shown to Walter. Walter's card is shown to Walter. Charles's card is shown to Walter. Kathryn's card is shown to Charles. Walter's card is shown to Charles. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathryn can now know whether Charles can know that Walter picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathryn","Walter","Charles"],"index":17293,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9321140647,"difficulty":1.9321140647}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Sherry. Theodore's card is shown to Brenda. Brenda's card is shown to Theodore. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Barbara can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sherry","Barbara","Brenda","Theodore"],"index":3179,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990509152,"difficulty":0.0009490848}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that June does not know whether June's forehead is muddy. It is publicly announced that Ethel knows whether June's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"June can now know whether Ethel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","June","Ethel"],"index":24804,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.997340858,"difficulty":0.002659142}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellen knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Ellen can now know whether Jesse is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesse","Lisa","Bertram","Ellen"],"index":62424,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976457953,"difficulty":0.0023542047}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Javier's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Janis can now know whether Harold can know that Harold's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Julio","Javier","Janis"],"index":49213,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993329644,"difficulty":0.0006670356}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to David. David's card is shown to Carmen. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janice can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Janice","Carmen"],"index":10302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990019202,"difficulty":0.0009980798}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Janet can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janet","Marshall","Michael","Julia"],"index":64130,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988815188,"difficulty":0.0011184812}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Stephanie can now know that Sherry can know whether Sherry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Allan","Elsie","Sherry"],"index":16547,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992954731,"difficulty":0.0007045269}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margorie does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Susan can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maura","Margorie","Susan","Joseph"],"index":21833,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990007281,"difficulty":0.0009992719}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda does not know whether Clinton is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Hope can now know that Hope is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hope","Alex","Clinton","Linda"],"index":55986,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9886921644,"difficulty":0.0113078356}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Felicia does not know whether James is thirsty. It is publicly announced that Felicia does not know whether Ruth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Ruth can now know that James can know that Felicia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Felicia","Ruth","James","Ashley"],"index":36429,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978641868,"difficulty":0.0021358132}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vaughn knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (~(1&2)) ] 0","hypothesis":"Vaughn can now know whether Ingrid can know that Vaughn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vaughn","Ingrid"],"index":56542,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992126226,"difficulty":0.0007873774}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Veronica does not know whether Veronica's forehead is muddy. It is publicly announced that Donald does not know whether or not everyone's forehead is muddy. It is publicly announced that Jenny knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Veronica can now know that Veronica's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Veronica","Donald","Bobby","Jenny"],"index":54885,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7540897727,"difficulty":1.7540897727}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carrie does not know whether Ross is thirsty. It is publicly announced that Carrie does not know whether Marian is thirsty. It is publicly announced that Ross does not know whether Marian is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Carrie can now know whether Carrie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marian","James","Carrie","Ross"],"index":36377,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9957279563,"difficulty":0.0042720437}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Ronald can now know whether Colleen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kelly","Colleen","Lois","Ronald"],"index":64025,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967139959,"difficulty":0.0032860041}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos does not know whether Carlos's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Terrance can now know that Carlos can know that Jason's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Terrance","Millie","Carlos","Jason"],"index":15086,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974364638,"difficulty":0.0025635362}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know whether Brian can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Brian","James"],"index":42786,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9978333116,"difficulty":0.0021666884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arturo does not know whether or not everyone is thirsty. It is publicly announced that Arturo does not know whether Ruth is thirsty. It is publicly announced that Ruth knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Ruth can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ruth","Arturo","Patricia"],"index":59629,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5158495903,"difficulty":0.4841504097}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Twanna does not know whether or not everyone's forehead is muddy. It is publicly announced that Cory knows whether Cory's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Twanna can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cory","Twanna"],"index":51990,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994626641,"difficulty":0.0005373359}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory does not know whether or not everyone is thirsty. It is publicly announced that Gregory does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Anna can now know that Gregory can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gregory","Michael","Anna"],"index":47028,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6810699701,"difficulty":0.3189300299}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Dorothy. Amy's card is shown to Troy. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Troy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Troy","Amy"],"index":13660,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958003163,"difficulty":0.0041996837}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jewel knows whether Noel's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agentb knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] 0","hypothesis":"Louis can now know that Jewel can know that Louis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Louis","Jewel","Noel"],"index":45639,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9894612432,"difficulty":0.0105387568}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Rudy knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Rudy can now know whether James can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rudy","James"],"index":4137,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992226362,"difficulty":0.0007773638}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Randi can now know that Tim can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Randi","William","Tim"],"index":27496,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9812912941,"difficulty":0.0187087059}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Kevin's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Linda can now know whether Paul can know whether Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Linda","Paul","Theodore"],"index":14386,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999438107,"difficulty":0.000561893}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Jason. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Ruth picked a red card. It is publicly announced that Jason picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Jason can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leslie","Jason","Ruth"],"index":11464,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994588494,"difficulty":0.0005411506}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janette does not know whether Anne is thirsty. It is publicly announced that Judy does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Janette can now know that Jane is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anne","Judy","Janette","Jane"],"index":19201,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9775956869,"difficulty":0.0224043131}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Cecil. Richard's card is shown to Richard. Nelson's card is shown to George. Cecil's card is shown to George. Richard's card is shown to George. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Cecil can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nelson","Cecil","Richard","George"],"index":59445,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9926819205,"difficulty":0.0073180795}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffany's card is shown to Tiffany. Tiffany's card is shown to Jonathan. Richard's card is shown to Jonathan. Richard's card is shown to Richard. Jason's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Jonathan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tiffany","Jonathan","Richard","Jason"],"index":58237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99939394,"difficulty":0.00060606}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sonia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Rafaela can now know that Stephanie can know that Sonia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rafaela","Stephanie","Sonia","Tim"],"index":8817,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5789436698,"difficulty":1.5789436698}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ramon's card is shown to William. Juan's card is shown to William. Juan's card is shown to Ramon. William's card is shown to Carmella. Juan's card is shown to Juan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ramon can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Ramon","Carmella","Juan"],"index":43750,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981335998,"difficulty":0.0018664002}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruby knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Roy can now know whether Richard can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roy","Ruby","Richard","Jerry"],"index":23820,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994108677,"difficulty":0.0005891323}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Deborah can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christina","Deborah","Sharon"],"index":40146,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989769459,"difficulty":0.0010230541}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether Roger's forehead is muddy. It is publicly announced that Roger's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Roger can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ashley","Roger"],"index":696,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993102551,"difficulty":0.0006897449}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shannon does not know whether Jimmy is thirsty. It is publicly announced that Shannon does not know whether or not everyone is thirsty. It is publicly announced that Shannon does not know whether Jimmy is thirsty. It is publicly announced that Jimmy knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jimmy can now know whether Shannon can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shannon","Jimmy"],"index":52182,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994707704,"difficulty":0.0005292296}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know that Justin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Estella","Cathy","Robert"],"index":46642,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9890564084,"difficulty":0.0109435916}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to Mattie. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Monica does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mattie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Monica","Mattie","Catherine"],"index":22238,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994605184,"difficulty":0.0005394816}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lou does not know whether Lou's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Ellen can now know whether Lou can know that Ellen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ellen","Elisha","Richard","Lou"],"index":39776,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7520892024,"difficulty":0.2479107976}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Myrtle. Victor's card is shown to Nathaniel. Myrtle's card is shown to Betty. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Victor can now know whether Nathaniel can know that Myrtle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victor","Myrtle","Nathaniel","Betty"],"index":61898,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9704491496,"difficulty":1.9704491496}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roderick is thirsty. It is publicly announced that Roderick does not know whether Ernest is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Ernest can now know whether Roderick can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Roderick","Ernest"],"index":3231,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994722009,"difficulty":0.0005277991}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Billy does not know whether or not everyone is thirsty. It is publicly announced that Jordan does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jordan can now know that Stanley is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stanley","Jordan","Billy"],"index":12762,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9904414415,"difficulty":0.0095585585}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eusebio's card is shown to Robert. Jason's card is shown to Robert. Robert's card is shown to Eusebio. Eusebio's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Jason picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card. It is publicly announced that Robert knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Eusebio can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Eusebio","Jason"],"index":62356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987213016,"difficulty":0.0012786984}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judith does not know whether Bruce is thirsty. It is publicly announced that Bruce is not thirsty. It is publicly announced that Judith is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] 0","hypothesis":"Terri can now know whether Bruce can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bruce","Judith","Terri","Michael"],"index":18223,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993579984,"difficulty":0.0006420016}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin's forehead is not muddy. It is publicly announced that Lula's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Lula can now know that Louis can know that Annette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Louis","Lula","Robin","Annette"],"index":16765,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970169067,"difficulty":0.0029830933}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosemarie is not thirsty. It is publicly announced that Rosemarie does not know whether Juana is thirsty. It is publicly announced that Jesus knows whether Jesus is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jesus can now know whether John can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosemarie","Juana","Jesus","John"],"index":32104,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993661046,"difficulty":0.0006338954}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bobby's card is shown to Debbie. Bobby's card is shown to Marie. Marie's card is shown to Bobby. Bobby's card is shown to Bobby. It is publicly announced that someone picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Bobby can now know whether Bobby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debbie","Marie","Bobby"],"index":25907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8892871141,"difficulty":0.1107128859}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ada does not know whether or not everyone is thirsty. It is publicly announced that Ada does not know whether or not everyone is thirsty. It is publicly announced that Ada does not know whether or not everyone is thirsty. It is publicly announced that Ada does not know whether Laura is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Laura can now know that Ada can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ada","Laura"],"index":24252,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994774461,"difficulty":0.0005225539}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leonard's card is shown to Mark. Leonard's card is shown to Leonard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gladys can now know whether Leonard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","Gladys","Crystal","Leonard"],"index":35180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9087187052,"difficulty":0.0912812948}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Geoffrey knows whether or not nobody is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Geoffrey can now know whether Jeffrey is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Geoffrey","Jeffrey","David"],"index":19466,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974430799,"difficulty":0.0025569201}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Emilio can now know that Emilio is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jose","Emilio","Lynn"],"index":39933,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9927960038,"difficulty":0.0072039962}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorenzo's card is shown to Danielle. Danielle's card is shown to Sharon. Sharon's card is shown to Sharon. It is publicly announced that someone picked a red card. It is publicly announced that Lorenzo does not know whether Carolyn picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Lorenzo can now know that Carolyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danielle","Lorenzo","Carolyn","Sharon"],"index":8017,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979025126,"difficulty":0.0020974874}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Mark. Miguel's card is shown to Mark. Jennifer's card is shown to Jennifer. Mark's card is shown to Victor. Miguel's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card. It is publicly announced that Miguel does not know whether Victor picked a red card. It is publicly announced that Miguel does not know whether Victor picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jennifer can now know that Miguel can know whether Victor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Jennifer","Miguel","Victor"],"index":55187,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5340263844,"difficulty":1.5340263844}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francis's card is shown to Wayne. Norma's card is shown to Wayne. Adam's card is shown to Adam. Norma's card is shown to Adam. Wayne's card is shown to Francis. Adam's card is shown to Norma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Norma can now know that Francis can know that Wayne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wayne","Adam","Francis","Norma"],"index":8194,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978613257,"difficulty":0.0021386743}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Sharon can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Robert","Sharon"],"index":5756,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989953637,"difficulty":0.0010046363}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Juan is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Charles is thirsty. It is publicly announced that Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] (Agentd knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Gary can now know that Charles is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Juan","Kayla","Gary"],"index":30711,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997128427,"difficulty":0.002871573}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to June. Mary's card is shown to June. June's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary picked a black card. It is publicly announced that June knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"June can now know whether Mary can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["June","Mary"],"index":50465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9464741349,"difficulty":0.0535258651}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Thelma. Kristina's card is shown to Thelma. Kristina's card is shown to Kristina. Thelma's card is shown to Antonio. Antonio's card is shown to Antonio. Kristina's card is shown to Carlos. Carlos's card is shown to Carlos. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Kristina picked a red card. It is publicly announced that Kristina knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Thelma can now know that Carlos can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thelma","Kristina","Antonio","Carlos"],"index":19790,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994459748,"difficulty":0.0005540252}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jessica can now know whether Jessica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Matthew","Jessica"],"index":24033,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994153976,"difficulty":0.0005846024}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Modesta knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jason can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Modesta","Melissa"],"index":39388,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989929795,"difficulty":0.0010070205}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Teodoro can now know that Candi can know whether Teodoro's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","Candi","Carlos","Teodoro"],"index":48620,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992858768,"difficulty":0.0007141232}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George knows whether or not nobody is thirsty. It is publicly announced that Garret does not know whether George is thirsty. It is publicly announced that George knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Richard can now know that Garret is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Norma","Richard","Garret"],"index":34330,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9906064272,"difficulty":0.0093935728}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonnie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"David can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Mark","Bonnie"],"index":138,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991987348,"difficulty":0.0008012652}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Mark. Mark's card is shown to Jose. Jose's card is shown to Jose. Mark's card is shown to Angela. Jose's card is shown to Ruth. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether Angela picked a red card. It is publicly announced that Mark knows whether Angela picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Ruth can now know that Mark can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Jose","Angela","Ruth"],"index":66206,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9314599037,"difficulty":0.0685400963}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Doris can now know whether Damian can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","Charles","Damian"],"index":670,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990192652,"difficulty":0.0009807348}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Stanley's card is shown to Eugenio. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Eugenio picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Stanley can now know that Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stanley","Charles","Eugenio"],"index":45848,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9921988845,"difficulty":0.0078011155}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Michelle. Michelle's card is shown to Manuel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charlotte can now know whether Michelle can know whether Manuel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Charlotte","Manuel"],"index":7453,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988352656,"difficulty":0.0011647344}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Raymond. Raymond's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan knows whether someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] 0","hypothesis":"Raymond can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Raymond","Jonathan"],"index":35422,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989404082,"difficulty":0.0010595918}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patty knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Doreen can now know that Patty can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patty","Doreen","Lloyd"],"index":23608,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993308783,"difficulty":0.0006691217}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Michaele can now know whether Gerald can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michele","Michaele","Gerald","David"],"index":25330,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999435246,"difficulty":0.000564754}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Travis's forehead is muddy. It is publicly announced that Paul does not know whether or not everyone's forehead is muddy. It is publicly announced that Travis knows whether or not everyone's forehead is muddy. It is publicly announced that Travis knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Travis can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Paul","Travis"],"index":35570,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990879297,"difficulty":0.0009120703}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred does not know whether Fred's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Rodney can now know whether Ellen can know whether Ellen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rodney","Ellen","Fred"],"index":53631,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9875648618,"difficulty":0.0124351382}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Oscar","Kenneth","Ann"],"index":52978,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9889345765,"difficulty":0.0110654235}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doreen can now know that Philip can know that Jeremy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Philip","Doreen","Dianne","Jeremy"],"index":34640,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976879358,"difficulty":0.0023120642}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Michelle does not know whether Raymond is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Raymond can now know whether Michelle can know that Michelle is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Curtis","Raymond","Michelle"],"index":37311,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.981456399,"difficulty":1.981456399}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not nobody's forehead is muddy. It is publicly announced that Donald's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Donald can now know that Karen can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donald","Karen"],"index":54408,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994332194,"difficulty":0.0005667806}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yaeko's card is shown to Yaeko. Sandra's card is shown to Eunice. Eunice's card is shown to Sandra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eldridge can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Yaeko","Eunice","Eldridge","Sandra"],"index":61913,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988406301,"difficulty":0.0011593699}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Michael. Timothy's card is shown to Michael. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Arlene does not know whether Arlene picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Arlene can now know that Michael can know whether Timothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Arlene","Timothy"],"index":42025,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5927060246,"difficulty":1.5927060246}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joanne's card is shown to Joanne. Carlos's card is shown to Paulene. Kelly's card is shown to Kelly. Carlos's card is shown to Carlos. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paulene can now know whether Carlos picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joanne","Paulene","Kelly","Carlos"],"index":13831,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9209313393,"difficulty":0.0790686607}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Randall. Randall's card is shown to Dana. Dana's card is shown to Dana. William's card is shown to William. Randall's card is shown to Dennis. William's card is shown to Dennis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dana can now know whether Dana picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Randall","Dana","William","Dennis"],"index":17531,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8593598604,"difficulty":1.8593598604}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Traci can now know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Traci","Robert"],"index":24983,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9951614738,"difficulty":0.0048385262}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Kenneth can now know that Kenneth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Raymond","Joseph","Kenneth"],"index":43787,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9876980186,"difficulty":0.0123019814}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"James can now know that Barry can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barry","James"],"index":61053,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999520421,"difficulty":0.000479579}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy. It is publicly announced that Tabetha knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Tabetha can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tabetha","David","John"],"index":36338,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994748235,"difficulty":0.0005251765}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Maria's forehead is muddy. It is publicly announced that Maria's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"John can now know that Maria can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["John","Maria"],"index":36827,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980298877,"difficulty":0.0019701123}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold knows whether someone's forehead is muddy. It is publicly announced that Krysta does not know whether Krysta's forehead is muddy. It is publicly announced that Sasha does not know whether or not everyone's forehead is muddy. It is publicly announced that Harold knows whether Harold's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agentc knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"George can now know that Sasha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Krysta","Harold","George","Sasha"],"index":47681,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.534937799,"difficulty":0.465062201}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Jennifer knows whether Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Carla can now know that Carla is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jennifer","Bessie","Carla"],"index":56256,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9246457219,"difficulty":0.0753542781}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Alonzo can now know that Shirley can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Shirley","Heath","Alonzo"],"index":63097,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993575215,"difficulty":0.0006424785}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Erwin does not know whether Clara is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Erwin can now know whether Martha can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martha","Clara","Erwin"],"index":45054,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994046688,"difficulty":0.0005953312}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Javier's forehead is muddy. It is publicly announced that Javier knows whether Camille's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Camille can now know that Javier can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Javier","Camille","Karla"],"index":22805,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5518803,"difficulty":0.4481197}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl knows whether Carl's forehead is muddy. It is publicly announced that Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Clyde can now know that Carl can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Clyde","Christopher","Lou"],"index":43290,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993226528,"difficulty":0.0006773472}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jane can now know that Frances can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Michael","Jane","Frances"],"index":3609,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979475141,"difficulty":0.0020524859}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angelica knows whether or not nobody is thirsty. It is publicly announced that Angelica does not know whether Peter is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Peter can now know whether Jennifer can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tony","Jennifer","Peter","Angelica"],"index":6181,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994268417,"difficulty":0.0005731583}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrea knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Diana can now know whether Andrea can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Andrea","Diana","Gerald"],"index":10008,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994125366,"difficulty":0.0005874634}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pauline does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jack can now know that Reynaldo can know that Pauline's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pauline","Jack","Reynaldo","Dana"],"index":27,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8175877333,"difficulty":1.8175877333}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julie does not know whether Julie's forehead is muddy. It is publicly announced that Harold knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Pam can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Pam","Harold","Jeremiah"],"index":44336,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9708643556,"difficulty":0.0291356444}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Judy can now know that Judy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judy","James","Sally"],"index":66348,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948418736,"difficulty":0.0051581264}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Catherine can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Catherine","Jessie","John"],"index":22274,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986460805,"difficulty":0.0013539195}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vernon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Vernon can now know whether Glenn can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Celeste","Glenn","Vernon"],"index":37671,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994526505,"difficulty":0.0005473495}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether Juanita's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Jennifer can now know whether Juanita can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["America","Jennifer","Juanita"],"index":24685,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993370175,"difficulty":0.0006629825}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Nell's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Nell can now know that Melissa can know that Beverly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Beverly","Melissa","Nell"],"index":30060,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981747866,"difficulty":0.0018252134}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Timothy can now know whether Kimberly is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Timothy","Kimberly"],"index":15773,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997189939,"difficulty":0.002810061}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether Elyse's forehead is muddy. It is publicly announced that Elyse does not know whether Elyse's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jane can now know that Elyse can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","Jane","Elyse"],"index":2076,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994550347,"difficulty":0.0005449653}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wendy does not know whether Beulah is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Connie can now know whether Beulah can know that Beulah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wendy","Connie","Beulah","Joseph"],"index":48140,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5438491106,"difficulty":0.4561508894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma knows whether Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Timothy can now know that Thelma can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sharon","Timothy","Thelma","Raymond"],"index":54993,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990022779,"difficulty":0.0009977221}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gordon's card is shown to Gordon. Lisa's card is shown to Marianne. Marianne's card is shown to Lisa. Lisa's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gordon can now know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Gordon","Marianne","Lisa"],"index":20289,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943060279,"difficulty":0.0056939721}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Betty's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] 0","hypothesis":"Betty can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Rodney","John","Michael"],"index":53885,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9943636656,"difficulty":0.0056363344}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1&2&3) ] 0","hypothesis":"Florence can now know whether Julie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Florence","Julie"],"index":32569,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994680285,"difficulty":0.0005319715}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ashley's card is shown to Derrick. Michael's card is shown to Derrick. Ashley's card is shown to Ashley. Michael's card is shown to Ashley. Derrick's card is shown to Michael. Ashley's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Derrick can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Derrick","Ashley","Michael"],"index":53106,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994347692,"difficulty":0.0005652308}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Sandra can now know whether Heather can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Heather","Sandra"],"index":50696,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994983673,"difficulty":0.0005016327}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that Thomas does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mary can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Thomas"],"index":21385,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7433768511,"difficulty":0.2566231489}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Mark can now know that Linda can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eva","Linda","Mark","Rebecca"],"index":20083,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99785465,"difficulty":0.00214535}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stacy's card is shown to Stacy. Mark's card is shown to Stacy. Stacy's card is shown to Mark. Mark's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Stacy knows whether Mark picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mark can now know that Stacy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stacy","Mark"],"index":13026,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994398952,"difficulty":0.0005601048}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clara knows whether Clara's forehead is muddy. It is publicly announced that Kimberly knows whether Clara's forehead is muddy. It is publicly announced that Clara knows whether Mariam's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentd knows that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Thomas can now know that Mariam can know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","Mariam","Clara","Thomas"],"index":3205,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979454875,"difficulty":0.0020545125}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wallace's card is shown to Micheal. John's card is shown to John. Wallace's card is shown to John. Wallace's card is shown to Wallace. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Micheal can now know whether Wallace can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Micheal","John","Wallace"],"index":65991,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998709321,"difficulty":0.001290679}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erline's card is shown to John. Carolyn's card is shown to Ilene. Erline's card is shown to Ilene. John's card is shown to Carolyn. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Carolyn picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"John can now know whether Ilene can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Ilene","Carolyn","Erline"],"index":5287,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9964821339,"difficulty":0.0035178661}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Steven can now know that Margaret can know whether Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Steven","Margaret"],"index":63852,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8554617167,"difficulty":0.1445382833}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Wendy can now know whether Ethel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ethel","James","Wendy"],"index":21611,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971112013,"difficulty":0.0028887987}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Fred can now know that Elizabeth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Fred","Elizabeth","William"],"index":56779,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988486767,"difficulty":0.0011513233}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew does not know whether Matthew's forehead is muddy. It is publicly announced that Salvador does not know whether Salvador's forehead is muddy. It is publicly announced that Sherill knows whether Sherill's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Matthew can now know whether Sherill can know whether Salvador's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Salvador","Sherill","Matthew"],"index":54323,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993021488,"difficulty":0.0006978512}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott is not thirsty. It is publicly announced that John does not know whether Lorie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Lorie can now know that John can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shawn","Lorie","John","Scott"],"index":52059,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990577102,"difficulty":0.0009422898}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ines does not know whether Catherine is thirsty. It is publicly announced that Catherine does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Anna can now know whether Catherine can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ines","Catherine","Kim","Anna"],"index":60355,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994946718,"difficulty":0.0005053282}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Colleen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Mary can now know whether Colleen can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lois","Mary","Colleen"],"index":65131,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.924390614,"difficulty":0.075609386}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Johnathon does not know whether Johnathon's forehead is muddy. It is publicly announced that James knows whether Johnathon's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Johnathon can now know that James can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessica","Mary","James","Johnathon"],"index":46724,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6021315455,"difficulty":0.3978684545}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Faye's card is shown to Evelyn. Evelyn's card is shown to Faye. Faye's card is shown to Faye. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Evelyn can now know that Faye can know that Evelyn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Evelyn","Faye"],"index":63631,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9959874749,"difficulty":0.0040125251}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"James can now know whether Alan can know that Alan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alan","James"],"index":10212,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991186261,"difficulty":0.0008813739}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario knows whether Max's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Mario can now know whether Max can know that Max's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mario","James","Max"],"index":48154,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993864298,"difficulty":0.0006135702}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Savannah's card is shown to Savannah. William's card is shown to Marvin. It is publicly announced that someone picked a red card. It is publicly announced that Savannah picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Savannah can now know whether Marvin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Savannah","Marvin"],"index":62359,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9837501645,"difficulty":0.0162498355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Karen knows whether Karen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Karen can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","John","Joe","Nancy"],"index":9086,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9403370023,"difficulty":0.0596629977}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory does not know whether Elena is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gregory can now know whether Rose is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Elena","Rose","Thomas"],"index":38431,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981294274,"difficulty":0.0018705726}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beverly's card is shown to Beverly. Rebecca's card is shown to Beverly. Rebecca's card is shown to Esther. Mary's card is shown to Esther. Rebecca's card is shown to Rebecca. Esther's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:3 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverly","Esther","Rebecca","Mary"],"index":1984,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7659649849,"difficulty":0.2340350151}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Roger can now know that Larry can know that Roger's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Larry","Roger"],"index":56923,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980169535,"difficulty":0.0019830465}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Monica can now know whether Mark can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Monica","Deana","Mark"],"index":46917,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994609952,"difficulty":0.0005390048}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ray knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Gregory can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Ray","Thomas","Kathryn"],"index":23199,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987367988,"difficulty":0.0012632012}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether or not everyone's forehead is muddy. It is publicly announced that Dudley does not know whether Dudley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Dudley can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Timothy","Paul","Mattie","Dudley"],"index":59675,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994627833,"difficulty":0.0005372167}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Greg knows whether Greg's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Fern can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Virginia","Greg","Fern","Sarah"],"index":8579,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994700551,"difficulty":0.0005299449}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Louise is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows whether (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Joshua can now know whether Linda can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessie","Louise","Joshua","Linda"],"index":40701,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994882345,"difficulty":0.0005117655}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether Peter's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Matthew can now know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Jane","Peter"],"index":48251,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9949764013,"difficulty":0.0050235987}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda knows whether Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jennifer can now know that Corrie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wanda","Eric","Corrie","Jennifer"],"index":66220,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983196855,"difficulty":0.0016803145}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Patricia. Carolyn's card is shown to Patricia. James's card is shown to George. George's card is shown to George. James's card is shown to Carolyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether George can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Patricia","George","Carolyn"],"index":43216,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993809462,"difficulty":0.0006190538}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Aaron's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Laura can now know whether Aaron can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Robert","Aaron","Laura"],"index":6234,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999342382,"difficulty":0.000657618}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Duane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Mohamed can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Mohamed","Leisa","Duane"],"index":50051,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994298816,"difficulty":0.0005701184}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Debra. Debra's card is shown to Scott. Scott's card is shown to Scott. Scott's card is shown to Louise. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Scott can now know that Debra can know that Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debra","Scott","Louise"],"index":35191,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974915981,"difficulty":0.0025084019}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Rhonda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Gary can now know whether Angel can know whether Gary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Elaine","Rhonda","Angel"],"index":28201,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9641636014,"difficulty":0.0358363986}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Frank can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judith","Frank","Renae"],"index":11295,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987757802,"difficulty":0.0012242198}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tina does not know whether Corey is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Tina can now know that Corey can know whether Beverly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tina","Beverly","Corey"],"index":21355,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982130527,"difficulty":0.0017869473}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christine's card is shown to Lori. Lori's card is shown to Anna. Anna's card is shown to Anna. Christine's card is shown to Anna. Anna's card is shown to Christine. Anna's card is shown to Claire. Christine's card is shown to Claire. It is publicly announced that someone picked a red card. It is publicly announced that Lori picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Christine can now know whether Anna can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lori","Anna","Christine","Claire"],"index":44305,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993035793,"difficulty":0.0006964207}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Gary. Gary's card is shown to Debra. Debra's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Debra picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Debra can now know whether Gary can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gary","Debra"],"index":48192,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994538426,"difficulty":0.0005461574}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Jewel can now know that Audra can know that Audra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Audra","Jewel"],"index":67112,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9921439886,"difficulty":0.0078560114}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Diane can now know that Michael can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Diane","Ashley","Adela"],"index":28551,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9454952478,"difficulty":0.0545047522}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gertrude knows whether Gertrude is thirsty. It is publicly announced that Gertrude is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Michael can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Ian","Gertrude"],"index":3759,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998999536,"difficulty":0.001000464}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Carl can now know whether Raymond can know that Raymond is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Raymond","Carl","Luz"],"index":18647,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9280564189,"difficulty":0.0719435811}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether or not everyone's forehead is muddy. It is publicly announced that Ralph knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Ralph can now know that Jose can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jose","Ralph"],"index":7094,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990555644,"difficulty":0.0009444356}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Genaro knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Marion can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marion","Juan","Ana","Genaro"],"index":37082,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988077879,"difficulty":0.0011922121}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Samuel. Kathy's card is shown to Brian. Kathy's card is shown to Kathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Samuel can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Samuel","Brian","Kathy"],"index":42439,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993231297,"difficulty":0.0006768703}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lucia can now know that Lucia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Lucia","George","Donald"],"index":33481,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9915059209,"difficulty":0.0084940791}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Ruth. Lorna's card is shown to Lorna. Ruth's card is shown to Bonnie. Lorna's card is shown to Bonnie. Bonnie's card is shown to Bonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ruth can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ruth","Lorna","Bonnie"],"index":9222,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993131161,"difficulty":0.0006868839}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Christopher. Christopher's card is shown to Curtis. Trevor's card is shown to Trevor. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ivan can now know that Christopher can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ivan","Christopher","Curtis","Trevor"],"index":37157,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993211031,"difficulty":0.0006788969}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Ruth can now know whether Danny can know whether Danny is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Danny","Dennis"],"index":49942,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9837079644,"difficulty":0.0162920356}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Tiffany. Elsie's card is shown to Tiffany. Elsie's card is shown to Barbara. Tiffany's card is shown to Elsie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elsie can now know whether Tiffany can know whether Elsie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tiffany","Barbara","Elsie"],"index":60384,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982773066,"difficulty":0.0017226934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Freddie does not know whether Jeffrey is thirsty. It is publicly announced that Jeffrey does not know whether Joseph is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jeffrey can now know that Vincent is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Freddie","Jeffrey","Joseph","Vincent"],"index":15075,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99820292,"difficulty":0.00179708}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Max's forehead is not muddy. It is publicly announced that Tony knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Max can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tony","Max","Adele"],"index":28327,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992707372,"difficulty":0.0007292628}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nina does not know whether Nina's forehead is muddy. It is publicly announced that Nina's forehead is muddy. It is publicly announced that Latonia's forehead is muddy. It is publicly announced that Don's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Latonia can now know that Don's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nina","Don","Latonia","Dana"],"index":7018,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6514374018,"difficulty":0.3485625982}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paul's card is shown to Paul. George's card is shown to Paul. James's card is shown to Jeremy. Paul's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that George does not know whether George picked a red card. It is publicly announced that Paul does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","George","Jeremy","James"],"index":58981,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999447763,"difficulty":0.000552237}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joe can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Travis","Joe","Bobby","Edith"],"index":59504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99894315,"difficulty":0.00105685}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Natalie's card is shown to Natalie. Lonny's card is shown to Natalie. Natalie's card is shown to Lonny. Lonny's card is shown to Lonny. It is publicly announced that someone picked a red card. It is publicly announced that Lonny knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Natalie can now know that Lonny can know that Lonny picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Natalie","Lonny"],"index":26956,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9882795811,"difficulty":0.0117204189}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa knows whether Jean's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Pam can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ena","Pam","Rosa","Jean"],"index":598,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989919066,"difficulty":0.0010080934}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Alfredo can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Charles","Alfredo","William"],"index":16792,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9907072783,"difficulty":0.0092927217}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Tina is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Tina can now know whether Sadie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sadie","Tina"],"index":14494,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9286366701,"difficulty":1.9286366701}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ramon's card is shown to David. Robert's card is shown to Linda. David's card is shown to Ramon. Ramon's card is shown to Ramon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Linda","Robert","Ramon"],"index":42398,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940132499,"difficulty":0.0059867501}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence's forehead is not muddy. It is publicly announced that Billy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Clarence can now know that Carol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Billy","Clarence","Carol"],"index":61665,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980995059,"difficulty":0.0019004941}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Charles can now know that Christian can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Christian","Eric","Deborah"],"index":66702,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993203878,"difficulty":0.0006796122}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty. It is publicly announced that Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] Agentc knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Tristan can now know whether Sandra can know whether Sandra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Mary","Tristan"],"index":57485,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9968308806,"difficulty":0.0031691194}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Delores knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","David","Amanda","Delores"],"index":3293,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9956874251,"difficulty":0.0043125749}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Manuel can now know that Douglas can know whether Douglas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","Brooks","Amy","Manuel"],"index":27893,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5601434708,"difficulty":1.5601434708}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Amber. Amber's card is shown to Nancy. Nancy's card is shown to Nancy. Sarah's card is shown to Nancy. Amber's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Sarah does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Amber can now know that Nancy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amber","Nancy","Sarah"],"index":57630,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994309545,"difficulty":0.0005690455}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Michele. Michele's card is shown to Cathy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cathy can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Michele","Cathy"],"index":6666,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8698000908,"difficulty":1.8698000908}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lourdes knows whether Lourdes's forehead is muddy. It is publicly announced that Lourdes knows whether Lourdes's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lourdes can now know that Lourdes's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lourdes","Ruth"],"index":20215,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8771597743,"difficulty":1.8771597743}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether someone's forehead is muddy. It is publicly announced that Maxine knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Ronald can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Maxine","Angela","Paul"],"index":65889,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9585742354,"difficulty":0.0414257646}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether Paula is thirsty. It is publicly announced that Maxie does not know whether Brenda is thirsty. It is publicly announced that Paula is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Robert can now know whether Paula is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Brenda","Paula","Maxie"],"index":45568,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7545610666,"difficulty":0.2454389334}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"William can now know that Shirley can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Shirley","George"],"index":45080,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994317889,"difficulty":0.0005682111}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan knows whether Thelma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Thelma can now know that Jonathan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thelma","Duane","Jonathan"],"index":37854,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998989284,"difficulty":0.001010716}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony does not know whether Donna is thirsty. It is publicly announced that Donna does not know whether Anthony is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Chris can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Chris","Anthony"],"index":5057,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988773465,"difficulty":0.0011226535}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether Nelda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Joyce can now know that Nelda can know whether Nelda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Nelda","Joyce"],"index":28381,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8748372793,"difficulty":1.8748372793}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Bari. Mary's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card. It is publicly announced that Mary does not know whether Bari picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Bari can now know that Mary can know that Bari picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Bari","Lisa"],"index":60947,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8859009743,"difficulty":0.1140990257}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to Ramona. Ramona's card is shown to Lauren. Lauren's card is shown to Lauren. June's card is shown to Lauren. June's card is shown to June. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lauren can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ramona","Lauren","June"],"index":46801,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994101524,"difficulty":0.0005898476}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benny's forehead is muddy. It is publicly announced that Stacey's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Kelly can now know that Arline's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stacey","Arline","Kelly","Benny"],"index":65794,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960599542,"difficulty":0.0039400458}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Georgia knows whether or not nobody is thirsty. It is publicly announced that Edward does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edward","Georgia","David","Julie"],"index":1071,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8292298913,"difficulty":0.1707701087}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debbie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Debbie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Tena","Kristen","Debbie"],"index":51745,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989972711,"difficulty":0.0010027289}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald does not know whether Lisa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Margaret can now know whether Sarah can know that Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Margaret","Donald","Sarah"],"index":30953,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9556770325,"difficulty":0.0443229675}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Eva. Patricia's card is shown to Eva. Dora's card is shown to Dora. Eva's card is shown to Ronald. Dora's card is shown to Ronald. Eva's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Ronald does not know whether Ronald picked a red card. It is publicly announced that Ronald does not know whether Ronald picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Eva can now know whether Ronald can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eva","Dora","Ronald","Patricia"],"index":54985,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992139339,"difficulty":0.0007860661}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carie does not know whether Carie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Clay can now know that Joshua can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carie","Joshua","Clay","Tabatha"],"index":33035,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989919066,"difficulty":0.0010080934}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Antonio can now know that Christopher can know whether Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Antonio","Christopher","Michael"],"index":607,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.985045135,"difficulty":0.014954865}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to John. Dorothy's card is shown to Dorothy. Dorothy's card is shown to Randy. Randy's card is shown to Randy. Randy's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Randy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Dorothy","Randy","William"],"index":62874,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9104470611,"difficulty":1.9104470611}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stacia does not know whether Mary is thirsty. It is publicly announced that Aurora does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether Kenneth can know whether Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Kenneth","Stacia","Aurora"],"index":57260,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998973608,"difficulty":0.001026392}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antonia knows whether Alexis is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Alexis can now know whether Alexis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Antonia","Alexis"],"index":8223,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973958731,"difficulty":0.0026041269}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Marcia knows whether Marcia's forehead is muddy. It is publicly announced that Lisa knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sheri can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marcia","Lisa","Earl","Sheri"],"index":33312,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993644357,"difficulty":0.0006355643}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donna can now know whether John can know whether Rosemary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosemary","John","Maryjo","Donna"],"index":24490,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992896318,"difficulty":0.0007103682}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miranda knows whether Ruby's forehead is muddy. It is publicly announced that Miranda knows whether Miranda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] Agentb knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Kyle can now know that Miranda can know that Ruby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruby","Kyle","Charlotte","Miranda"],"index":65653,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971017241,"difficulty":0.0028982759}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. Gerald's card is shown to Beatrice. Joseph's card is shown to Beatrice. John's card is shown to Gerald. John's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether Joseph picked a red card. It is publicly announced that Gerald knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"John can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Beatrice","Gerald","Joseph"],"index":31785,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989734888,"difficulty":0.0010265112}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel's forehead is muddy. It is publicly announced that Betty does not know whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Rachel can now know that Timothy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Timothy","Rachel","Betty"],"index":56809,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990267754,"difficulty":0.0009732246}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Leonard. Allyson's card is shown to Leonard. Manuel's card is shown to Louise. Leonard's card is shown to Manuel. Allyson's card is shown to Manuel. Leonard's card is shown to Allyson. Allyson's card is shown to Allyson. It is publicly announced that someone picked a red card. It is publicly announced that Louise does not know whether Allyson picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Manuel can now know that Allyson picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leonard","Louise","Manuel","Allyson"],"index":8981,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9929161072,"difficulty":0.0070838928}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Patty. Benjamin's card is shown to Patty. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Patty does not know whether Billy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Patty can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patty","Robert","Benjamin","Billy"],"index":43404,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993885756,"difficulty":0.0006114244}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Elizabeth. Leigh's card is shown to Elizabeth. Elizabeth's card is shown to Leigh. It is publicly announced that someone picked a red card. It is publicly announced that Leigh knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Leigh can now know whether Elizabeth can know that Leigh picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elizabeth","Leigh"],"index":43922,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9507312775,"difficulty":0.0492687225}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Sarah's card is shown to Avril. Avril's card is shown to Edward. Joan's card is shown to Sarah. Edward's card is shown to Sarah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Avril can now know whether Joan can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joan","Avril","Edward","Sarah"],"index":64709,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9811713696,"difficulty":0.0188286304}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether or not everyone's forehead is muddy. It is publicly announced that Charles's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Edgar can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Edward","Edgar"],"index":1571,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994664788,"difficulty":0.0005335212}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Isaac's forehead is muddy. It is publicly announced that Isaac knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Joel can now know whether Sherman can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joel","Donald","Isaac","Sherman"],"index":44293,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9642595649,"difficulty":0.0357404351}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Aaron","Robert","Charles"],"index":43664,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992071986,"difficulty":0.0007928014}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isreal is not thirsty. It is publicly announced that Amanda knows whether or not everyone is thirsty. It is publicly announced that Robert is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Isreal can now know whether Robert can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Isreal","Robert"],"index":45805,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994816184,"difficulty":0.0005183816}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charles's card is shown to John. Sarah's card is shown to John. Charles's card is shown to Sarah. John's card is shown to Janet. Sarah's card is shown to Janet. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Charles can know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Charles","Sarah","Janet"],"index":2009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988691211,"difficulty":0.0011308789}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dwain's card is shown to Dwain. Cindy's card is shown to Cindy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] (Agentb knows whether (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Cindy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dwain","Cindy"],"index":16304,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9928014278,"difficulty":0.0071985722}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Katharine's card is shown to William. William's card is shown to Katharine. Katharine's card is shown to Katharine. Katharine's card is shown to Deloris. Deloris's card is shown to Deloris. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deloris can now know that Katharine can know whether Deloris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Katharine","Deloris"],"index":60926,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5753446817,"difficulty":1.5753446817}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina's forehead is not muddy. It is publicly announced that Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 1 ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Tina can now know that Calvin can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Timothy","Tina","Calvin"],"index":58896,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987131357,"difficulty":0.0012868643}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas does not know whether Nicholas's forehead is muddy. It is publicly announced that Nicholas does not know whether Nicholas's forehead is muddy. It is publicly announced that Kristin knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Kristin can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nicholas","Kristin"],"index":67520,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994177818,"difficulty":0.0005822182}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Frederick can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Kenneth","Frederick"],"index":53801,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9918118715,"difficulty":0.0081881285}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Jamie can now know whether Susan can know that Jamie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jamie","Susan"],"index":66010,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9847004414,"difficulty":0.0152995586}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephanie does not know whether Angelica is thirsty. It is publicly announced that Lan is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agenta knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Lan can now know that Angelica can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lan","Stephanie","William","Angelica"],"index":48900,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977048039,"difficulty":0.0022951961}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dean's card is shown to Vivian. Rosa's card is shown to Phil. Dean's card is shown to Dean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Phil can now know whether Dean can know that Phil picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vivian","Phil","Dean","Rosa"],"index":49126,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6406978369,"difficulty":1.6406978369}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Alana can now know that Alana's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Helen","Alana"],"index":40213,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9703537226,"difficulty":0.0296462774}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kimberly can now know whether Matthew can know whether Kimberly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","Matthew","Richard"],"index":46762,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990172386,"difficulty":0.0009827614}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Tamara can now know whether Sarah can know that Tamara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tamara","Alice","Helen","Sarah"],"index":37171,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993827343,"difficulty":0.0006172657}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Madaline does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Terri can now know whether John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Terri","John","Madaline"],"index":63093,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7559887767,"difficulty":0.2440112233}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luke's card is shown to Luke. Amber's card is shown to Luke. Luke's card is shown to Bernice. Bernice's card is shown to Bernice. Bernice's card is shown to Amber. Amber's card is shown to Amber. It is publicly announced that someone picked a red card. It is publicly announced that Amber does not know whether Luke picked a red card. It is publicly announced that Bernice does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Bernice can now know whether Amber can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Luke","Bernice","Amber"],"index":59200,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6041947007,"difficulty":0.3958052993}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia does not know whether Steven is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jill can now know that Steven is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jill","Virginia","Steven"],"index":45409,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9918017983,"difficulty":0.0081982017}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Marie can now know that Jolyn can know that Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marie","Paul","Christine","Jolyn"],"index":27258,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9951375127,"difficulty":0.0048624873}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janna does not know whether Janna's forehead is muddy. It is publicly announced that Janna does not know whether Janna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Joel can now know that Janna can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janna","Joel"],"index":16509,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994452596,"difficulty":0.0005547404}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal knows whether or not everyone's forehead is muddy. It is publicly announced that Crystal knows whether Jamie's forehead is muddy. It is publicly announced that Crystal knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Crystal can now know whether Jamie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Crystal","Jamie"],"index":17295,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994164705,"difficulty":0.0005835295}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paulette does not know whether Brad is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Paulette can now know whether Frank can know that Frank is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paulette","Frank","Brad"],"index":35360,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9569353461,"difficulty":0.0430646539}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Patricia is thirsty. It is publicly announced that Patricia does not know whether Christopher is thirsty. It is publicly announced that Christopher is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Patricia can now know that Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Patricia","Christopher","Kevin"],"index":62966,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8090006709,"difficulty":0.1909993291}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie's forehead is muddy. It is publicly announced that Marie knows whether Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Marie can now know that Alecia can know that Alecia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alecia","Sheila","Marie"],"index":13866,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9817633033,"difficulty":0.0182366967}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annie does not know whether Denise is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Fredricka can now know that Denise is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annie","Denise","Fredricka"],"index":9639,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979688525,"difficulty":0.0020311475}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"John can now know that Richard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","John"],"index":55444,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99903512,"difficulty":0.00096488}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kenneth's card is shown to Kenneth. Gail's card is shown to Kenneth. Willie's card is shown to Gail. Kenneth's card is shown to Willie. It is publicly announced that someone picked a red card. It is publicly announced that Willie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know whether Gail can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Gail","Willie"],"index":60708,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.845762372,"difficulty":0.154237628}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephen can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joy","Jason","Stephen"],"index":25206,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993645549,"difficulty":0.0006354451}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Ernest. Janet's card is shown to Ian. Ian's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Janet can now know that Ernest can know that Ian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ernest","Ian","Janet"],"index":12487,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997000277,"difficulty":0.002999723}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Gail. Gail's card is shown to Helen. Marcus's card is shown to Marcus. Marcus's card is shown to Reginald. It is publicly announced that someone picked a red card. It is publicly announced that Reginald does not know whether Helen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Helen can now know that Reginald can know that Marcus picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gail","Helen","Marcus","Reginald"],"index":13393,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996388793,"difficulty":0.003611207}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether Glenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Patrick can now know that Lisa can know whether Patrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Glenda","Patrick"],"index":60545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993539453,"difficulty":0.0006460547}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Carolyn can now know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carolyn","Eileen","Linda"],"index":41004,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978625178,"difficulty":0.0021374822}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Todd is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Walter can now know whether Judith can know whether Walter is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judith","Matthew","Todd","Walter"],"index":60659,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990614057,"difficulty":0.0009385943}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Augusta. Jonathan's card is shown to Joan. Jonathan's card is shown to Jonathan. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Augusta picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jonathan can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Augusta","Joan","Jonathan"],"index":33620,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993703961,"difficulty":0.0006296039}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Lisa can now know that Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lisa","Clyde","Pedro"],"index":59722,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965045452,"difficulty":0.0034954548}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Donna can now know that Lenora can know whether Lenora's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lenora","Donna","Delbert","Sara"],"index":34127,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9880332947,"difficulty":0.0119667053}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wanda knows whether Wanda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentc knows that (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Lawrence can now know that Jessie can know whether Wanda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Becky","Jessie","Lawrence","Wanda"],"index":24705,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6082874537,"difficulty":0.3917125463}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Phillip knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Philip can now know that Phillip can know that Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Philip","Phillip","Steve"],"index":49148,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9926338792,"difficulty":0.0073661208}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregory's card is shown to Gregory. Darrell's card is shown to Lesli. Stephen's card is shown to Lesli. Darrell's card is shown to Darrell. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gregory can now know that Darrell picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gregory","Lesli","Darrell","Stephen"],"index":28578,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970350266,"difficulty":0.0029649734}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know whether Victor can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Marian","Victor","Robert"],"index":4638,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993739724,"difficulty":0.0006260276}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert is thirsty. It is publicly announced that Catherine does not know whether Jody is thirsty. It is publicly announced that Allene knows whether or not nobody is thirsty. It is publicly announced that Allene is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Jody can now know whether Catherine can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jody","Catherine","Allene","Robert"],"index":53876,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994086027,"difficulty":0.0005913973}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francisca is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Francisca can now know whether Francisca is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brian","Mark","Francisca"],"index":15686,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977768064,"difficulty":0.0022231936}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Edwin. Holly's card is shown to Edwin. Jerry's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jerry can now know that Edwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edwin","Jerry","Holly","Nancy"],"index":33494,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975591898,"difficulty":0.0024408102}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George does not know whether or not everyone's forehead is muddy. It is publicly announced that George knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Doris can now know that Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sammie","Doris","George","Myron"],"index":57580,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7170824409,"difficulty":0.2829175591}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether Allan is thirsty. It is publicly announced that Edward knows whether Edward is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Stephen can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Allan","Edward","Stephen","Veronica"],"index":25830,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994755387,"difficulty":0.0005244613}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Cameron can now know that Juanita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cameron","Jeff","Juanita","William"],"index":47586,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9931671023,"difficulty":0.0068328977}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pauline knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lauren can now know whether Alice can know that Alice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lauren","Pauline","Alice"],"index":61375,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9454904795,"difficulty":1.9454904795}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louise's card is shown to Louise. Daisy's card is shown to Louise. Louise's card is shown to Daisy. Daisy's card is shown to Daisy. Louise's card is shown to Roger. Daisy's card is shown to Roger. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daisy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Louise","Daisy","Roger","John"],"index":46085,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990215302,"difficulty":0.0009784698}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori's forehead is not muddy. It is publicly announced that Paula's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Paula can now know that Lori's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Paula","Lori"],"index":63591,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9714452028,"difficulty":0.0285547972}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Deborah can now know whether Richard can know whether Deborah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jacqueline","Chad","Richard","Deborah"],"index":18650,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993834496,"difficulty":0.0006165504}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerardo's card is shown to Marilyn. Gerardo's card is shown to Ronny. John's card is shown to Gerardo. Gerardo's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marilyn","Ronny","Gerardo","John"],"index":3694,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989674091,"difficulty":0.0010325909}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Laurence. Laurence's card is shown to Sarah. Karen's card is shown to Sarah. Jewel's card is shown to Sarah. Sarah's card is shown to Jewel. It is publicly announced that someone picked a red card. It is publicly announced that Laurence does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Laurence can now know whether Laurence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laurence","Sarah","Karen","Jewel"],"index":45943,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5029165149,"difficulty":1.5029165149}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether John's forehead is muddy. It is publicly announced that Sarah knows whether Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Brittany can now know whether Sarah can know whether Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Lula","Brittany","Sarah"],"index":23334,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994286895,"difficulty":0.0005713105}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrel's card is shown to Eddie. Chester's card is shown to Chester. Darrel's card is shown to Chester. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Chester does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Chester can now know that Michael can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eddie","Chester","Michael","Darrel"],"index":16533,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994280934,"difficulty":0.0005719066}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Abraham knows whether or not nobody is thirsty. It is publicly announced that Abraham does not know whether Eleanor is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] Agentb knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Francis can now know that Abraham can know that Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Francis","Eleanor","Abraham"],"index":18093,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982904792,"difficulty":0.0017095208}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. John's card is shown to Christopher. Rebecca's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether John can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","John","Rebecca"],"index":46637,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.746972084,"difficulty":0.253027916}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darrell's card is shown to Darrell. Rosie's card is shown to Darrell. Jewel's card is shown to Patricia. Darrell's card is shown to Rosie. Patricia's card is shown to Rosie. Jewel's card is shown to Jewel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jewel can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darrell","Patricia","Rosie","Jewel"],"index":35049,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989230037,"difficulty":0.0010769963}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mark's card is shown to Mark. Mark's card is shown to Dennis. Donald's card is shown to Dennis. Jennifer's card is shown to Dennis. Dennis's card is shown to Jennifer. Donald's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dennis can now know that Donald can know whether Dennis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Dennis","Donald","Jennifer"],"index":40991,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5705665946,"difficulty":1.5705665946}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to June. June's card is shown to Dean. Dean's card is shown to Dean. Silvia's card is shown to Dean. June's card is shown to Silvia. Dean's card is shown to Silvia. It is publicly announced that someone picked a red card. It is publicly announced that June knows whether June picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Silvia can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["June","Dean","Silvia"],"index":28579,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994475245,"difficulty":0.0005524755}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Willie. Willie's card is shown to Roberta. Roberta's card is shown to Roberta. Valerie's card is shown to Roberta. Roberta's card is shown to Valerie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Willie can now know that Valerie can know that Roberta picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Willie","Roberta","Valerie"],"index":4034,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974727035,"difficulty":0.0025272965}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Barbara's card is shown to Robert. Robert's card is shown to David. Jessica's card is shown to Barbara. David's card is shown to Jessica. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessica can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","David","Barbara","Jessica"],"index":1515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989567995,"difficulty":0.0010432005}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Eva. Alisa's card is shown to Eva. Alisa's card is shown to Alisa. Jeremy's card is shown to Alisa. Jeremy's card is shown to Jeremy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeremy can now know whether Eva picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eva","Alisa","Jeremy"],"index":30652,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5613088608,"difficulty":1.5613088608}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether Amanda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","David","Amanda","Kenneth"],"index":28030,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992079139,"difficulty":0.0007920861}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Pauline. Yolanda's card is shown to Pauline. Esther's card is shown to Yolanda. Pauline's card is shown to Benjamin. Benjamin's card is shown to Benjamin. Esther's card is shown to Benjamin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pauline can now know that Yolanda can know that Benjamin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pauline","Yolanda","Benjamin","Esther"],"index":15147,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983958602,"difficulty":0.0016041398}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Danny can now know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danny","Joe","Barbara","Stephanie"],"index":20506,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977260232,"difficulty":0.0022739768}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathan's card is shown to Leslie. Leslie's card is shown to Thomas. Thomas's card is shown to Thomas. Jean's card is shown to Thomas. Thomas's card is shown to Jean. It is publicly announced that someone picked a red card. It is publicly announced that Thomas does not know whether Leslie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Leslie can now know that Nathan can know that Nathan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leslie","Nathan","Thomas","Jean"],"index":58930,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969556332,"difficulty":0.0030443668}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fred's card is shown to Jeremy. Michael's card is shown to Jeremy. Fred's card is shown to Fred. Fred's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeremy can now know that Fred can know that Fred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeremy","Fred","Michael"],"index":12125,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963921905,"difficulty":0.0036078095}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doris's card is shown to Doris. Nicole's card is shown to Doris. Annette's card is shown to Doris. Annette's card is shown to Nicole. Doris's card is shown to Annette. Doris's card is shown to Barbara. Nicole's card is shown to Barbara. Annette's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Doris knows whether Nicole picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Barbara can now know that Annette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doris","Nicole","Annette","Barbara"],"index":29937,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925040007,"difficulty":0.0074959993}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Ray can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christine","Mary","Michele","Ray"],"index":21150,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988926053,"difficulty":0.0011073947}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia does not know whether Beatriz is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Beatriz can now know whether Jonathan can know that Beatriz is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Virginia","Jose","Beatriz","Jonathan"],"index":31527,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9109078646,"difficulty":0.0890921354}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Robert","Dave"],"index":65899,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9108347893,"difficulty":0.0891652107}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leslie knows whether someone is thirsty. It is publicly announced that Jesus knows whether Jesus is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Leslie can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jesus","Leslie"],"index":10934,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994629025,"difficulty":0.0005370975}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Linda. Linda's card is shown to Linda. James's card is shown to Randy. Linda's card is shown to Randy. James's card is shown to Matthew. Linda's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Randy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Linda","Randy","Matthew"],"index":17939,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9877609015,"difficulty":0.0122390985}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy. It is publicly announced that Aaron's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Charles can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Aaron","Charles"],"index":5689,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988588095,"difficulty":0.0011411905}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to Robert. Joe's card is shown to Robert. Robert's card is shown to John. Joe's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Robert can know whether John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","John","Melissa","Joe"],"index":3830,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980549812,"difficulty":0.0019450188}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carter knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Carter can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carter","Robert"],"index":18741,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9898882508,"difficulty":0.0101117492}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leland's card is shown to Leland. Peggy's card is shown to Peggy. Shawn's card is shown to Peggy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Peggy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leland","Peggy","Shawn"],"index":48731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989145994,"difficulty":0.0010854006}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Agnes can now know that Julia can know that Agnes's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julia","Agnes","Deborah","Melissa"],"index":32524,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983720183,"difficulty":0.0016279817}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Glenn","Robert","Allan","Ashley"],"index":14737,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9634590745,"difficulty":0.0365409255}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacqueline knows whether Jacqueline is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Susan can now know whether Jacqueline is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","David","Jacqueline","Allen"],"index":59003,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9633685946,"difficulty":1.9633685946}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Therese. Helen's card is shown to Helen. George's card is shown to Helen. Therese's card is shown to George. Helen's card is shown to George. George's card is shown to George. Helen's card is shown to Harold. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Therese can now know that George can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Therese","Helen","George","Harold"],"index":35002,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9881249666,"difficulty":0.0118750334}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilbert knows whether or not nobody's forehead is muddy. It is publicly announced that Herman knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Herman can now know that Herman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alfreda","Herman","Wilbert"],"index":10290,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973264933,"difficulty":0.0026735067}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joann knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Joann can now know whether Bernice can know that Joann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sean","Bernice","Joann"],"index":20722,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9914611578,"difficulty":0.0085388422}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Sarah. Juanita's card is shown to Juanita. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Juanita can now know that Juanita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sarah","Juanita"],"index":16796,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9416999817,"difficulty":0.0583000183}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. John's card is shown to Richard. Richard's card is shown to Richard. Richard's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Richard","Randall","William"],"index":50099,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994075298,"difficulty":0.0005924702}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Elaine. Kimberly's card is shown to Kimberly. Oscar's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Elaine can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elaine","Kimberly","Oscar"],"index":37824,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994126558,"difficulty":0.0005873442}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank does not know whether or not everyone's forehead is muddy. It is publicly announced that Rosetta knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Rosetta can now know that Frank can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frank","Patrick","Leticia","Rosetta"],"index":47144,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7471924424,"difficulty":0.2528075576}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen does not know whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Karen can now know whether Claire can know whether Dion's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Claire","Dion"],"index":25263,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990583062,"difficulty":0.0009416938}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Robert can now know whether Mark can know that Shirley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Shirley","Robert"],"index":48364,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5102118254,"difficulty":1.5102118254}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucretia's card is shown to Lucretia. Ethel's card is shown to Lucretia. Lucretia's card is shown to Ethel. It is publicly announced that someone picked a red card. It is publicly announced that Ethel knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Lucretia can now know whether Ethel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lucretia","Ethel"],"index":43150,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9403698444,"difficulty":0.0596301556}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina knows whether Michelle's forehead is muddy. It is publicly announced that Michelle knows whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Christina can now know that Michelle can know that Irene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Michelle","Christina","Irene"],"index":44135,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971827269,"difficulty":0.0028172731}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorothy's card is shown to Dorothy. Dorothy's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Mary can now know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dorothy","Mary"],"index":45627,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.988363564,"difficulty":0.011636436}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne does not know whether Anne's forehead is muddy. It is publicly announced that Anne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Anne can now know that Lena can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anne","Liza","Lena","Christopher"],"index":46038,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994959831,"difficulty":0.0005040169}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Bennie knows whether Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"John can now know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Bennie","Janice","John"],"index":65635,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993517995,"difficulty":0.0006482005}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Trina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Trina can now know whether Gary can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Trina","Helen","Gary","Cheryl"],"index":29488,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994435906,"difficulty":0.0005564094}